UNIVERSITY OF CINCINNATI
July 3
02
_____________
, 20 _____
Mohan Krishna Chirala
I,______________________________________________,
hereby submit this as part of the requirements for the
degree of:
Master of Science
________________________________________________
in:
Electrical Engineering
________________________________________________
It is entitled:
Design, Simulation and Modeling of Collector-up GaInP/GaAs
________________________________________________
Heterojunction Bipolar Transistors
________________________________________________
________________________________________________
________________________________________________
Approved by:
Dr. Kenneth Roenker
________________________
Dr. Marc Cahay
________________________
Dr. Punit Boolchand
________________________
________________________
________________________
DESIGN, SIMULATION AND MODELING OF
COLLECTOR-UP GaInP/GaAs HETEROJUNCTION
BIPOLAR TRANSISTORS
A Thesis Submitted to the
Division of Research and Advanced Studies
of the University of Cincinnati
in partial fulfillment of the
requirement for the degree of
MASTER OF SCIENCE
in the Department of Electrical and Computer Engineering and
Computer Science of the College of Engineering
2002
by
Mohan K. Chirala
B.E. (Honors) in Electronics and Communications Engineering,
Osmania University, Hyderabad, India, 2000.
Committee Chair :
Committee Members:
Dr. Kenneth P. Roenker
Dr. Marc Cahay, Dr. Punit Boolchand
ABSTRACT
The immense demand for communication systems world wide has created an enormous
market for semiconductors devices in variegated applications. While scaled CMOS is consolidating
its stronghold in the analog and RF domains, the wide gamut of microwave frequencies is being
competed for by the various types of III-V heterojunction based semiconductor devices, which were
made amenable to high-volume production, thanks to rapid improvements in bulk-processing and
fabrication techniques in the last decade. Among these devices, the quest for faster, more powerful
and low cost transistors has led researchers to investigate innovative topologies. The availability of
powerful CAD tools that incorporate the most intricate physical phenomenon in the modeling
process has provided a much needed impetus to this ongoing research. Of the scores of disparate
devices that have been investigated, Heterojunction Bipolar Transistors (HBTs) have carved a
niche for themselves owing to their high speeds and greater power handling capabilities.
In this work, the design of an innovative HBT with a collector-up topology, i.e., with the collector
situated on top of the device and emitter on the substrate side, is carried out and optimized for
maximizing the high frequency performance. The material system used here is GaxIn1-xP/GaAs (with
x=0.51 indicating lattice matched composition), which has relatively superior material properties and
etching characteristics than the conventional AlxGa1-xAs/GaAs material system. The material
properties of the ternary were investigated and the most suitable values were ascertained through
meticulous research. These parameters, along with the mobility models (that were derived by
investigating published results), were made compatible to an emitter-up HBT and incorporated into
a two dimensional, physically-based, numerical simulator called ATLAS by Silvaco Inc. The motive
was to verify the correctness of the material parameters and models derived. The simulation results
compared favorably with the published results. With these verified material parameters and mobility
ii
models, a collector-up GaInP/GaAs HBT structure with unetched extrinsic emitter was simulated.
After a performance appraisal with the emitter-up structure, the impact of having an undercut in the
extrinsic base region was investigated. It was found that this undercut drastically improved the high
frequency performance as well as DC characteristics of the collector-up structure. This was
documented by a significant increase in cutoff frequency (fT) from 109 GHz to 140 GHz. It was even
more pronounced in maximum frequency of oscillation (fmax), which is more practically useful than
cutoff frequency, from 76 GHz to 233 GHz. These simulation results are much better than the
practically experimented values.
The high frequency parametric values described here were
achieved after scrupulously optimizing the collector-up HBT structure. Towards the end of the
thesis, two promising collector-up structures with completely etched extrinsic emitters were
simulated and their performance compared with the first collector-up HBT structure.
iii
ACKNOWLEDGEMENTS
First and foremost of all, I’d like to thank my advisor, Prof. Kenneth P. Roenker for his
excellent guidance and patience in advising me. His perennial encouragement was a major source
of inspiration in successfully completing this work. I also express my sincere thanks to the other
members of my thesis committee, Prof. Cahay and Prof. Boolchand for their participation in my
thesis defense.
I’d like to thank my labmates Shivani, Pradeep, Aniket, Rama and Dave for bearing with me
and discussing various issues relating to ATLAS software application and maintaining a suitable
working ambience in the lab. I should also thank them for giving me due consideration in allowing
access to Deckbuild licenses when I needed to run simulations with more than my due share of
simulators and for their friendly, helpful nature. I also wish to thank my friends at Dr. Cahay’s lab,
especially Krishna’s and Rajesh’s role in helping me out when I was feeling down and for their
wonderful company. I also wish to acknowledge the role of my friends Arpit, Awanish, Akshay, Anuj
and Saurabh in making my stay at UC a pleasant and memorable one.
Last but not the least important of all, I convey my heartfelt gratitude to my family, especially
my parents and sister, for their love and encouragement. I wish to acknowledge the blessings of my
grandparents and would like to mention all my adorable cousins for their warmth and love.
iv
TABLE OF CONTENTS
Title Page
Abstract ………………………………………..……………………………………….. .ii
Acknowledgements ………………………………………..……………………………iv
Table of Contents ………………………………………..………………………………v
List of Figures ………………………………………..………………………………......x
List of Tables ………………………………………..…………………………………xvii
Chapter 1:
INTRODUCTION
1.1
Overview of HBT Technology………………………………………….2
1.2
Comparison with BJT Technology…………………………………….5
1.3
InGaP/GaAs HBT Technology…………………………………………8
1.4
Collector-up InGaP/GaAs HBT Technology………………………...10
1.5
Organization of the Thesis……………………………………………15
REFERENCES…………………………………………………………………17
Chapter 2:
MATERIAL PROPERTIES OF GaxIn1-xP
2.1
Introduction……………………………………………………………..21
2.2
Unit Cell Structure Properties………………………………………...22
v
2.2.1 Crystal Structure……………………………………………….22
2.2.2 Lattice Constant………………………………………………..23
2.3
Band Structure…………………………………………………………24
2.3.1 Determination of Conduction Band Structure………………26
2.3.2 Determination of Valence Band Structure…………………..27
2.3.3 Bandgap Variation with Composition………………………..28
2.3.4 Bandgap Variation with Doping………………………………32
2.3.5 Bandgap Variation with Temperature………………………..34
2.4
Effective Masses of Electrons and Holes…………………………...35
2.4.1 Determination of effective mass of electrons……………….35
2.4.2 Determination of effective mass of holes……………………37
2.4.3 Electron effective masses in different sub-bands…………..37
2.5
Effective Density of States and Intrinsic Carrier Concentration…..38
2.5.1 Effective Density of States……………………………………38
2.5.2 Intrinsic Carrier Concentration………………………………..41
2.6
Band Discontinuities at Hetero-interfaces…………………………..41
2.7
Mobility Modeling………………………………………………………43
2.7.1 Electron Mobility variation with Doping……………………...44
2.7.2 Electron Mobility variation with Composition………………..50
2.7.3 Electron Mobility variation with Temperature……………….51
2.7.4 Hole Mobility variation with Doping………………………….53
2.8
Drift Velocity……………………………………………………………53
2.8.1 Electron Drift Velocity variation with Electric Field…………53
2.8.2 Hole Drift Velocity variation with Electric Field……………..55
vi
2.9
Summary of Ga0.51In0.49P Material Parameters…………………….55
2.10
Conclusion……………………………………………………………...56
REFERENCES…………………………………………………………………58
Chapter 3: SIMULATION OF InGaP/GaAs HBTs AND MODEL
VERIFICATION
3.1
Simulation Procedure………………………………………………….64
3.1.1 Poisson’s Equation…………………………………………….65
3.1.2 Continuity Equations…………………………………………..65
3.1.3 Transport Equations…………………………………………...66
3.2
Device Modeling……………………………………………………….67
3.2.1 Structure and Mesh Specification for Efficient
Simulation………………………………………………………68
3.2.2 Material Parameters…………………………………………..69
3.2.3 Material Models………………………………………………..71
3.2.3.1
Shockley-Read-Hall Recombination Model…….71
3.2.3.2
Caughey-Thomas Doping Dependent Mobility
Model……………………………………………….73
3.2.3.3
Parallel Electric Field Model for Electron and Hole
Mobilities……………………………………………78
3.2.4 Input File Setup and Output Result Extraction……………..82
3.3
Model Verification……………………………………………………..83
vii
3.3.1 High Performance Emitter-up InGaP/GaAs HBT…………..83
3.3.2 ATLAS Simulations……………………………………………87
3.3.3 Inference from Simulation Results…………………………..96
3.4
Collector-up HBT Structure Simulation……………………………..96
3.5
Conclusions…………………………………………………………...105
REFERENCES……………………………………………………………….106
Chapter 4:
SIMULATION AND OPTIMIZATION OF InGaP/GaAs
COLLECTOR-UP HBTs
4.1
High Frequency Parameters………………………………………..108
4.1.1 Small Signal Current Gain (βac) and Cutoff Frequency
(fT)……………………………………………………………...109
4.1.2 Unilateral Power Gain (U) and Maximum Frequency of
Oscillation (fmax)………………………………………………112
4.2
Effect of Base Undercut on Device Performance…….…………..115
4.2.1 Theoretical Basis for Extrinsic Base Undercut……………116
4.2.2 Simulation Results for GaInP/GaAs Collector-up HBT with
Extrinsic Base Undercut……………………………………..119
4.3
Optimization of the Collector-up Structure (SR) ………………….130
4.3.1 Optimization of the Base Layer…………………….……….130
4.3.2 Optimization of the Emitter Layer…………………………..134
4.3.3 Optimization of the Collector Layer………………………...138
4.3.4 Optimization of the Sub-collector Layer……………………144
4.4
Final Optimized Structure……………………………………………144
viii
4.5
Typical Collector-up Structure ……………………………………...147
4.5.1 Structure with 9 Layers (SR1) ……………………………...147
4.5.2 Performance Comparison…………………………………...153
4.6
Conclusions…………………………………………………………...154
REFERENCES…………………………………………………………….…156
Chapter 5: CONCLUSIONS AND FUTURE WORK
5.1
Conclusions…………………………………………………………...158
5.2
Future Directions……………………………………………………..161
REFERENCES……………………………………………………………… 163
APPENDIX
A………………………………………………………………………………..165
B………………………………………………………………………………..170
C………………………………………………………………………………..176
ix
LIST OF FIGURES
Figure 1.1 Energy band diagram of a normal biased HBT in common emitter
Configuration….……..……..……..……..……..……..……..……………………3
Figure 1.2 Original collector-up HBT proposed by Kroemer……..……..……..………...11
Figure 2.1 Lattice unit cells of disordered (left) and ordered GaInP. In disordered GaInP,
group III lattice sites are randomly occupied by Ga and In…………………...22
Figure 2.2 Lattice constant as a function of alloy composition parameter, x, for
GaxIn1-xP……..……..……..……..……..……..……..……..……..………………24
Figure 2.3 Band Structure of GaInP for (a) x≤0.63 (b) x≥0.74……..……..……..……. .26
Figure 2.4 Elementary cell and valence band structure of disordered and ordered
GaInP………………………………………………………………………………..27
Figure 2.5 Energy separations between Γ-, X- and L-conduction band minima and top of
the valence band versus composition parameter x at 300K……..…..………29
Figure 2.6 Energy separations between Γ-, X- and L- conduction band minima and top of
the valence band versus composition parameters x at 10K……..……..……..30
Figure 2.7 Composition dependence of direct and indirect bandgap energies Eg and EΓ-X
energies of In1-xGaxP at 77K..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ...31
Figure 2.8 Energy bandgap narrowing versus donor (curve 1) and acceptor (curve 2)
doping density for x=0 (InP) at 300K..… ..… ..… ..… ..… ..… ..… ..… ..… …32
Figure 2.9 Energy bandgap narrowing versus donor (curve 1) and acceptor (curve 2)
doping density for x=1 (GaP) at 300K..… ..… ..… ..… ..… ..… ..… ..… ..…..34
Figure 2.10 Temperature dependence of energy bandgap Eg for GaxIn1-xP for x=0.62
(curve 1) and x=0.64 (curve 2) ..… ..… ..… ..… ..… ..… ..… ..… ..… ..……34
x
Figure 2.11 Temperature dependence of effective density of states in the conduction
band, Nc for the direct gap (1) and for the indirect gap (2) ..… ..… ..…39
Figure 2.12 Temperature dependence of effective density of states in the valence band
Nv..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… 40
Figure 2.13 Temperature dependence of intrinsic concentration for x=0.2 (curve 1),
x=0.5 (curve 2) & x=1 (curve 3) ..… ..… ..… ..… ..… ..… ..… ..… ..……41
Figure 2.14 Electron Mobility as a function of carrier concentration forGa0.52In0.48P…..44
Figure 2.15 Hall electron mobility of GaInP at 300K at room temperature..… ..… ……45
Figure 2.16 Electron Mobility for Ga0.5In0.5P using Hall Measurements for samples at
300K ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..…..46
Figure 2.17 Composite experimental data for GaInP Electron Mobility..… ..… ..… …..47
Figure 2.18 Derived Caughey-Thomas model of the electron mobility versus doping for
GaInP..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..…..48
Figure 2.19 Electron Hall mobility versus composition in GaxIn1-xP..… ..… ..… ..… …..50
Figure 2.20 Temperature dependence of electron mobility in GaxIn1-xP at x=0.5..……..51
Figure 2.21 Concentration Dependence of Hole Hall mobility versus Hole
concentration…....…..…..…..…..…..…..…..…..…..…..…..…..…..…..……..52
Figure 2.22 Field dependence of electron drift velocity in Ga0.52In0.48P..… ..… ..… .…..53
Figure 2.23 Field dependence of hole drift velocity in Ga0.52In0.48P..… ..… ..… ..… .…..54
Figure 3.1 TONYPLOT presentation of the Mesh Structure of an InGaP/GaAs emitter-up
HBT..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..….69
Figure 3.2 Derived Caughey-Thomas model of the electron mobility versus doping for
GaInP..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..…….76
Figure 3.3 Caughey-Thomas mobility model for electrons in GaAs..… ..… ..… ..… .…..77
xi
Figure 3.4 Caughey-Thomas mobility model for holes in GaAs..… ..… ..… ..… ..… .…78
Figure 3.5 Field dependence of electron drift velocity in Ga0.52In0.48P..… ..… ..… … ...80
Figure 3.6 Field dependence of hole drift velocity in Ga0.52In0.48P..… ..… ..… ..… ..… .80
Figure 3.7 Field dependence of electron drift velocity in GaAs..… ..… ..… ..… ..… .….81
Figure 3.8 Field dependence of hole drift velocity in GaAs at various temperatures......81
Figure 3.9 Simulation Code showing gradually incremented bias steps..… ..… ..… …..82
Figure 3.10 Schematic cross sections of a conventional HBT (a) and an HBT scaled
down by Oka et al.’s approach (b) ..… ..… ..… ..… ..… ..… ..… ..… ..… 84
Figure 3.11 Collector current dependence of fT and fmax of the fabricated HBTs with
(a) SE1 = (0.5X4.5 µm2) and (b) SE2 = (0.25X1.5 µm2) at VCE of 1.5 V…….86
Figure 3.12 Simulated emitter-up InGaP/GaAs HBT structure..… ..… ..… ..… ..… ..…..89
Figure 3.13 Gummel Poon (DC characteristics) of the emitter-up InGaP/GaAs HBT
structure from Oka et al. [3-10] ..… ..… ..… ..… ..… ..… ..… ..… ..… ….…90
Figure 3.14 Gummel Poon characteristics of the simulated emitter-up InGaP/GaAs
HBT..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..……..… ..91
Figure 3.15 Frequency response of the current gain for the simulated emitter-up
InGaP/GaAs HBT..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..……...… ..…..92
Figure 3.16 AC current gain variation with collector current density for the
simulated emitter-up InGaP/GaAs HBT..… ..… ..… ..… ..… ..… ..… ..… …93
Figure 3.17 Maximum unilateral power gain variation with collector current density for
the simulated emitter-up InGaP/GaAs HBT..… ..… ..… ..… ..… ..… ..…….94
Figure 3.18 fT(°), fmax(•) vs DC collector current for an emitter up HBT with SE=0.5X4.5 µm2
xii
reported by Oka et al. [3-10] ..… ..… ..… ..… ..… ..… ……………………….95
Figure 3.19 fT, fmax vs total DC collector current of simulated emitter-up InGaP/GaAs
HBT..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..….95
Figure 3.20 Proposed collector-up InGaP/GaAs HBT with unetched extrinsic emitter…97
Figure 3.21 Gummel-Poon characteristics of the simulated InGaP/GaAs
collector-up HBT..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… …..99
Figure 3.22 Variation of AC current gain at a frequency of 2 GHz with collector current
density..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..…100
Figure 3.23 AC response of the simulated collector-up InGaP/GaAs HBT..… ..… ..…..100
Figure 3.24 fT(• ), fmax(♦ ) variation with collector current density..… ..… ..… ..… ..… ..101
Figure 3.25 Maximum unilateral power gain (at 2 GHz ) variation with
collector current density..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..…...101
Figure 3.26 Simulation of unilateral power gain’s frequency response for the
InGaP/GaAs collector-up extrinsic emitter unetched HBT..… ..… ..… ..……102
Figure 3.27 Illustration of intrinsic and extrinsic impedance and capacitive components
for an emitter-up HBT..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… …..104
Figure 4.1 Equivalent Circuit for HBT Giving rise to the Transit Time Components..……110
Figure 4.2 HBT model showing distributed resistances and base-collector
capacitances..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… …….113
Figure 4.3 fT and fmax variation with collector current density for a fixed base-collector
xiii
bias..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… …...…114
Figure 4.4 Simulated collector-up InGaP/GaAs HBT with partially etched extrinsic
emitter..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..………116
Figure 4.5 Original concept behind collector-up HBTs illustrating the importance of
having an inactivated extrinsic emitter region..… ..… ..… ..… ..… ..… ………117
Figure 4.6 Gummel Poon Characteristics for the extrinsic emitter unetched collector-up
InGaP/GaAs HBT..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ……120
Figure 4.7 Gummel Poon Characteristics for the extrinsic emitter completely etched
collector-up InGaP/GaAs HBT..… ..… ..… ..… ..… ..… ..… ..… ..… ..… .......120
Figure 4.8 Collector current density as a function of base-emitter Voltage for various
percentages of base undercut for VCE=2 V..… ..… ..… ..… ..… ..… ..… ……..122
Figure 4.9 Current Gain as a function of base-emitter Voltage for various percentages of
base undercut for VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ……122
Figure 4.10 AC Characteristics for the unetched extrinsic emitter collector-up
InGaP/GaAs HBT ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… .............123
Figure 4.11 AC Characteristics for the extrinsic emitter etched collector-up
InGaP/GaAs HBT ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ............124
Figure 4.12 fT as a function of base-emitter voltage for various percentages of base
undercut for VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..……….. 125
Figure 4.13 fmax as a function of base-emitter Voltage for various percentages of base
undercut for VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ……126
xiv
Figure 4.14 UMAX as a function of base-emitter voltage for various percentages of base
Undercut for VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ……127
Figure 4.15 Collector current density as a function of undercut percentage for a fixed
VBE=1.47 V and VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..………..128
Figure 4.16 Current gain as a function of percentage undercut for a fixed
VBE=1.47 V and VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..………..128
Figure 4.17 fT, fmax as a function of percentage undercut for a fixed
VBE=1.47 V and VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..……….129
Figure 4.18 Umax at 2 GHz as a function of percentage undercut for a fixed
VBE=1.47 V and VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ……129
Figure 4.19 fT vs base-emitter voltage for various base doping levels for VCE=2 V..…….131
Figure 4.20 fmax vs base-emitter voltage for various base doping levels for VCE=2 V……132
Figure 4.21 fT vs base-emitter voltage as a function of base width for VCE=2 V..… ……..133
Figure 4.22 fmax vs base-emitter voltage as a function of base width for VCE=2 V..… …...134
Figure 4.23 Variation of fT, fmax and emitter charging time (τe) as a function of total emitter
resistance RE..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… …...135
Figure 4.24 Emitter charging time (τe) as a function of collector current density (Jc) for
various emitter doping values for an AlGaAs/GaAs HBT..… ..… ..… …..........136
Figure 4.25 fT vs base-emitter voltage for various emitter doping levels for
VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..……………..137
Figure 4.26 fmax vs base-emitter voltage for various emitter doping levels for
VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… …............138
Figure 4.27 fT vs base-emitter voltage for several collector widths for VCE=2 V..…….. ….140
xv
Figure 4.28 fmax vs base-emitter voltage for several collector widths for VCE=2 V..….......141
Figure 4.29. fT vs base-emitter voltage for various collector doping levels for
VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..……….142
Figure 4.30 fmax vs base-emitter voltage for various collector doping levels for
VCE=2 V..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..………..143
Figure 4.31 Simulated InGaP/GaAs fully optimized collector-up HBT structure with 100%
extrinsic base undercut..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ...........145
Figure 4.32 Gummel-Poon characteristics of the fully optimized InGaP/GaAs collector-up
HBT structure..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… …..146
Figure 4.33 AC response of the fully optimized InGaP/GaAs collector-up HBT
structure..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… ..…........146
Figure 4.34 Simulated collector-up structure of SR1..… ..… ..… ..… ..… ..… ..… ..……..149
Figure 4.35 Gummel Poon characteristics of SR1..… ..… ..… ..… ..… ..… ..… ..… …….149
Figure 4.36 AC response of SR1. Note the distortion at lower frequencies..… ..… ……..150
Figure 4.37 Current gain vs collector current density for the collector-up structure
designed by Mochizuki et al. ..… ..… ..… ..… ..… ..… ..… ..… ..… ..… …….151
Figure 4.38 Current gain vs collector current density for SR1..… ..… ..… ..… ..… ..….....151
Figure 4.39 fT, fmax vs collector current density for SR1..… ..… ..… ..… ..… ..… ..… .......152
Figure 4.40 Umax vs collector current density for SR2..… ..… ..… ..… ..… ..… ..… ..…….153
xvi
LIST OF TABLES
Table 2.1 Measurement Techniques and Values of Band Offsets for
Ga0.51In0.49P…………………………………………………………………….42
Table 2.2 Temperature dependence of Electron Mobility…………………………….51
Table 2.3 Material Parameters of Ga0.51In0.49P used in GaInP/GaAs HBT Device
Simulations…………………………………………………………………….55
Table 3.1 Material Properties for Ga0.51In0.49P and GaAs…………………………….70
Table 3.2 Shockley-Read-Hall Model Lifetime Parameters………………………….73
Table 3.3 Caughey-Thomas electron and hole Mobility Model Parameters………..75
Table 3.4 Parameters for Parallel-electric field Mobility Model………………………79
Table 3.5 Epitaxial Layered Structure of Emitter-up GaInP/GaAs HBTs by
Oka et al………………………………………………………………………...85
Table 3.6 Device Parameters Extracted from Fabricated GaInP/GaAs HBTs
by Oka et al……………………………………………………………………..87
Table 3.7 Layer-wise dimensions of the simulated Emitter-up GaInP/GaAs HBT….88
xvii
Table 3.8 Electrode dimensions of the simulated Emitter-up GaInP/GaAs HBT……….89
Table 3.9 Epitaxial structure of GaInP/GaAs Collector-up HBT………………………….98
Table 4.1 Peak Parametric Values for the Final Optimized Structures…………………144
Table 4.2 Final Optimized Epitaxial Structures for GaInP/GaAs Collector-up HBT……145
Table 4.3 Final Simulation Results for the Optimized GaInP/GaAs Collector-up
HBT…………………………………………………………………………………147
Table 4.4 Epitaxial Structure of GaInP/GaAs HBT identified as SR1…………………...148
Table 4.5 Comparison of signal AC characteristics of the two collector-up structures (SR)
and (SR1) …………………………………………………………………………154
Table 5.1 Final Optimized Structures of the Collector-up InGaP/GaAs HBT…………..160
Table 5.2 Simulation Results for Optimized GaInP/GaAs Collector-up HBT…………..160
Table 5.3 Comparison of Simulation Results for the Two Investigated Structures……161
xviii
1. INTRODUCTION
Since Bardeen and Brattain invented the transistor in 1947 [1], semiconductor devices have
developed at an astonishing pace. Their application has provided the basic foundation for the
growth and development of the electronic industry and fueled intensive research in solid-state
devices. Developments in this field have been made feasible by continual improvements in
semiconductor growth, device processing and lithographic techniques that have led to dramatic
shrinking of the device size, greatly enhancing device speed and dramatically increasing the level of
Integrated Circuit (IC) complexity. The development of sophisticated epitaxial growth techniques,
such as Molecular Beam Epitaxy (MBE) and Metal Organic Chemical Vapor Deposition (MOCVD),
has paved the way in recent years for the development of a new class of materials and devices
based on the use of heterojunctions with their unique electronic and optical properties [2].
A heterojunction can be defined, in layman’s terms, as a junction between two dissimilar
semiconductors. Owing to their silicon like outer quartet electronic configurations, semiconductors
composed of elements from columns three and five of the periodic table, the so-called III-V
materials, are the most suitable material systems for forming heterojunction based devices. Of the
numerous heterojunction based electronic devices reported to date, Heterojunction Bipolar
Transistors (HBTs) are of prime importance for use in high frequency and high power applications.
This thesis focuses on the design and simulation of an innovative III-V HBT, with a collector-up
design that could be used in such applications.
1.1 Overview of HBT Technology
The basic idea behind the concept of a HBT is that the performance of a Bipolar Junction
Transistor (BJT) could be greatly enhanced by varying the emitter material
1
composition to increase its energy gap relative to the base [3]. This wide bandgap emitter would
minimize back injection of holes into the emitter of an n-p-n transistor or electron back injection in a
p-n-p transistor, which would increase the emitter injection efficiency and so the current gain of the
device would be significantly enhanced. The bipolar transistor concept was originally propounded
by Shockley [4] and the advantages of having a wide bandgap emitter was thoroughly analyzed by
Kroemer [5] in the late 1940’s and 1950’s, respectively. A significant delay in implementing
Kroemer’s ideas was caused by the problems of achieving interfaces between material systems
that were imperfection free. Interface imperfections are primarily caused by structural defects that
arise due to mismatched lattices between the two semiconductors. In recent years, the
development of epitaxial growth techniques has greatly assuaged this problem and provided the
necessary impetus for fueling continued interest in this field. Still, relatively few material systems
have proved themselves amenable for implementing high performance HBTs owing to prohibitive
substrate and epitaxial growth techniques, manufacturing costs and lattice mismatch problems
inherent with the choice of semiconductors for forming the heterojunctions.
2
Figure 1.1 Energy band diagram of a normal biased HBT in common emitter
configuration [6].
The major attractive feature of the HBT lies in its emitter-base heterojunction. Figure 1.1
shows the energy band diagram of a typical N-p-n HBT biased in the active region for the common
emitter configuration. Like in a BJT, electrons are injected across the emitter-base junction into the
base. They diffuse across the base, or are aided by a drift field for a graded energy bandgap in the
base. Finally, they are nudged along into the collector by the action of electric fields due to reverse
biased collector-base junction. The additional design freedom imparted by the availability of
different materials of varying energy bandgaps and compositions in the emitter and base regions,
lends the HBT an upper hand over its bipolar counterpart.
3
For the HBT, owing to the peculiar alignment of conduction and valence bands, a larger
potential barrier, due to the valence band discontinuity ∆Ev, is presented to the hole flow rather than
to the electron flow. Compared to a homojunction with similar doping densities, mobilities and
minority carrier lifetimes, the ratio of hole current, Ih, to electron current, Ie, across the emitter-base
heterojunction is given by the relation from [6]:
 Ih

 Ie

I 
 (∆EG − ∆EC ) 
 =  h 
exp −

kT


 Het  I e  Homo
(1.1)
where the hole to electron current ratio for a homojunction is given by the pre-factor, while ∆EC and
∆EG are the conduction band discontinuity and bandgap difference across the junction, respectively.
Since, ∆EG > ∆EC and ∆EG-∆EC = ∆Ev, the reverse hole current is significantly lowered in a HBT
enhancing the emitter injection efficiency to almost unity. A more accurate expression for emitter
injection efficiency is given from [7] by:
 ∆E g
Ie
pv
= γ e ≈ 1 − b h exp −
Ie + Ih
ne ve
 kT



(1.2)
where ne is the emitter electron concentration (≈ND), ve is the effective velocity of electrons injected
into the base, pb is the base hole concentration (≈NA), vh is the velocity of holes injected into the
emitter and ∆Eg is the difference in bandgaps of the emitter and base. Due to bandgap narrowing
effects in the heavily doped base layer, ∆Eg is negative and exp(∆Eg/kT) tends to be less than unity
in a BJT. With HBTs, ∆Eg is positive and a mere discontinuity of 0.2 V can yield a value of 2000 for
the same factor. This yields a good emitter efficiency value (γe≈1) no matter what the emitter and
base doping levels are. As a result, for the HBT, a substantial drop in emitter doping (~ 1017 cm-3)
and increase in base doping (~ 1019 cm-3) are possible while keeping γe≈1. Further, the reduced
hole injection in the base drastically cuts down the minority charge storage in the neutral emitter
4
and significantly improves the speed of the device [6]. Hence, device engineers can design devices
operating with adequate gain at high frequencies without compromising on efficiency or current gain
using heterojunction concepts. We also note, however, that in many cases III-V semiconductors
possess superior material properties. For example, the electron mobility in lightly doped GaAs is
~8500 cm2/V-s compared to a significantly lower value of 1500 cm2/V-s in Silicon.
1.2 Comparison with BJT Technology
Heterojunction Bipolar Transistors outperform the Bipolar Junction Transistors in a number of
important ways. We summarize a number of these advantages briefly [7]:
•
Back Injection Current In BJTs, the current flow is bipolar as holes from the base are backinjected into the emitter and constitute an unwanted current component. This increases the
need for having a greater doping in the emitter than in the base, to have some significant
current gain. This problem is overcome in HBTs by having a wider-bandgap emitter which
presents a larger energy barrier for holes than for electrons, which suppresses hole back
injection into the emitter. This dramatically improves the emitter injection efficiency and
current gain and also has the significant advantage of allowing the base to be doped higher
than the emitter, which leads to lower base resistance values augmenting power gain of the
device manifold as well as improving the device speed.
•
Base Ballasting The process of base ballasting involves placing a ballasting resistor in
series with the base bias that serves the purpose of ensuring adequate thermal stability
without compromising on the large signal transistor performance. However, Si BJTs do not
respond positively to this scheme. This is due to the fact that their current gain increases
with increasing temperature. Adding additional ballast to their base would induce more
5
thermal instability, even at very low current densities. In HBTs, on the other hand, current
gain decreases with rising temperature.
This decreasing current gain at elevated
temperatures can be used to provide the negative feedback action in the base ballasted
HBT, i.e., if thermal instability were to occur, there would be more ballasting resistance to
counter the current variations.
•
Early Effect When a small Vcb is applied over the biasing collector voltage VCB, the neutral
base thickness is lightly decreased because the applied perturbation voltage causes the
depletion region at the base-collector junction to expand. As the base is doped more highly
than the collector, much of the expansion is on the collector side. But, there is not an
insignificant shrinkage on the base side too, which constitutes base width modulation. This
leads to an unwanted increase in collector current and a slight tilt in the I-V characteristics in
the saturation region. The Early Voltage is a measure of this tilt with a high Early Voltage
corresponding to a smaller tilt. This phenomenon is more pronounced in Si BJTs than in
HBTs as the base is doped lighter in the former when compared to the latter. Further, owing
to greater thermal resistance of III-V semicondutors over Si, HBTs operate at higher junction
temperatures as collector-emitter bias increases. Since current gain decreases with
increasing temperature, collector current is actually reduced when VCE increases. This effect
enhances the Early Voltage in III-V HBTs.
•
Energy Gap Narrowing The lowering of the energy bandgap due to heavy doping effects
that leads to excessive increase of the minority carrier concentration is called energy gap
narrowing. Energy gap narrowing is more likely to occur in the emitter region of the BJT and
in the base region of the HBT as they are the most highly doped regions in the respective
devices. This would produce an unfavorable impact on current gain in BJTs while causing
yet another positive impact on HBT performance. In BJTs, as the energy gap of the emitter
6
shrinks due to doping, the hole back injection into the emitter is enhanced. This would lower
the current gain quite significantly. An exactly opposite phenomenon occurs in HBTs. Due to
lowering of base energy bandgap, the valence band discontinuity is increased, which
suppresses the hole back injection more efficiently. However, since minority carrier current
in the base is already near zero, due to the large value of ∆Ev, it doesn’t significantly
improve the current gain in practice.
•
High Frequency Performance HBTs outperform BJTs in their high frequency performance,
owing to the following reasons. Firstly, for the HBT, the emitter being doped lighter than the
base leads to significant lowering of the emitter junction capacitance, Cje, which in turn
reduces the emitter charging time. Another important degree of freedom available in HBTs is
in increasing the base doping. The facility to increase base doping to almost the solubility
limit of the material enables significant reduction in base sheet resistance. This is quite
unlike the BJTs where emitter doping must exceed that of base to have practically useful
current gain. Typical sheet resistance values of HBTs are on the order of 200-300 Ω/sq,
while those of state-of-the-art BJTs are 104 Ω/sq. This has a profound impact on the values
of maximum frequencies of oscillation in both cases and enabling the HBTs to have larger
values. Further, by incorporating the grading of the energy gap in the base, HBTs can
develop large quasi-electric fields in the base at higher base doping levels. This would
significantly minimize base transit time thereby boosting cutoff frequency values.
•
Thermal Runaway This phenomenon is caused by the property of Si BJTs that current gain
increases with rising temperature. When critical current conditions are reached, the
transistor becomes hot due to self heating from Joule losses and current gain starts
increasing. The increased current gain causes more and more collector current to be drawn
until the device reaches thermal runaway and eventually burns out. This problem is
7
nonexistent in GaAs based HBTs as the current gain decreases with increasing
temperature.
1.3 InGaP/GaAs HBT Technology
The InGaP/GaAs III-V material system is emerging as a viable alternative to the
conventional AlGaAs/GaAs system owing to the superior electronic and physical properties of
InGaP over AlGaAs. The first InGaP/GaAs HBT was reported by Mondry et al [8] in 1985 and
since then the relatively immature technology has undergone tremendous changes to become a
widely acknowledged practically feasible option. The following are some advantages of
InGaP/GaAs over AlGaAs/GaAs :
(1) Due to absence of Al, the material quality of InGaP is highly improved over that of AlGaAs. It
doesn’t have deep traps and DX centers, which have been a problem in AlGaAs due to its
higher reactivity with oxygen [9]. Hence, recombination sites can be minimized in the
emitter, which greatly simplifies the epitaxial regrowth process for sophisticated electronic or
optical structures [10].
(2) The band offsets in InGaP/GaAs HBT technology are more conducive to providing greater
emitter injection efficiency. The conduction band offset for InGaP/GaAs is quite small
(typically ∆Ec ≈ 137 meV [11]), while that of AlGaAs/GaAs system is much larger (∆Ec ≈ 240
meV [7]). Further, the valence band offset constitutes most of the energy gap difference (∆Ev
≈ 310 meV [12]) which is significantly higher than that of AlGaAs/GaAs material system (∆Ev
≈ 130 meV [7]). The smaller conduction band offset for InGaP/GaAs system, eliminates the
necessity of compositionally grading the base-emitter interface as has been required for the
AlGaAs/GaAs material system [13]. Also, the large valence band discontinuity for
8
InGaP/GaAs suppresses hole back injection into the emitter more efficiently than in the
AlGaAs/GaAs heterojunction.
(3) Probably the most important advantage of InGaP over AlGaAs lies in the etch selectivity of
InGaP and GaAs layers with respect to each other. This enables the use of natural etchstops at hetero-interfaces. This greatly facilitates emitter mesa etching while stopping the
etching process at the base layer thereby preserving the base layer, which is one of the
most crucial steps in device fabrication. Higher fabrication yields and device reproducibilities
are, therefore, achievable when InGaP replaces AlGaAs [13].
(4) InGaP doesn’t allow Carbon to form acceptor states like it does in AlGaAs. Therefore,
Carbon can be used to heavily dope the base layer without creating unwanted
compensation in the adjacent n-type emitter. This has the advantage of reducing outdiffusion of the base doping profile into the emitter region and eliminating the necessity for
compensating (increasing) the emitter doping [14].
(5) The dependence of current gain versus collector current density on temperature is minimal
in InGaP/GaAs HBTs and no ledge passivation is found to be necessary in device
fabrication, which is a significant improvement over the AlGaAs/GaAs HBT technology [13].
(6) InGaP/GaAs HBTs exhibit better reliability compared to their AlGaAs/GaAs counterparts.
Takahashi et al. [15] report a time to failure of 106 hours at a junction temperature of 200°C,
which is far superior to those results reported for AlGaAs based HBTs.
9
1.4 Collector-up InGaP/GaAs HBT Technology
The interest in having a collector-up HBT configuration and its reported use are
discussed in this chapter as a background for this study. The Collector-up configuration has
some significant benefits that make it attractive for high frequency applications. Since the
days of initial design of the first transistor, efficient charge collection was a prime concern
for designers that made it imperative to have a larger collector than emitter area. However,
this resulted in a significant compromise in high frequency performance of the device owing
to the large junction capacitance associated with the larger collector area. An ingenious
solution to this quandary was proposed by Kroemer [5] in 1982 by suggesting a structure
with a smaller collector area and inverted in configuration, such that the device’s collector
rests on top of the emitter. In order to retain the efficient charge collection aspect of the
emitter-up structures, he proposed the inactivation of that part of emitter-base junction that
is not immediately opposite to a part of collector-base junction. This is illustrated in Fig. 1.2.
Figure 1.2. The original collector-up HBT proposed by Kroemer [5].
10
It must be understood, that this inversion was suggested keeping a wide bandgap emitter in
mind. Since Kroemer’s original proposal, there have been a number of theoretical and experimental
studies conducted with collector-up HBTs prompting a rapid improvement in collector-up HBT
technology. Collector-up topologies have significantly improved the high frequency performance of
HBTs in material systems as diverse as AlGaAs/InGaAs/GaAs (Chang et al. [16]) and Ge/GaAs
(Kawanaka et al. [17]). The fmax and fT values in case of the former are 65 GHz and 102 GHz for an
800 A° base, doped at 1X1020 cm-3 and collector width of 2.6 µm while those of the latter are 25
GHz and 112 GHz for an 1800 A° base, doped at 2X1020 cm-3 with a 2.2 µm thick collector. The
former was the first Collector-up HBT reported in literature to operate at microwave frequencies and
beyond [16]. Other Collector-up HBTs reported in literature include those with AlGaAs/GaAs HBT
technology [18] with an fT of 70 GHz and fmax of 128 GHz for a 2-µm X 10-µm collector. Many novel
techniques to improve the DC characteristics of this technology are available, a noteworthy one
being the insertion of AlAs layer into the emitter layer to suppress collector current flow into the
intrinsic portions of the device thereby augmenting current gain significantly. The highest DC
current gain obtained by this technique was around 50 [19].
Several papers [20]-[25], report Collector-up HBTs with the InGaP/GaAs material system with
satisfactory high frequency operation. The maximum reported values of fT and fmax were close to 31
GHz [20] and 115 GHz [21] for a 120 nm base doped 5X1019 cm-3 in both cases. The high fmax
structure is a Double Heterojunction Bipolar Transistor (DHBT), which was the first of its kind in the
InGaP/GaAs material system [21]. Other reports [22]-[25] have concentrated mostly on improving
the power gain efficiency, particularly at low supply voltages, for potential use of such devices is in
microwave power amplifiers. They utilized the concept of having a tunneling collector layer, a thin
GaInP layer at the Base-Collector (BC) junction, which serves the purpose of reducing the
thickness of the wide bandgap material in the collector to an extent that allows electrons to tunnel
through the BC conduction-band barrier, but, simultaneously blocks holes in the base from diffusing
11
into the collector when the BC junction is forward biased [22]. In doing this, therefore, the majority of
advantages of HBTs and DHBTs are incorporated into a single optimal device structure. Mochizuki
et al. [23]-[25], used structures that incorporated such layers and report near zero collector-emitter
offset voltage (10- 14 mV), which is independent of device size and temperature.
To sum up, the following advantages have been identified for Collector-up HBTs by Kroemer
[5], the most optimum realization of which has been the aim of all device structures discussed
above:
(1) The primary advantage of using a collector-up HBT is the significant reduction in collector
junction area, which greatly minimizes the collector junction capacitance. Compared to
conventional emitter up HBTs, the switching times of the device are thereby reduced by a
factor of nearly one-third.
(2) A Double Heterostructure (DH) implementation of I2L logic becomes feasible using the
collector-up configuration. A series of discrete collectors could be placed on top of the
narrow gap base layers such that the emitter can inject only into those portions of base
directly beneath the collectors. This enhances the HBT’s switching speed tremendously
while retaining the low dissipation feature of I2L.
(3) The large lead inductance in series with the emitter, present in the conventional emitter-up
configuration, can now be avoided altogether. This is a major limiting factor in realizing high
values of cutoff frequency, which can now be expected to improve significantly.
These advantages can significantly boost the high frequency performance of the device. In
particular, the minimization of the emitter junction capacitance would have a direct impact on both
12
the cutoff frequency (fT) and maximum frequency of operation (fMAX) as is evident from the following
expressions for these frequencies [7]:
fT ∝
f max =
1
1
=
τ e + τ c ηkT .(C + C ) + ( R + R ).C
je
jc
E
C
jc
qI C
fT
8πrbC jc
(1.3)
(1.4)
where Cje and Cjc are the emitter and collector junction capacitances, RE and RC are the emitter and
collector series contact resistances respectively, IC is the collector current and rb is the base
resistance. From these expressions, it is obvious that any lowering of the collector junction
capacitance would have an enhanced effect on the maximum frequency of operation (fmax) as well
as the cutoff frequency (f T).
The applications of such high frequency devices could be in very high speed digital circuits in
telecommunications and data conversion products, high efficiency microwave power amplifiers,
compact microwave gain blocks and low phase noise microwave oscillators [26]. The low offset
characteristics of Collector-up Tunneling-Collector
(C-up TC) GaInP/GaAs HBTs make them
suitable candidates for implementing microwave power amplifiers [23]-[25].
13
1.5 Organization of the Thesis
Overall, this thesis is divided into five chapters. The first chapter, concluding here, provides a
brief introduction to the HBT’s operation, the InGaP/GaAs material system, its comparative
advantages over AlGaAs/GaAs material system and the collector-up HBT’s advantage. The second
chapter is dedicated to describing the most suitable material parameters of InGaP for use in this
device modeling. The selection of these values assumes critical importance as most of them are
somewhat uncertain and reported values vary over a wide range of values. A few crucial material
models are derived by drawing results from numerous research studies. Chapter three starts with a
brief overview of the device simulator used in the current work, ATLAS by Silvaco International.
Only a brief but self-explanatory presentation is provided. In order to confirm the validity of the
parameters and models derived in the previous chapter, they are incorporated into the simulation
models in chapter three and used to compare the device simulation results with published results
for an emitter-up InGaP/GaAs HBT. An unoptimized and extrinsic emitter unetched, collector-up
structure is also presented in that chapter along with its frequency performance and DC
characteristics. In the penultimate fourth chapter, the high frequency parameters are initially
introduced and explained in detail. The influence of etching the extrinsic emitter region (the emitter
region beneath the extrinsic base) on the performance of the collector-up structure suggested in
chapter three is then discussed with simulation results from ATLAS. The impact of optimizing each
layer of the transistor is then analyzed and the results presented for each layer optimized for both fmax
and fT. Towards the end of the chapter, two promising structures are suggested and their
simulation results are compared with those of the optimized collector-up structure suggested and
simulated in the same chapter. The final chapter concludes the thesis work with a summary of
results achieved and future work possible in this field.
14
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15
[9] Pastor, J.M., Camacho, J., Rudamas, C., Cantarero, A., Gonzalez, L. and Syassen, K., “Band
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[11] O’shea, J.J., Reaves,C.M., Den- Baars, S.P., Chin, M.A. and Narayanamurti, V., “Conduction
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Microscopy”, Appl. Phys. Lett., Vol. 69, no. 20, pp. 3022-3024, Nov. 1996.
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[13] Delage, S., di Forte-Poisson, M.A. and Pons, D., “GaInP/GaAs HBTs For Microwave
Applications”, Conference Proceedings, Fifth International Conference on Indium Phosphide and
Related Materials, pp. 561 –564, May. 1993.
[14] Fresina, M.T., Ahmari, D.A., Mares, P.J., Hartmann, Q.J., Feng, M. and Stillman, G.E., “HighSpeed, Low Noise InGaP/GaAs Heterojunction Bipolar Transistors,” IEEE Elect. Dev. Lett., Vol. 16,
No. 12, pp. 540-541, Dec. 1995.
[15] Takahashi, T., Sasa, S., Kawano, A., Iwai, T., Fujii, T., “High-reliability InGaP/GaAs HBTs
Fabricated by Self-aligned Process”, IEDM, Technical Digest, pp. 191 –194, 1994.
16
[16] Kawanaka, M., Iguchi, N. and sone, J., “112-GHz Collector-up Ge/GaAs Heterojunction Bipolar
Transistors with Low Turn-On Voltage,” IEEE Trans. On Elect. Dev., Vol. 43, No. 5, pp. 670-675,
May 1996.
[17] Chang, M.F., Sheng, N.H., Asbeck, P.M., Sullivan, G.J., Wang, K.C., Anderson, R.J. and
Higgins, J.A., “Self-aligned AlGaAs/InGaAs/GaAs Collector-up Heterojunction Bipolar Transistors
for Microwave Applications,” IEEE Trans. On Elect. Dev., Vol. 36, No. 11, p. 2600, Nov. 1989.
[18] Yamahata, S., Matsuoka, Y. and Ishibashi, T., “High-fmax Collector-up AlGaAs/GaAs
Heterojunction Bipolar Transistors with a Heavily Carbon-Doped Base Fabricated Using OxygenIon Implantation,” IEEE Trans. On Elect. Dev., Vol. 14, No. 4, pp. 173-175, Apr. 1993.
[19] Massengale, A.R., Larson, M.C., Dai, C. and Harris Jr., J.s., “Collector-up AlGaAs/GaAs HBTs
Using Oxidized AlAs,” Device Research Conference, 1996. Digest. 54th Annual, pp. 36 –37, 1996.
[20] Girardot, A., Henkel, A., Delage, S.L., diForte-Poison, M.A., Chartier, E., Floriot, D., Cassette,
S. and Rolland, P.A., “High-Performance Collector-up InGaP/GaAs Heterojunction Bipolar
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H.L.,”Collector-up InGaP/GaAs Double Heterojunction Bipolar Transistors with High fMAX,” IEEE
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17
[23] Mochizuki, K., Oka, T. and Ohbu, I., “Size and Temperature Independent Zero-Offset CurrentVoltage Characteristics of GaInP/GaAs Collector-up Tunneling-Collector Heterojunction Bipolar
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Elect. Dev. Lett., Vol. 36, No. 3, pp. 264-265, Feb. 2000.
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“GaInP/GaAs Collector-up Tunneling-Collector Heterojunction Bipolar Transistors (C-Up TC HBTs):
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18
2. MATERIAL PROPERTIES OF GaxIn1-xP
2.1 Introduction
Efficient simulation of any heterojunction based device hinges critically on the accuracy of
parameters used in the modeling process. In case of the GaInP/GaAs heterojunction, while the
material properties of GaAs have been thoroughly studied and ascertained with little ambiguity in
documented values, the material properties of GaInP need to be scrupulously verified owing to the
relatively wide variation in existent values available in literature.
This verification beckons the
devotion of an entire chapter of my thesis work toward establishing the most suitable electrical
parameters of GaInP to be used for modeling purposes.
The GaInP semiconducting alloys form a continuous, single phase, solid solution throughout
the whole composition range.
Owing to their relatively large bandgap (Eg=1.849 eV for
Ga0.51In0.49P), purportedly thought to be useful in LEDs and visible lasers, this material system has
been thoroughly studied. However, there are some disagreements in most experimental values.
Discussing all the documented properties for the entire alloy would be beyond the scope of this
work. Hence, only those parameters crucial to electronic device performance will be discussed with
suitable explanation on the criteria of their choice. Further, GaxIn1-xP lattice matched to GaAs (for
x=0.51) is the primary material of interest here as other compositions of Ga enhance the risk of
lattice strains and deteriorate device performance. The primary reference used in this discussion of
material properties is Goldberg [1].
19
2.2 Unit Cell Structure Properties
2.2.1 Crystal Structure
In1-xGaxP has a zincblende structure in the bulk-disordered form while epitaxially grown crystals
tend to exhibit a natural super lattice ordering characterized by Ga-rich and In-rich (111) crystal
planes and CuPtB crystal structure [2]. Both of the structures are depicted in Fig. 2.1.
Figure 2.1 Lattice unit cells of disordered (left) and ordered GaInP. In disordered GaInP, group III
lattice sites are randomly occupied by Ga and In [2].
The Zinc-blende structure is based on the cubic space group F43m in which the lattice atoms
are tetrahedrally bound in network arrangements related to those of the group IV (diamond-type)
semiconductors. The disordered InGaP, crystallizing in the cubic zinc-blende structure is the
simplest type of crystal, lacking a center of symmetry and, hence, capable of exhibiting piezoelectric
and related effects depending on polar symmetry [3].
20
The CuPtB crystalline structure in an ordered GaInP layer is such that sheets of pure Ga, P, In and
P atoms alternate on the (001) planes of the basic unit-cell, without the intermixing of the Ga and In
atoms on the same lattice plane [4]. This reduces the symmetry of the crystal from that of the
random alloy’s statistically equal cubic cells [5]. This reduced symmetry also impacts several
electrical properties which vary significantly from their disordered counterparts. However, a
discussion of the impact of ordering on all of them is beyond the scope of this work. The interested
reader is referred to the available literature [6-9] for a conceptual understanding as well as a
comprehensive overview of this phenomenon.
2.2.2 Lattice Constant
The lattice constant for GaxIn1-xP in the Zinc Blende structure varies with the composition x.
Experimentally, the lattice parameter measurement carried out by Onton et al [10], involved X-ray
powder pattern observation and analysis of atomic absorption. Measurement of lattice parameter
as a function of alloy composition is shown in Fig. 2.2. There are two distinct regions in this plot.
For x between 0.5 and 1.0, the curve follows a linear dependence between the end points perfectly.
For x between 0 and 0.5, there is a positive deviation from the linear law by a maximum of 0.015 Aº
near x=0.2. The experimentally observed analytical dependence of lattice parameter a0 on alloy
composition x for GaxIn1-xP is given by [10]:
a 0 = [5.8687 − 0.4182 x + (0.0802 − 0.1614 x 2 )1 / 2 ] A o
(2.1)
Experimentally, it can be shown that at x=0.51, GaxIn1-xP is lattice matched to GaAs. As a
result, this is the composition of most interest for GaxIn1-xP/GaAs heterojunction bipolar transistors
(HBTs), which are studied in this work.
21
Figure 2.2 Lattice constant as a function of alloy composition parameter, x, for GaxIn1-xP [10].
2.3 Band Structure
The electronic band structure of GaxIn1-xP has been thoroughly studied by a number of
experimental groups [11]-[17]. Their results are well summarized by Goldberg et al [1]. In addition,
a wide variety of band-structure calculations have been performed by them so that the energy band
structure of GaxIn1-xP has been thoroughly understood. The discussion of GaxIn1-xP’s band structure
is first presented followed by a comprehensive overview of its conduction and valence band
structure determination. To date, considerable attention has been paid to the energy bandgap’s
variation with respect to various parameters including ordering, temperature, hydrostatic pressure,
composition and doping.
Of these, only the effects of doping and composition are of primary
interest in this study. Although temperature effects are not incorporated in our device simulations,
they are discussed here as they are a major factor influencing bandgap values and become
important when device self-heating is considered in device modeling.
22
Fig. 2.3 shows the direct and indirect energy bandgap structures of GaxIn1-xP at low and high
values of x obtained from piezomodulation and cathodoluminesence studies [11] – [17]. At low x,
the bandgap is direct (like GaAs), while at higher values of x, it is indirect (like GaP). A key point of
contention in the complete determination of band structure is the Γ-X crossover of the conduction
band minima.
Using standard absorption [11] and modulated spectroscopy [12], several
researchers found this to occur at xc= 0.64 at 300K, while cathodoluminsence [13] and transport
experiments [14] yielded a higher value of xc=0.74. This large disagreement has been attributed to
material inhomogenities or imperfections introduced by different crystal preparations.
In 1974,
using high pressure Hall-Effect measurements on vapor epitaxial crystals of GaInP, Pitt et al. [15]
observed the Γ-L & L-X electron transfers and by extrapolating their results, found that these
crossovers occur exactly at xc= 0.63 & 0.74 respectively. Merle et al. [16] confirmed these values
using the piezomodulation techniques discussed above. The variation with energy bandgap with
composition is discussed in the subsequent section.
(a)
23
(b)
Figure 2.3 Band Structure of GaInP for (a) x≤0.63 (b) x≥0.74 [1].
2.3.1
Determination of Conduction Band Structure
A brief description of the procedure followed to determine the conduction band structure is
presented here. Piezomodulation studies are based on the principle of measurement of Piezo
transmission spectra of GaxIn1-xP samples for varying values of x. The predetermined spectra of
GaP is used as a standard to interpret the transmission spectra of GaInP samples. Since GaP is an
indirect bandgap semiconductor, for samples having low indium content, it is expected that one
lowest band edge corresponds to indirect transitions from valence band maximum (Γ15v) to the
lowest conduction band minimum (X1c). The main structures observed on GaxIn1-xP (at x=1), at
helium temperature, corresponds to the excitonic indirect process assisted by the emission of
Longitudinal Acoustic (LA) phonons, via an intermediary state.
The energy gap Egx can be
determined by measuring the longitudinal and transverse acoustic and optical phonon energies.
24
The phonon energy values are accurately determined from the energy difference between emitted
and absorbed phonon energies plotted with respect to increasing temperature. Further, for accurate
determination of conduction band minima at varying concentration of Ga, piezo transmission and
reflection studies are carried out. They involve comparison of net photoreflectivity with transmission
spectra to investigate for phase inversion that can be attributed to valence-conduction band
transitions at different minima. These values are then verified with theoretical piezomodulation
calculations of direct and indirect gaps [16].
2.3.2 Determination of Valence Band Structure
On the other hand, the determination of valence band structure is mainly characterized by the
Γ-sub band split off determination, which results from the natural superlattice ordering of GaInP2.
Kiesel et al [17], used photoluminsence excitation measurements at low temperatures to get an
accurate value of this splitting. Fig 2.4 shows the transformation’s effect on the valence band
structure.
Figure 2.4 Elementary cell and valence band structure of disordered and ordered GaInP [17].
25
This measurement technique is based on the principle that, by applying a bias voltage Upn to a
double hetero GaInP p-i-n structure, grown by MOVPE lattice matched to GaAs, one can change
the internal field of the i-layer over a wide range leading to tilting of the band edges parallel to the
field direction with the corresponding electron wave functions coupling to new eigen states. The
associated changes of the optical absorption spectra (∆α) are known as Franz- keldysh (FK) effect.
A simple expression for these field induced absorption changes deduced from transmission
measurements is given as [17]:
∆α = − ln{Ptr (U pn ) / Ptr (0V )} / d
(2.2)
where Ptr is transmitted optical power, d is the thickness of absorption layer and Upn is the applied
voltage. The ∆α curves for different field changes reveal one common intersection point which can
be interpreted as the bandgap energy, Eg, for disordered material. For ordered GaInP, however, the
interpretation is quite sophisticated requiring immense physical and mathematical rigor to
recalculate absorption changes for the fundamental band-band transitions (Γv4,Γv5Æ Γc6 & Γv6Æ Γc6)
that facilitate the valence band split off calculation. The so obtained value of valence band splitting
∆EVBS is ~21 meV which concurs exactly with theoretically derived value [17].
2.3.3
Bandgap variation with composition
While evaluating the variation of bandgap with composition, the key factor that must be kept
constant is the temperature, as it significantly influences the conduction and valence band
structures and inter-valley phonon transitions. Hence, experimental studies in the literature have
been based on determining bandgap variation with composition at a specific temperature. Bandgap
variation with composition of Ga, therefore, is presented at three different temperatures.
26
AT 300 K
Lange et al. [18] and Krutogolov et al. [19], determined the direct and indirect bandgap
transitions of InGaP at room temperature by Electro-reflection (ER) and Derivative Reflection (DR)
studies. A comprehensive description of these techniques is beyond the scope of this thesis. Using
a least-squares fit of the experimental points, they quantified the compositional (x) dependence of
the X, L and Γ edges as parabolic relations given by [17,18]:
E Γ = 1.349 + 0.668 x + 0.76 x 2
(2.3)
E X = 1.85 − 0.06 x + 0.71x 2
(2.4)
Figure 2.5 Energy separations between Γ-, X- and L- conduction band minima and top of the
valence band versus composition parameter x at 300K [1,18,19].
From the figure, it is apparent that the semiconductor has a direct bandgap upto x≈0.68 where the
L-band minimum takes over. At x=0.78, the X band becomes smallest.
27
AT 10K
At low temperatures, the energy band gap expressions were derived on the basis of
piezoreflectance studies on the GaxIn1-xP alloys by Auvergne et al. [20] as given below. The indirect
edges correspond to Eind . X − E ex + hω LA( X ) and Eind . L − E ex + hω LO ( L ) that correspond to the most
accurate energies that could be determined from modulation spectroscopy.
E Γ = 1.418 + 0.77 x + 0.648 x 2
(2.5)
E X = 2.369 − 0.152 x + 0.147 x 2
(2.6)
The corresponding graphs for these energy values are presented in Fig. 2.6.
Figure 2.6 Energy separations between Γ-, X- and L- conduction band minima and top of the
valence band versus composition parameters x at 10K [1, 20].
In this case, the Γ-L and L-X crossover points nearly merge at x ≅ 0.65.
28
AT 77K
Lange et al. [18] used Electroreflectance and Derivative Reflectance measurements to
observe the direct (E0) and indirect (EΓ-X) band gap transitions at liquid nitrogen temperature (77 K).
A least-squares fit of the experimental points and threshold energies gave the following relations in
each case [18]:
E 0 = 1.405 + 0.702 x + 0.764 x 2
E Γ − X = 2.248 + 0.072 x
(2.7)
(2.8)
The corresponding figure is shown in Fig. 2.7. In this case, no composition is found where the Lband minimum dominates.
Figure 2.7 Composition dependence of direct and indirect bandgap energies Eg and EΓ-X energies
of In1-xGaxP at 77K [1,18].
29
2.3.4
Bandgap variation with doping
Energy bandgap narrowing (∆Eg) arises at high donor and acceptor doping density in most
semiconductors. Bandgap reduction occurs due to columbic interaction forces that come into the
picture due to increasing doping densities [21]. For GaInP, the effects of heavy doping have not
been extensively studied, but, numerous research studies exist for InP and GaP. The results can be
used to interpolate to estimate the result for Ga0.51In0.49P. The following plots (see Fig. 2.8) and
analytical expressions are experimental fits obtained from photoluminescence studies for InP [1]:
n-type
∆E g = 17.2 X 10 −9 N d
1/ 3
+ 2.62 X 10 −7 N d
1/ 4
+ 98.4 X 10 −12 N d
1/ 2
(2.9)
p-type
∆E g = 10.3 X 10 −9 N a
1/ 3
+ 4.43 X 10 −7 N a
1/ 4
+ 3.38 X 10 −12 N a
1/ 2
(2.10)
Figure 2.8 Energy bandgap narrowing versus donor (curve 1, Bugajski et al. [21]) and acceptor
(curve 2, Jain et al. [22]) doping density for x=0 (InP) at 300K.
30
Jain et al [22] derived the following analytical expressions to predict band gap narrowing of any
semiconductor due to doping concentrations:
∆E g
R
=
1
1.83 Λ
0.95 π
. 1/ 3 + 3 / 4 + . 3 / 4
rs N b
2 rs N b
rs
* 

1 + mmin 
*

mmaj 

(2.11)
wherin R is the Rydberg energy for a carrier bound to a dopant atom, and rs is the average distance
between majority carriers, normalized to the effective Bohr radius,
rs = ra / a
with
(2.12)
ra = (3 / 4πN )1 / 3 ,
(2.13)
a = 4πεh 2 / m * e 2
(2.14)
where Λ is a correction factor which accounts for anisotropy of the bands, in n-type semiconductors,
and for interaction between heavy and light hole bands in p-type semiconductors. Nb is the number
of equivalent band extrema. mmaj* and mmin* are majority and minority carrier density of state and
effective masses, respectively.
Using the above equations, Goldberg [1] calculated the energy gap variations with respect to
donor and acceptor doping density variations for GaP. The following are the analytical expressions
he obtained for x=1 (GaP). Shown in Fig. 2.9 are the plots of these bandgap reductions for p and ntype GaP.
n-type
∆E g = 10.7 X 10 −9 N d
1/ 3
+ 3.45 X 10 −7 N d
1/ 4
+ 9.97 X 10 −12 N d
1/ 2
(2.15)
p-type
∆E g = 12.7 X 10 −9 N a
1/ 3
+ 5.85 X 10 −7 N a
1/ 4
+ 3.90 X 10 −12 N a
31
1/ 2
(2.16)
Figure 2.9 Energy bandgap narrowing versus donor (curve 1) and acceptor (curve 2) doping density
for x=1 (GaP) at 300K [1].
2.3.5 Bandgap variation with temperature
Figure 2.10 Temperature dependence of energy bandgap Eg for GaxIn1-xP for x=0.62 (curve 1) and
x=0.64 (curve 2) [1, 23].
32
With increasing temperature, the energy bandgap decreases for most semiconductors. Shown
in Fig. 2.10 is the experimental reduction seen for two compositions of GaxIn1-xP. The experimental
data fitted in these curves by Chin et al. [23] were obtained by photoluminescence experiments.
The energy gap variation with temperature for Ga0.5In0.5P, follows a similar dependence on
temperature which was recorded by t’Hooft et al. [24] as:
Eg = 1.937 − 6.12.10
−4
T2
(eV )
T + 204
(2.17)
which is better known as the Varshni equation.
2.4
2.4.1
Effective masses of electrons and holes
Determination of effective mass of electrons
Until the early 1990’s, despite significant research efforts, effective masses of the charge
carriers in GaxIn1-xP had not been accurately determined. In 1994, Emanneulson et al. [25]
performed Optically Detected Cyclotron Resonance (ODCR) measurements on both ordered and
disordered Ga0.5In0.5P to give an accurate estimate of electron and hole effective masses. The
principle of ODCR differs slightly from the conventional cyclotron resonance. In ODCR, during
cyclotron resonance conditions, electrons increase their energy by absorbing Far Infra Red (FIR)
laser power, pumped by a CO2 laser, and impact ionize shallow donors thereby changing their
Photoluminous (PL) intensity. This change in PL intensity is monitored as a function of magnetic
field and the effective mass can be calculated from the simple relation:
ω c = qB / m ∗
(2.18)
33
where ω c is the cyclotron angular frequency experimentally observed, q is the magnitude of the
elementary electron charge, B is the magnetic field, and m ∗ is the effective mass of the electrons
(holes). In the conventional cyclotron experiment, on the other hand, only the FIR transmission is
measured and the change in the photoluminescence isn’t considered. The so obtained PL peaks of
both ordered and disordered samples are analyzed for resonance peaks due to Γc-Γv transitions. It
is found that electrons of disordered GaInP have a higher effective mass than ordered GaInP, i.e.,
meD = (0.092 ± 0.003) * m0 compared to meo = (0.088 ± 0.003) * m0 of ordered. Since these values
correspond very well with theoretical estimates of Stubner et al [26], who used the “K.P theory” and
also took into consideration the Γ-L sub-band mixing as well as increase in conduction and valence
band interactions due to ordering, they’ve been used in the current simulations without any
additional correction factors.
2.4.2 Determination of effective mass of holes
The effective masses of heavy and light holes was compiled by Goldberg [1] as
mh = (0.6 + 0.19 x)m0 and ml = (0.09 + 0.05 x)m0 wherein x is the Gallium concentration (mole
fraction). The values for lattice matched GaInP (to GaAs) are: mh = 0.7 m0 and ml = 0.12m0 .
Experimental verification of these values was not provided. A possible reason for the lack of this
data would be the fact that n-type Ga0.5In0.5P is nearly solely employed either as the emitter or
collector and not as a base layer in typical commercially used n-p-n InGaP/GaAs HBTs. Hence,
there is little interest in the effective mass of holes for GaInP.
2.4.3 Electron effective masses in different sub-bands
The following is a listing of the effective masses of electrons in different sub-bands from
Goldberg [1]:
34
For Γ- valley,
x=0 (InP)
mΓ=0.08m0
(2.19)
x=0.5
mΓ=(0.088± 0.003)m0
(2.20)
x=0 (GaP)
mΓ=0.09m0
(2.21)
For L- valley,
mLd ≈ (0.63 + 0.13x) m0
(2.22)
For X- valley,
mXd ≈ (0.66 + 0.13x) m0
(2.23)
From these results it is clear that at high Ga concentration (large x) where the GaxIn1-xP
becomes indirect, the effective mass of electrons increases dramatically. As a result, the electron
mobility will drop considerably for these higher values of x.
2.5
Effective density of states and Intrinsic carrier concentration
2.5.1 Effective density of states
The effective density of states for the conduction and valence bands are essential parameters
for device modeling. They are characterized by the following two equations for conduction and
valence bands [27]:
 2πmde kT 
N C = 2

2
 h

 2πmde kT 
N V = 2

2
 h

3/ 2
MC
(2.24)
3/ 2
(2.25)
35
where Mc is the number of equivalent minima in the conduction band. It is evident from these two
equations that these parameters depend on both the effective masses as well as temperature.
However, the impact of effective masses on these parameters is typically minimal when compared
with that of temperature. The effective mass variations with composition have been described
previously. Hence, only the temperature variation of these parameters is considered here.
The temperature dependences of effective density of states in conduction and valence bands
have been derived by Goldberg [1]:
Conduction band
N C ≅ 1.2 X 1014 T 3 / 2 ( cm −3 )
for x ≤ 0.63 (direct gap)
(2.26)
N C ≅ 4.82 X 1015 T 3 / 2 (0.66 + 0.13x ) 3 / 2 ( cm −3 )
for x ≥ 0.78 (indirect gap)
(2.27)
From these equations, the direct dependence of effective density of states on temperature is
quite evident. The lower value of effective density of states for direct bandgap can be attributed to
the lowered value of electron effective masses in the Γ subvalley than in the X-valley, which
characterizes the indirect nature of bandgap (see sec 2.4.3). A MATLAB plot of these values is
presented in Fig. 2.11.
36
Figure 2.11 Temperature dependence of effective density of states in the conduction band, Nc for
the direct gap (1) and for the indirect gap (2).
Valence band
The dependence of valence band density of states on temperature and effective masses is
quite similar. The following expression from Goldberg [1] is valid for both direct and indirect
compositions:
N V ≅ 4.82 X 1015 T 3 / 2 (0.6 + 0.19 x) 3 / 2 (cm −3 )
(2.28)
A MATLAB plot of this expression is shown in Fig. 2.12. The above expressions suggest that the
temperature dependence of effective density of states in valence band and indirect gap conduction
band is quite similar.
37
Figure 2.12 Temperature dependence of effective density of states in the valence band Nv.
2.5.2 Intrinsic carrier concentration
The intrinsic carrier density is given by the following expression from Sze [27]:
ni = N C N V exp(− E g / kT )
(2.29)
From the above expression, we can anticipate an increase of intrinsic concentration with
increasing temperature as both effective densities increase with temperature while band gap
decreases. Experimental results from Goldberg [1] confirm this variation of intrinsic carrier
concentration with respect to temperature:
38
Figure 2.13 Temperature dependence of intrinsic concentration for x=0.2 (curve 1), x=0.5 (curve 2)
& x=1 (curve 3) [1].
2.6
Band discontinuities at hetero-interfaces
Two of the crucial parameters needed for the design of MODFETs and HBTs are the
conduction and valence band discontinuities (∆Ec and ∆Ev respectively). A large valence band
discontinuity, for instance, reduces the base currents in bipolar transistor applications. For nchannel MODFETs, a large ∆Ec is essential. These heterojunction potential barriers also facilitate
stimulated emission in semiconductor lasers by contributing to carrier confinement. In hot electron,
microwave and even some digital device applications, the knowledge of these interfaces is quite
important for device design. Hence, an accurate knowledge of these parameters is certainly of
utmost importance. For modeling the performance of N-p-n InGaP/GaAs HBTs from experimental
considerations, however, these band discontinuities have been found to strongly depend upon the
epitaxial growth technique employed in their fabrication. The band offset values of this hetero-
39
interface grown by different fabrication techniques and measurement techniques are presented
below [25-31]:
Table 2.1 Measurement Techniques and Values of Band Offsets for Ga0.51In0.49P
∆Ec
∆Ev
(V)
(V)
0.2
0.28
Measurement Technique
Fabrication
Technique
Deep Level Transient
LP –MOCVD
Spectroscopy (DLTS)
0.095
0.31
0.38
Bhattacharya
et al. [28]
IV measurements at constant
SS- MBE
temperatures
-
Reference
Lindell et al.
[29]
AL- MBE
High pressure
Martinez et al.
[30]
Photoluminescence
Experiments (HPPE)
0.137
-
Ballistic Electron Emission
MOCVD
Microscopy (BEEM)
O’Shea et al.
[31]
From such a broad gamut of values available, the criterion by which these parameters must be
chosen must be such that it reflects uniformity in considerations as those for other parameters.
Hence, the criteria on which the current parameters are chosen are: fabrication technique employed
and presence of lattice ordering. Based on these criteria, the values selected in this work are:
∆EC = 137 meV & ∆EV = 310 meV. The ∆Ec value has been chosen because the impact of
ordering on band offset was taken into consideration only by O’Shea et al. [31], of all the papers
surveyed. The valence band offset value was chosen on account of MBE grown samples used in
measurement by
40
Lindell et al. [29]. The material chosen for GaInP/GaAs HBTs in this current work was the lattice
matched Ga0.51In0.49P which was assumed to be ordered and hence an energy bandgap of 1.839 eV
(much lower than that of randomly disordered samples) was taken for all subsequent simulations.
2.7
Mobility modeling
In view of it being seen as a key performance factor, carrier mobility in GaInP assumes
tremendous significance. Higher mobilities at a given composition and carrier concentration are
associated with higher quality crystals. Therefore, in this work, all the available literature on the
mobility of GaInP has been studied thoroughly and a composite mobility model is drawn from the
majority of values. This model is then superimposed and fitted to the empirical Caughey-Thomas
mobility model for drift-diffusion. Further, owing to it being exclusively used as an n-type
semiconductor, especially in the emitter, only a discussion of electron mobility of GaInP is carried
out for the sake of relevance. Hence, the hole mobility is taken from a single reliable reference
without further investigation.
2.7.1 Electron mobility variation with doping
The impact of doping on In1-xGaxP’s electron mobility can be described briefly as follows. For
n-type In1-xGaxP crystals, with x≤0.4, most of the electrons are in the Γ- conduction band minimum.
In the doping range 1017≤ND≤1018, the 300 K mobility is in the range 1000-1500 cm2/V-s (and is not
a strong function of ND). At higher donor concentrations, the mobility decreases, probably due to
increased ionized impurity scattering.
The main sources from which electron mobility of GaInP was calculated are: Masselink et al.
[32], Shitara et al. [33] & Quigley et al. [34]. The other references on this aspect, Ohba et al [35] &
41
Blood et al [36], weren’t used because of the use of Se & Sn doped samples in their works. Our
derived values were, however, compared with those of Brennan & Chiang [37] and also with
Goldstein [1]. The three prominent works are first discussed and the mobility model derivation is
presented on that basis.
Shitara et al. [33] were one of the first to present an electrical characterization of a solid source
MBE grown In0.48Ga0.52P film on GaAs (001) substrate. The Hall mobility values presented by them
yielded a carrier concentration of up to 1.2X1019 cm-3 at a growth rate of 1ML/s with a peak mobility
value of 1.1X103 cm2/V-s at 1.1X1016 cm-3. Shown in Fig. 2.14 is a comparison of their results with
previous results.
Figure 2.14 Electron Mobility as a function of carrier concentration for Ga0.52In0.48P [33].
Using Gas Source Molecular Beam Epitaxy (GSMBE), InGaP lattice matched to GaAs and
doped with Si was investigated by Quigley et al. [34]. The highest value of Hall mobility obtained
was for an unintentionally doped sample with a mobility of 1210 cm2/V-s at 300K for an electron
concentration of 2.7X1016 cm-3. Shown in Fig. 2.15 are their results for the mobility as a function of
42
the doping level. Their results are in reasonable agreement with Shitara et al’s results seen in Fig.
2.14.
Figure 2.15. Hall electron mobility of GaInP at 300K at room temperature [34].
Similarly, Masselink et al. [32] used GSMBE grown samples and measured the electron
mobility using the Hall effect. They obtained samples with greater electron mobilities and lower
carrier concentrations, than previously published GSMBE results. For instance they obtained a very
high value of 2X103 cm2/V-s at 1X1015 cm-3. These results are illustrated in Fig. 2.16. Again, their
results are in reasonable agreement with the previously published results discussed above.
43
Figure 2.16 Electron Mobility for Ga0.5In0.5P using Hall Measurements for samples at 300K [32].
A cursory comparison of these mobility values indicates that electron mobility of GSMBE
grown films is comparable to MBE but lower than that of MOCVD. A suitable explanation for
sporadic high mobility values would be the formation of a parasitic 2DEG in MOCVD samples. The
basis of comparison, however, is not on common ground because the MOCVD grown samples in
consideration were doped with “Se” instead of “Si”.
The values derived from these papers were initially compiled, then plotted and superimposed
over the empirical Caughey-Thomas model [38]. The compiled experimental data is presented in
Fig. 2.17. Though it was not possible to extract all the data points of all experimental results shown
above, a significant segment of data was incorporated to ensure the relevance of the subsequently
derived model.
44
2500
2
Electron M obility (cm /V-s)
2000
1500
1000
500
0
14
10
10
15
10
16
10
17
10
18
10
19
10
20
-3
N (cm )
D
Figure 2.17 Composite experimental data for GaInP Electron Mobility.
The Caughey Thomas model is an analytical low-field mobility model that can be used to
describe the doping dependence and is given by the following expression [38] :
µ n ( N ) = µ min +
µ max − µ min
 N
1 + 
 NC



α
(2.30)
The Caughey-Thomas model is a useful one in that it is a model readily available in ATLAS
device simulation software from Silvaco and its parameters (α, µmin, µmax and NC) can be adjusted to
45
model the GaInP electron mobility. However, due to the wide variability of the data seen in Figs.
2.14-2.16, the Caughey Thomas model parameters were adjusted to give a reasonably good
approximation to the observed dependence of electron mobility on the doping. Since the exact data
couldn’t be accurately obtained from reading the figures, a rigorous fit to the data was not
attempted. The function, obtained by curve fitting the extracted experimental data with the
Caughey-Thomas model is presented in Fig. 2.18.
1800
1400
2
Electron M obility (cm /V-s)
1600
1200
1000
800
600
400
200
14
10
10
15
10
16
10
17
N , cm
10
18
10
19
10
20
-3
D
Figure 2.18 Derived Caughey-Thomas model of the electron mobility versus doping for GaInP.
46
2.7.2 Electron mobility variation with composition
Macksey et al. [14] studied the composition’s effect on the electron mobility in GaInP. To
identify the impact of mobility variation with respect to composition, doping has to be confined to a
narrow range (1017≤n≤1.5.1018), so that the mobility doesn’t vary significantly with electron
concentration in either the direct or indirect bandgap regions. The mobility points at x < 0.4 apply to
crystals all of whose carriers are in the direct minimum of the conduction band. The mobility points
at x ≥ 0.73 indicate that most of the carriers are in the indirect minima (L valley or X valley). For
intermediate values of x, some of the carriers are in direct minima while others in indirect minima,
thus giving intermediate values of mobility. The following are two special cases for x=0 and x=1
corresponding to InP and GaP, respectively, at very low and high doping levels.
at x=0 (InP)
at x=1 (GaP)
for n0=3.1013 cm-3
µn=5.103 cm2/Vs
for n0=8.1017 cm-3
µn=1.8.103 cm2/Vs
for n0=5.1016 cm-3
µn=200 cm2/Vs
for n0=2.5.1018 cm-3
µn=100 cm2/Vs
Shown in Fig. 2.19 is the electron mobility as a function of composition x for the GaxIn1-xP. The
mobility falls off dramatically at high values of x due to higher effective mass of electrons in the X
valley for GaP.
47
Figure 2.19 Electron Hall mobility versus composition in GaxIn1-xP [1,14].
2.7.3 Electron mobility variation with temperature
As a function of temperature, the electron’s Hall mobility varies as follows. Up to about 100K
the mobility increases with temperature according to, µH∝T1.5, which is a characteristic of the
dominance of ionized impurity scattering. Between 150-300K, the mobility varies much less in
accordance with µH∝T-0.3, indicating the scattering of electrons by optical phonons is dominant.
Above 300K, the effect of temperature on mobility is to cause further degradation due to enhanced
phonon scattering as shown in Fig. 2.20.
48
Figure 2.20 Temperature dependence of electron mobility in GaxIn1-xP at x=0.5 [39].
At any given temperature, the observed mobility can be calculated theoretically from the
temperature dependences of mobility’s components [39]:
µ −1 = µ i −1 + µ1 −1 + µ a −1 + µ a.sc −1
(2.31)
with µi being ionized impurity scattering; µ1, polar-optical phonon scattering; µa, alloy scattering and
µa.sc, space-charge scattering. The following tabulation from Zhang et al [39] shows the dominance
of different mobility components over different regions of temperatures:
Table 2.2 Temperature dependence of Electron Mobility [39]
Range of Temperature
Dominant Mobility Component
T<25 K
Impurity band conduction
25 K < T < 77K
Ionized impurity scattering
77 K < T < 300 K
Alloy scattering and/or space charge scattering
49
2.7.4 Hole mobility variation with doping
Ikeda et al. [40] measured the hole mobility in p-type Ga0.5In0.5P for Zn doped samples. The
samples were MOCVD grown and the mobility values were verified with other LPE grown samples
in literature. The mean mobility was around 34 cm2/V-s for p0=1018 cm-3. Shown in Fig. 2.21 is the
observed variation in the mobility with doping.
Figure 2.21 Concentration Dependence of Hole Hall mobility versus Hole concentration [40]
2.8
Drift Velocity
2.8.1 Electron drift velocity variation with electric field
Brennan and Chiang [37] calculated the steady state electron drift velocities in GaInP at 300K
; their results are shown in Fig. 2.22.
50
Figure 2.22 Field dependence of electron drift velocity in Ga0.52In0.48P [37].
They predicted the occurrence of negative differential resistance in bulk GaInP, which is apparently
due to the significant inter-valley separation energies in GaInP as well as the sizeable optical
phonon energy and polar optical scattering rate present. As has been found in studies of electron
drift velocity in bulk GaAs, the existence of negative differential resistance, the value of the
threshold field and the peak drift velocity are influenced by the extent to which electrons are
confined within the Γ- valley. Given that the inter-valley separation energies are significantly greater
than the mean thermal energy, the confinement depends principally on the magnitude of polar
optical phonon scattering rate and optical phonon energy. In GaInP, the optical phonon energy as
well as the polar optical scattering rate are relatively large leading to significant low-field carrier
confinement within the gamma valley. As a consequence, as the applied electric field is increased,
negative differential resistance is bound to occur.
51
2.8.2 Hole drift velocity variation with electric field
The steady state hole drift velocities in bulk Ga0.52In0.48P are shown in Fig. 2.23 as reported by
Brennan and Chiang [37]. The valence band properties and structure of Ga0.52In0.48P are quite
similar to those of Al0.26Ga0.26In0.48P. Hence hole mobility properties of these two materials are quite
similar.
Figure 2.23 Field dependence of hole drift velocity in Ga0.52In0.48P [37].
2.9
Summary of Ga0.51In0.49P parameter values
To summarize on the discussions presented in this chapter, the following table contains a
succinct list of the important material parameters of GaxIn1-xP (x=0.51) used in the device
simulations that form the basis of this Thesis.
52
Table 2.3 Material Parameters of Ga0.51In0.49P used in GaInP/GaAs HBT Device Simulations
Parameter Name
Ga0.51In0.49P Values
Crystal Structure
Zinc Blende (disordered)
CuPtB (Ordered)
[2]
Dielectric Constant
11.8
[1]
Lattice Constant (Aº)
5.653
[3]
Effective Electron mass (me)
Goldberg
[1]
Γ- valley
0.088m0
L- valley
0.6963m0
X- valley
0.7263m0
Effective Heavy hole mass (mh)
0.7m0
Effective Light hole mass (ml)
0.12m0
Energy Gap (eV)
1.849
[1]
Effective Conduction band density of states (cm-3)
6.5X1017
[1]
Effective Valence band density of states (cm-3)
1.45X1019
[1]
Conduction Band offset, ∆Ec (meV)
137
[31]
Valence Band offset, ∆Ev (meV)
310
[29]
Breakdown field (V/cm)
5X105
[1]
[1]
2.10 Conclusion
In this chapter the reported values of various material properties of lattice matched InGaP on
GaAs were presented and discussed. The selection of the most suitable values of those parameters
was carried out to enable their incorporation into subsequent device simulations. Among the
parameters that were discussed were the energy bandgap, lattice constant, effective masses of
charge carriers, energy band offsets, conduction and valence band effective density of states and
53
carrier mobilities. A Caughey Thomas mobility model for electrons was derived on the basis of
experimental data available for GaInP in the literature. The incorporation of these parameters into
our simulations and modeling of InGaP/GaAs HBT device performance is described in subsequent
chapters.
54
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[19]
Krutogolov, Yu.K., Dovzhenko, S.V., Diordiev, S.A., Krutogolova, L.I., Kunakin, Yu.I. and
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Auvergne, D., Merle, P. and Mathieu, H., “Band Structure Enhancement of Indirect
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Lewandowski,
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Jain, S.C., McGregor, J.M.
and Roulston, D.J., “Band-gap Narrowing in Novel III-V
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[23] Chin, T.P., Chang, J.C.P., Kavanagh, K.L., Tu, C.W., Kirchner, P.D. and Woodall, J.M., “Gas
Source Molecular Beam Epitaxy Growth, Characterization and Light-emitting Diode Application of
In1-xGaxP on GaP (100),” Appl. Phys. Lett., vol. 62, no. 19, pp. 2369-2371, 1993.
[24] t’Hooft, G.W., Riviere, C.J.B., Krijn, M.P.C.M., Liedenbaum, C.T.H.F. and Valster, A., “Ordering
Induced Splitting of Light-hole and Heavy-hole Bands in GaInP Grown by Organometallic VPE,”
Appl. Phys. Lett., vol. 61, no. 26, pp. 3169-3171, 1992.
[25] Emmanuelsson, P., Drechsler, M., Hofmann, D.M., Meyer, B.K., Moser, M. and Scholz, F.,
“Cyclotron Resonance Studies of GaInP and AlGaInP,” Appl. Phys. Lett., vol. 64, no. 21, pp. 28492851, May 1994.
[26]
Stubner, R., Winkler, R. and Pankratov, O., “Generalization of K.P Theory for Periodic
Perturbations,” Phys. Rev. B, vol. 62, no. 3, pp. 1843-1850, Jul. 2000.
[27] Sze, S.M., Physics of Semiconductor Devices, John Wiley & sons, New York, 2nd ed, 2001.
[28] Bhattacharya, P., Debbar, N., Biswas, D., Razheghi, M., Defour, M. and Omnes, F., “Band
Offsets in GaAs/Ga0.51In0.49P Hetero-structures grown by MOCVD,” Proc. of Int. Symp. GaAs and
Related Compounds, Kuruizawa, Japan, 1989.
[29] Lindell, A., Pessa, M., Salokatve, A., Bernardini, F., Nieminen, R.M., Paalanen, M., “Band
Offsets at the GaInP/GaAs Heterojunction,” J. Appl. Phys., vol. 82, no. 7, pp. 3374-3380, Oct. 1997.
58
[30] Pastor, J.M., Camacho, J., Rudamas, C., Cantarero, A., Gonzalez, L. and Syassen, K., “Band
Alignments in In1-xGaxP/GaAs Hetero-structures Investigated by Pressure Experiments,” Phys. Stat.
Sol. (a), vol. 178, pp. 571-576, 2000.
[31] O’Shea, J.J., Reaves, C.M., Den-Baars, S.P., Chin, M.A. and Narayanamurti, V., “Conduction
Band Offsets in Ordered-GaInP/GaAs Hetero-structures Studied by Ballistic-Electron-emission
Microscopy,” Appl. Phys. Lett., vol. 69, no. 20, pp. 3022-3024, Nov. 1996.
[32] Masselink, W.T., Zachau, M., Hickmott, T.W. and Hendrickson, K., “Electronic and Optical
Characterization of InGaP grown by Gas-Source Molecular-beam Epitaxy,” J. Vac. Sci. Technol. B,
vol. 10, no. 2, pp. 966-968, Mar/Apr. 1992.
[33] Shitara, T. and Eberl, K., “Electronic Properties of InGaP Grown by Solid-source MBE with a
GaP Decomposition Source,” Appl. Phys. Lett., vol. 65, no. 3, pp. 356-361, 1994.
[34] Quigley, J.H., Hafich, M.J., Lee, H.Y., Stave, R.E. and Robinson, G.Y., “Growth of InGaP on
GaAs using Gas-source Molecular-beam Epitaxy,” J. Vac. Sci. Technol. B, vol. 7, no. 2, pp. 358360, Mar/Apr. 1989.
[35] Ohba, Y., Ishikawa, U., Sugawara, H., Yamamoto, M. and Nakanisi, T., “Growth of High-quality
InGaAlP Epilayers by MOCVD using Methyl Metal-organics and Their Application to Visible
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[36] Blood, P., Roberts, J.S. and Stass, J.P., “GaInP grown by Molecular Beam Epitaxy Doped with
Be and Sn,” J. Appl. Phys., vol. 53, pp. 3145-3149, 1982.
59
[37] Brennan, K.F. and Chiang, P.K., “Calculated Electron and Hole Steady State Drift Velocities in
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[38] ATLAS Reference Manual, vol. 1, Silvaco Intnl, Santa Clara, CA., 1997.
[39] Zhang, B., Lan, S., Li, L.Q., Xu, W.J., Yang, C.Q. and Liu, H.D., “Low Temperature Electrical
Transportation Behavior of In0.5Ga0.5P Grown on GaAs (100) Substrate by LPE,” Solid State
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[40] Ikeda, M. and Kaneko, K., “Selenium and Zinc Doping in Ga0.5In0.5P and (Al0.5Ga0.5)0.5In0.5P
Grown by MOCVD,” J. Appl. Phys., vol. 66, no. 11, pp. 5285-5289, 1989.
60
3.
SIMULATION OF InGaP/GaAs HBTs AND MODEL VERIFICATION
This chapter concentrates on incorporation of the material properties and their models in the
simulation of a typical InGaP/GaAs HBT. A conventional emitter-up InGaP/GaAs HBT was chosen
for study since experimental results are more readily available for such a structure than for
collector-up structures. A typical collector-up HBT structure is then proposed and the simulation
results for it are compared with those of the emitter-up structure. In the following chapter, the results
of more extensive simulations are presented where the optimization of the collector-up HBT is
investigated.
3.1 Simulation Procedure
The modeling procedure followed in the course of the current simulations is described here.
The software used for this device modeling is a physically based, numerical device simulator from
SILVACO called ATLAS (ver 3.11.5.R) [1]. ATLAS is a physics-based, two dimensional device
simulator that predicts the device’s electrical behavior and enables the design of high performance
semiconductor devices. It also provides significant insight into the mechanisms involved in device
operation in that it can provide a two dimensional profile of carrier concentration, electric potential
profiles, electric field lines and current density profiles. A complete documentation of ATLAS can be
found in the available manual from Silvaco International [1].
The simulation procedure followed by the device simulation software, ATLAS, is presented in
this section. The technique followed by this software is to solve a set of fundamental equations,
which link the electrostatic potential and the carrier densities, numerically and in a holistic manner.
The set of fundamental equations comprise of Poisson’s equation, the continuity equations and the
transport equations. These are described as follows [2].
61
3.1.1 Poisson ’s Equation
Poisson’s Equation relates variations in the electrostatic potential to local charge densities [1].
It is mathematically described by the following relation [2]
∇ ⋅ (ε∇ψ ) = − ρ
(3.1)
where ψ is the electrostatic potential, ε is the local permitivity and ρ is the local space charge
density. The reference potential is always taken as the intrinsic Fermi potential for simulations in
ATLAS. The local space charge density is the sum of all contributions from all mobile and fixed
charges, including electrons, holes and ionized impurities [1].
3.1.2 Continuity Equations
For electrons and holes, the continuity equations are defined as follows [2 ]
∂n 1
= ∇ ⋅ J n + Gn − Rn
∂t q
(3.2)
∂p 1
= ∇ ⋅ J p + Gp − Rp
∂t q
(3.3)
where n and p are the electron and hole concentrations, Jn and Jp are the electron and
hole current densities, Gn (Rn) and Gp (Rp) are the generation (recombination) rates for
the electrons and holes, respectively and q is the magnitude of the charge on the electron. ATLAS
incorporates both eqns. (3.2) and (3.3) in simulations, but, also gives the user an option to turn off
62
one of the two equations and solve either the electron continuity equation or the hole continuity
equation [1].
3.1.3 Transport Equations
While equations (3.1)-(3.3) provide the general framework for device simulation, there are
secondary equations that need to specify particular physical models for electron and hole current
densities and generation (recombination) rates [1]. The Current density equations are obtained by
using the “drift-diffusion” charge transport model. The reason for this choice lies in the inherent
simplicity and the limitation of the number of independent variables to just three, ψ, n and p. The
accuracy of this model is excellent for all technologically feasible feature sizes. The drift-diffusion
model is described as follows [2]
J n = qnµ n E n + qDn ∇n
(3.4)
J p = qpµ p E p − qD p ∇p
(3.5)
where µn and µp are the electron and hole mobilities, Dn and Dp are the electron and
hole diffusion constants, En and Ep are the local electric fields for electrons and holes, respectively,
and ∇ is the three dimensional spatial gradient.
The local electric fields are defined as follows [1]


kT
E n = −∇ψ + L ln nie 
q


(3.6)


kT
E p = −∇ψ − L ln nie 
q


(3.7)
63
where nie is the local effective intrinsic carrier concentration. A key point here is that, ATLAS
inherently assumes that the Einstein relationship holds good for the drift-diffusion model so that the
diffusion constants and mobilities are proportional [1]
Dn =
kT
µn
q
(3.8)
Dp =
kT
µp
q
(3.9)
The simulation procedure numerically and self-consistently solves the above equations and
obtains electron and hole concentrations (n and p) and electrostatic potential (ψ) at all nodal points.
The biasing voltages, junction and contact lengths form the boundary conditions under which these
equations are solved. A brief description of the modeling procedure is presented in the next section.
3.2 Device Modeling
For the purpose of modeling InGaP/GaAs HBTs, three core issues need to be addressed:
(1) Device structure and mesh specification for efficient simulation,
(2) Material parameter and model incorporation, and
(3) Input file setup and output result extraction.
In the following sub-sections, we discuss each in turn.
64
3.2.1 Structure and Mesh Specification for Efficient Simulation
To obtain an accurate structure and mesh description for device simulation, the following
procedure is used. The Mesh is basically a two dimensional grid that covers the domain of physical
simulation. It is defined by a series of horizontal and vertical lines and the spacing between them.
The simulation of the device performance crucially depends on the density of mesh. The area
contained within alternate horizontal and vertical lines is the basic cell for performing calculations.
Care must be taken to ensure that the mesh is neither too coarse nor too fine, as a coarser grid
would provide a very rough evaluation of the device while a very fine one would encumber the
simulations by leading to excessively large processing times. Mesh optimization, therefore, is quite
crucial for achieving the desired results in as quick an amount of time as possible. One possible
way to achieve the desired results is to make use of the inherent symmetry of any transistor
structure and simulate only half the device. This has the advantage of consuming less simulation
time, yet would still yield all the device parameters correctly and with adequate accuracy. A useful
guideline to use in the mesh construction is to incorporate a fine mesh where parameters, such as
the potential or a carrier concentration, change rapidly, e.g., the base region for an HBT, and use a
coarser grid elsewhere. A typical mesh structure is shown in Fig. 3.1 for an emitter up GaInP/GaAs
HBT.
65
Figure 3.1 TONYPLOT presentation of the Mesh Structure of an InGaP/GaAs emitter-up HBT.
3.2.2 Material Parameters
An important step in achieving accurate performance simulations for the device is
incorporation of well documented material parameters and their dependences, like that of mobility
on the doping level. Research must be carried out scrupulously to examine the available material
and modeling parameters for the material system in context. For the HBT, the material properties
of the base, emitter and collector regions are needed to ensure valid results for the HBT’s
simulation. For the GaInP/GaAs HBT, the InGaP and GaAs material systems are, therefore, of
interest. The material parameter values of the InGaP and GaAs used in the current simulations are
presented below. All the values are those for 300K since the effects of transistor self-heating were
66
not investigated in this work. For GaAs, the material system is well known and the essential
material parameters have already been incorporated in a library in ATLAS. For the GaInP, the
material has been less thoroughly studied so that a survey of the literature was necessary. The
results of that survey were presented in the last chapter. We describe here the incorporation of
those results in the Silvaco software. Shown in Table 3.1 are a number of the key material
properties for GaInP and GaAs that were used in subsequent simulations.
Table 3.1 Material Properties for Ga0.51In0.49P and GaAs.
Material Properties
InGaP
GaAs
Energy Gap, Eg (eV)
1.849
[3]
1.424
[4]
Electron Affinity, χ (eV)
4.1
[3]
4.07
[4]
Effective Density of States in CB, Nc,cm-3
6.5X1017 [3]
9.2X1017
[4]
Effective Density of States in VB, Nv, cm-3
1.45X1019[3]
1.286X1019 [4]
Steady-state Recombination Lifetime of Electrons, τn0 , ns
0.09
[1]
5
[1]
Steady-state Recombination Lifetime of holes, τp0 , ns
0.09
[1]
3
[1]
Saturation Velocity of Electrons, Vsatn, *107cm/s
1
[1]
2.0
[1]
Saturation Velocity of holes, Vsatp, *107cm/s
1
[1]
1.8
[1]
The recombination lifetimes and saturated velocity values for Ga0.51In0.49P have been taken
from the inbuilt library of Silvaco software. The lack of adequate literature on these parameters for
Ga0.51In0.49P is most possibly due to the fact that the lifetime parameters are more crucial in the
base region than in other regions as recombination attains prominence in view of the narrowness of
this region. The base region consists of GaAs, which has been thoroughly investigated. Hence, the
lifetime values incorporated in Silvaco have been used without any additional alterations for this
region.
67
3.2.3 Material Models
The main material models used in all the device simulations in this thesis are:
(1) Shockley-Read-Hall doping dependent lifetime recombination model,
(2) Caughey-Thomas doping dependent mobility model, and
(3) Electric field-dependent mobility model.
In the following sub-sections, we describe each of these models.
3.2.3.1
Shockley-Read-Hall Recombination Model
The carrier lifetimes used in the Shockley-Read-Hall (SRH) recombination model are known to
be a function of impurity concentration decreasing as the doping level increases. The Silvaco
software incorporates a doping dependent lifetime in accordance with the model proposed by
Roulston et al. [5], which is described by the following equations [2]
2
RSRH
pn − nie
=
ETRAP
ETRAP
τ p [n + nie exp(
)] + τ n [ p + nie exp( −
)]
kTL
kTL
(3.10)
τn =
TAUN 0
1 + N /( NSRHN )
(3.11)
τp =
TAUP0
1 + N /( NSRHP )
(3.12)
where RSRH is the rate of electron-hole pair recombination, n and p are the electron and hole
concentrations, respectively, nie is the effective intrinsic carrier concentration (including the bandgap
narrowing due to high doping effects), τn and τp are the electron and hole recombination lifetimes,
68
respectively, TL is the lattice temperature and ETRAP is the location in energy of the deep level trap
acting as the recombination center in the material (usually near midgap for the semiconductor). The
parameters TAUN0 and TAUP0 are the lifetimes of electrons and holes, respectively, at very low
doping levels and NSRHN and NSRHP are the doping levels above which the lifetime degrades.
In (3.11) and (3.12), N corresponds to the local doping for the region of interest in the device.
These lifetimes are important, particularly the minority carrier electron lifetime in the p-type GaAs
base region of the N-p-n GaInP/GaAs HBT of interest here. To a lesser extent, the hole lifetime in
the n-type GaInP emitter is important in determining the hole back injection current from the base
into the emitter that contributes to the base current, which impacts the device’s current gain.
The values of the parameters TAUN0, TAUP0, NSRHN and NSRHP chosen are given in Table
3.2. All these parameters are default values incorporated in the Silvaco software’s internal library.
Table 3.2. Shockley-Read-Hall Model Lifetime Parameters
Material Properties
InGaP
TAUN0
0.09 (ns)
[1]
5 (ns)
[1]
TAUP0
0.09 (ns)
[1]
3 (ns)
[1]
NSRHN
5e16 (cm-3)
[1]
5e16 (cm-3)
[1]
NSRHP
5e16 (cm-3)
[1]
5e16 (cm-3)
[1]
3.2.3.2
GaAs
Caughey Thomas Doping Dependent Mobility Model
The Caughey and Thomas model [6] is an empirical model that has been derived to specify
the mobility as a function of doping and temperature at low electric fields. The general form of the
doping dependence of this model is shown below:
69
µ n ( N ) = µ min +
µ max − µ min
 N
1 + 
 NC



α
(3.13)
where N is the total dopant density, µmax, µmin, NC and α are parameters chosen to fit measured
data (usually at room temperature).
The mobility equation above is incorporated in ATLAS implementing this doping dependence
model, but also incorporating the temperature dependence of the fitting parameters. The electron
and hole mobility equations are then given by [1]
µ n 0 = MU 1N .CAUG.(
TL ALPHAN .CAUG
)
+
300 K
TL BETAN .CAUG
T
)
− MU 1N .CAUG.( L ) ALPHAN .CAUG
300 K
300 K
TL GAMMAN .CAUG
N
1+ (
)
.(
) DELTAN .CAUG
NCRITN .CAUG
300 K
MU 2 N .CAUG.(
µ p 0 = MU 1P.CAUG.(
TL ALPHAP.CAUG
+
)
300 K
TL BETAP.CAUG
T
− MU 1P.CAUG.( L ) ALPHAP .CAUG
)
300 K
300 K
TL GAMMAP .CAUG
N
DELTAP .CAUG
1+ (
)
.(
)
300 K
NCRITP.CAUG
MU 2 P.CAUG.(
(3.14)
(3.15)
where the correspondence of the model parameters in (3.14) and (3.15) with those of (3.13) is clear
and where the temperature dependence has been added for each parameter in the form of
(TL/300)α. Since all the simulations are carried out at 300K, this factor becomes unity and so doesn’t
have much significance for the device modeling study.
For the GaInP, the Caughey-Thomas mobility model was graphically illustrated in the previous
chapter. A complete tabulation of all the Caughey Thomas parameters used in the simulations is
presented in Table 3.3 below. These values were extracted from the Caughey-Thomas plot which
was obtained by curve fitting the Caughey Thomas mobility model in the previous chapter and
70
shown in Fig. 3.2 below. A more rigorous description of the derivation of these parameters is
presented in Appendix A.
Table 3.3 Caughey-Thomas electron and hole Mobility Model Parameters
Mobility Parameters
InGaP
GaAs
MU1N.CAUG (cm2/V-s)
300
0
MU2N.CAUG (cm2/V-s)
2000
7200
MU1P.CAUG (cm2/V-s)
49.7
0
MU2P.CAUG (cm2/V-s)
479.37
380
ALPHAN.CAUG
0
0
ALPHAP.CAUG
0
0
BETAN.CAUG
-2.3
0
BETAP.CAUG
-2.2
0
GAMMAN.CAUG
-3.8
0
GAMMAP.CAUG
-3.7
0
DELTAN.CAUG
0.59
0.3108
DELTAP.CAUG
0.7
0.3494
NCRITN.CAUG (cm-3)
2.25X1016
2.443X1017
NCRITP.CAUG (cm-3)
1.606X1017
3.0363X1017
71
1800
1400
2
Electron M obility (cm /V-s)
1600
1200
1000
800
600
400
200
14
10
10
15
10
16
10
17
N , cm
10
18
10
19
10
20
-3
D
Figure 3.2 Derived Caughey-Thomas model of the electron mobility versus doping for
GaInP.
As explained in the previous chapter, a derivation of Caughey-Thomas mobility model for
holes couldn’t be accomplished due to a paucity of published literature on this topic. The tabulated
values of Caughey-Thomas mobility model for holes in InGaP in Table 3.3 were obtained from
Silvaco software’s default model for this material system [1].
By contrast, owing to the fact that GaAs has been very well studied and all its properties
extensively documented, it was possible to derive the Caughey-Thomas mobility model parameters
for both electrons and holes. The mobility dependent characteristics are shown in Figs. 3.3 and 3.4
72
for electrons and holes, respectively. The extraction of Caughey-Thomas model parameters for
both the electrons and hole mobility models for GaAs, which are incorporated in this simulation
study, is detailed in Appendix B.
3000
2
Electron M obility, cm /V-s
2500
2000
1500
1000
500
18
10
10
19
10
20
-3
Donor Doping Concentration, (cm )
Figure 3.3 Caughey-Thomas mobility model for electrons in GaAs.
73
160
120
(cm
2
/ V-s)
140
Hole Mobility
100
80
60
40
18
10
10
19
10
A c c e p to r D o p in g C o n c e n tr a tio n , (c m
-3
20
)
Figure 3.4 Caughey-Thomas mobility model for holes in GaAs.
3.2.3.3
Parallel Electric Field Model for Electron and Hole Mobilities
This model takes into account the phenomenon that, when carriers are accelerated in an
electric field, their velocity will begin to saturate at high electric fields. The following Caughey
Thomas expression [6] is used to implement a field-dependent mobility that provides a sufficiently
accurate description of the low to high field transition and the resulting changes in effective mobility
as a result of velocity saturation
1
1
µn ( E ) = µn0 [
] BETAN
µ n 0 E BETAN
1+ (
)
VSATN
74
(3.16)
µ p ( E ) = µ p0 [
1+ (
1
µ p0 E
VSATP
1
(3.17)
] BETAP
)
BETAP
where E is the parallel electric field along the direction of motion, µn0 and µp0 are the low field
electron and hole mobilities, VSATN and VSATP are the electron and hole saturation velocities and
BETAN and BETAP are fitting parameters, respectively. The low field mobilities are obtained from
the evaluation of low-field analytical Caughey-Thomas doping dependent mobility model described
above. The impact of the inclusion of this field mobility model is to reduce the effective mobility
since the magnitude of drift velocity is the product of effective mobility times the component of
electric field in the direction of current flow. Since the drift velocity must remain constant at higher
electric fields at its saturation value, an increase in electric field must result in a lower effective
mobility. The parameteric values used in the current simulations are listed below. For GaAs, the
default parameters incorporated in the Silvaco library were used. Since GaInP is used in the emitter
layer of the HBT, its velocity saturation properties are less important than those of GaAs. As a
result, default values for GaAs were also used for GaInP. Shown below are reported velocity-field
characteristics for GaAs and GaInP for both electrons and holes.
Table 3.4 Parameters for Parallel-electric Field Mobility Model
Model Parameter
InGaP
GaAs
VSATN (*107cm/s)
1
[1]
2
[1]
VSATP (*107cm/s)
1
[1]
1.8
[1]
BETAP, BETAN
1
[1]
1
[1]
ECRITP,ECRITN
4000
[1]
4000
[1]
(V/cm)
The velocity field characteristics for electrons and holes in GaInP and GaAs are shown in the
following figures. Figs. 3.5 and 3.6 show the variation of electron and hole velocities with respect to
75
electric field for GaInP while the variation of the same parameters for GaAs is shown in Figs. 3.7
and 3.8. A more elaborate discussion of these variations is presented in the previous chapter and
the present reference to these figures is merely for the sake of illustrating their respective variations
with electric field.
Figure 3.5 Field dependence of electron drift velocity in Ga0.52In0.48P [3,7].
Figure 3.6 Field dependence of hole drift velocity in Ga0.52In0.48P [3,7].
76
Figure 3.7 Field dependence of electron drift velocity in GaAs [4,8].
Figure 3.8 Field dependence of hole drift velocity in GaAs at various
temperatures [4,9].
77
3.2.4 Input File Setup and Output Result Extraction
For device modeling, the simulation is initially done with no applied biases and
subsequently the voltages to be applied are incremented. The sweep of the DC biases yields
the device’s DC characteristics, i.e., the Gummel plot of IB and IC versus VBE. For AC analysis,
after the desired DC bias point is reached, the AC bias is applied and the AC performance
parameters are extracted. The definition and application of input voltage should be done very
carefully. Improper application of Input voltage might lead to extremely error prone programs.
The main technique to avoid problems is to minimize the bias steps to as small an extent as
possible, but not at the expense of overburdening the simulator resulting in extremely large
processing times. Voltages must be stepped up gradually so as to facilitate convergence of the
simulation. Further, the collector-emitter voltage is usually fixed prior to varying the base voltage
to have convergence in the process simulation. The base voltage is then varied gradually using
the SOLVE command as is shown below from the following piece of ATLAS code shown in
Figure 3.9 :
solve v2=0.01 ac freq=10 direct
solve v2=0.025 vstep=0.025 electr=2 nstep=2 ac freq=1e6 direct
solve v2=0.1 vstep=0.1 electr=2 nstep=5 ac freq=1e6 direct
solve v2=0.65 vstep=0.05 electr=2 nstep=6 ac freq=1e6 direct
solve v2=0.975 vstep=0.025 electr=2 nstep=3 ac freq=1e6 direct
Figure 3.9 Simulation Code showing gradually incremented bias steps.
Since high frequency AC characteristics of the device are to be evaluated subsequently, it is
essential to have all the voltage application part simulated initially at extremely low frequencies,
78
e.g., 1 MHz. Subsequently, the frequency can be increased until the desired value (~100 GHz) in a
gradual manner similar to the base voltage ramp up to obtain results as a function of frequency.
3.3 Model Verification
To begin use of the software to model GaInP/GaAs HBTs using the above described material
parameters and models, a conventional emitter-up HBT was identified in literature and it’s
performance simulated.
3.3.1 High Performance Emitter-up InGaP/GaAs HBT
This section deals with the initial GaInP/GaAs HBT modeling to verify the mobility models and
material parameters mentioned above. As a test of the modeling results, comparison was made
with published results, keeping in mind the inherent nature of discrepancy in device modeling,
owing to the fact that simulated results could never take into account the practical effects in which
devices operate however efficiently modeled, a leeway of around 5-10% in obtained values was
expected to be acceptable.
The device chosen for model verification was reported in “High Speed Small-Scale
InGaP/GaAs HBT technology and its Application to Integrated Circuits” by T. Oka et al. [10]. This
paper deals with the enhancement of the high speed performance of InGaP/GaAs HBTs using a
WSi/Ti base electrode with a buried SiO2 to reduce the extrinsic collector area. The aim of this
approach was to investigate the feasibility of a fabrication technology that enables simultaneous
79
reduction of the emitter size and the parasitic capacitance of the extrinsic base-collector junction,
thereby allowing the device to operate at higher frequencies and low collector currents.
The structure of the chosen GaInP/GaAs HBT is shown in Figure 3.10 along with a
conventional device structure for comparison.
Figure 3.10 Schematic cross sections of a conventional HBT (a) and an HBT scaled down by Oka
et al.’s approach (b) [10].
This structure’s design is intended to lower the parasitic collector capacitance by over 50%
compared to previous designs by reducing the area of the base-collector junction. This is achieved
by reducing the extent of the base-collector junction’s lateral extent under the base contacts. The
80
epitaxial layer structure parameters of the fabricated GaInP/GaAs HBTs are summarized in the
following table (Table 3.5).
Table 3.5 Epitaxial Layered Structure of Emitter-up GaInP/GaAs HBTs by Oka et al. [10]
The fabricated devices, one (SE1) with an emitter area of 0.5 X 4.5 µm2 and another (SE2)
with an emitter area of 0.25 X 1.5 µm2, were evaluated for DC and high-frequency performance
metrics. The high frequency characteristics were determined by measuring S-parameters with onwafer RF probes in the range of 100 MHz to 40 GHz. The fT and fmax values were estimated in the
usual fashion with –20 dB/decade extrapolations from the small signal current gain |h21|2 and the
unilateral power gain, UG, respectively. These fT and fmax parameters were measured as a function
of collector current density as shown in Fig. 3.11 (a) and 3.11 (b), respectively. The collectoremitter bias point was kept fixed at 1.5 V. For the HBT (SE1) with the larger emitter area, a peak fT
of 156 GHz and peak fmax of 255 GHz were obtained at a collector current of 3.5 mA, while the
smaller device (SE2) yielded the corresponding values of 114 GHz and 230 GHz at an IC of 0.9 mA.
81
(a)
(b)
Figure 3.11 Collector current dependence of fT and fmax of the fabricated HBTs with
(a) SE1 = (0.5X4.5 µm2) and (b) SE2 = (0.25X1.5 µm2) at VCE of 1.5 V [10].
The other parameters that were measured included small signal AC current gain (hfe),
DC current gain hFE, breakdown voltage BVCEO, epitaxial bulk resistances, junction
capacitances and charging times. Further, contact resistivities of the base and
emitter/collector contacts were measured to be 5X10-7 and 5X10-8 Ohm-cm2, respectively.
The parameter values for the two devices are listed in Table 3.6.
Table 3.6 Device Parameters Extracted from Fabricated GaInP/GaAs HBTs by Oka et
al. [10]
82
3.3.2 ATLAS Simulations
To begin this device modeling study, the emitter-up GaInP/GaAs HBT described above
was modeled using the Silvaco’s software with the material parameters and models
previously described. The parameters that could be extracted from simulations include the
Gummel Poon plots (DC characteristics) and fT, fmax variation with collector current (AC
characteristics). The validation of these device results provides evidence for the
correctness of the assumed material parameters and models used in device simulation.
To
ensure
more
accurate
simulations,
contact
resistances
for
base
and
emitter/collector regions, measured and presented in this work [10] based on contact
resistivity values of 5X10-7 and 5X10-8 Ohm-cm2, respectively, were also incorporated into
83
the simulation model. The models and material parameters used in the process have
already been described above in section 3.2.
The device structure used for simulation is similar to the larger emitter-up HBT (SE1)
developed by Oka et al. [10]. The epitaxial structure is depicted in Table 3.5. The device
structure discussed here, however, doesn’t correspond exactly to the SE1 HBT of Oka et
al. [10], owing to the fact that it wasn’t possible to determine from the published results all
of the lateral dimensions for the device’s structure. The complete device structure and
profile is summarized in Tables 3.7 and 3.8 and shown in Figure 3.12.
Table 3.7 Layer-wise dimensions of the simulated emitter-up InGaP/GaAs HBT.
Region
Lateral Dimensions (nm) 1
Vertical Dimensions (nm)
InGaAs emitter-cap
250
50
GaAs emitter-cap
250
100
InGaP emitter-cap
250
50
InGaP emitter
250
100
GaAs base
750
30
GaAs collector
750
200
GaAs sub-collector
1250
800
1
All values to be scaled by a factor of 2
84
Table 3.8 Electrode dimensions of the simulated emitter-up InGaP/GaAs HBT.
Electrode
Lateral Dimensions
Vertical Dimensions Electrode Spacing
(nm)
(nm)
(nm)
Emitter
250 2
20
-
Base
400
20
100
Collector
400
20
100
name
The device cross section is shown in Figure 3.12 where it has been cut into half to
reduce simulation time. Care, however, has been taken to ensure that the current values
are properly scaled.
Figure 3.12 Simulated emitter-up InGaP/GaAs HBT structure.
2
To be scaled by a factor of 2
85
The simulation results of the structure in Fig 3.12 are presented below. Firstly, the
Gummel-Poon characteristics of the larger HBT structure (SE1) given by Oka et al. [10] are
presented in Figure 3.13. The simulated Gummel-Poon characteristics are then shown in
Figure 3.14. The close conformity in the shapes of these two plots is clearly evident. The
maximum collector current at 1.6 V for the structure designed by Oka et al. [10] was of the
order of a few milli-amperes while that for the simulated structure is in the order of a few
tens of milli-amperes.
Figure 3.13 Gummel Poon (DC characteristics) of the emitter-up InGaP/GaAs HBT
structure from Oka et al. [10]
86
Figure 3.14 Gummel Poon characteristics of the simulated emitter-up InGaP/GaAs HBT.
The frequency response of the simulated structure is presented in Figure 3.15. This
shows a very high value of AC current gain (typically around 80 dB), much larger than that
is usually expected for an emitter-up InGaP/GaAs HBT structure (whose typical value is
around 30-50 dB). From Figure 3.13, Oka et al. [10] reports a current gain of around 20 dB.
A possible reason for such high simulation values could be the fact that the nonexperimental simulations do not take into account the presence of stray resistances, lead
resistances and other dissipative lossy elements that will induce losses in practice.
87
Figure 3.15 Frequency response of the current gain for the simulated emitter-up
InGaP/GaAs HBT.
A plot showing the variation of the AC current gain with DC collector current density,
JC, is presented in Fig. 3.16. The variation with JC is nonetheless along expected lines. It
rises with JC and, after reaching a peak of 81.8 dB, it falls-off substantially owing to high
current effects such as base pushout.
88
82
AC Current G ain, dB
81.5
81
80.5
80
79.5
0.01
0.1
1
10
100
Collector Current Density, KA/cm
1000
2
Figure 3.16 AC current gain variation with collector current density for the
simulated emitter-up InGaP/GaAs HBT.
Maximum unilateral power gain (which is defined and discussed in detail in the next
chapter) is another parameter of significant interest for any microwave transistor. The
calculated variation of this parameter with collector current density is presented in Figure
3.17. As anticipated, the variation is roughly parabolic and tends to decrease substantially
with increased collector density due to high current effects for JC beyond 100 KA/cm2. Oka
et al. [10] didn’t report current and power gain results as a function of
89
the collector current density as a more detailed comparison with the simulation results is
not possible.
75
70
60
U
max
(dB)
65
55
50
45
0 .0 1
0 .1
1
10
100
1000
2
C o lle c to r C u r re n t D e n s ity ( K A /c m )
Figure 3.17 Maximum unilateral power gain variation with collector current density for the
simulated emitter-up InGaP/GaAs HBT.
The high frequency parameters are also of interest and are extracted from the AC
frequency response curve for successive bias points throughout the active region in
common-emitter configuration. A comparison of cutoff frequency (fT) and maximum
frequency of operation (fmax) is presented next in Figs. 3.18 and 3.19. The former figure
shows the measured results from Oka et al. [10] while the latter shows the extracted results
from high frequency simulations.
90
Figure 3.18 fT(°), fmax(•) vs DC collector current for an emitter up HBT with SE=0.5X4.5 µm2
reported by Oka et al. [10].
3 0 0
fT
2 5 0
max
(GHz)
2 0 0
T
f ,f
(G H z )
fm a x (G H z )
1 5 0
1 0 0
5 0
0
0 .0 0 0 1
0 .0 0 1
0 .0 1
0 .1
1
1 0
C o lle c to r C u r r e n t ( m A )
Figure 3.19 fT, fmax vs total DC collector current of simulated emitter-up InGaP/GaAs
91
HBT.
3.3.3 Inference from Simulation Results
As can be inferred from comparison of these figures, there is a reasonable agreement
between the theoretical and published values for the high frequency performance
parameters. The peak values of fT and fmax that were obtained from simulations of an
emitter-up HBT with SE1=0.5X4.5 µm2 are 158 GHz and 267 GHz, respectively. The
published values from Oka et al. [10] for the same device are 156 GHz and 255 GHz,
respectively. This close conformity in the AC performance characteristics provides some
vindication of the models and parameters used in the current and subsequent simulations.
The DC characteristics shown in Figs. 3.13 and 3.14, are in approximate agreement,
though the simulated gain (~104) is considerably larger than the observed gain (~25), which
is typically the case with emitter-up HBTs. Various factors, including the effect of bulk
resistances in the active regions of the device not being incorporated into simulations and
other stray parasitic resistances that come into the picture in measuring device
performance and not in simulations, might be part of the reason for this huge discrepancy.
There may also be additional base current components , e.g. surface recombination, that
degrade the current gain in practice, but which have not been incorporated into the device
modeling.
3.4 Collector-up HBT Structure Simulation
Collector-up HBTs are based on the principle that reduction of the base-collector
capacitance associated with the extrinsic base region is the key to a successful increase in
the high-frequency performance of these devices. The reason for a conventional bipolar
transistor with a large collector area is efficient charge collection. This was the reason
behind the familiar emitter-up configuration with collector at the bottom and emitter at the
top shown in Fig. 3.7. There is also the constraint imposed by the necessity for all contacts
92
need to be located on the top surface of the device for planar wafer processing. However, it
has been shown by Kroemer [11] that, even with larger emitter areas, it is possible to have
the same high emitter injection efficiency ( ≈ 1) and a much improved high frequency
performance in an inverted structure with the collector contact on top. This is possible,
provided that the region of emitter directly beneath the base contact is highly passivated so
that it cannot inject any more electrons into the extrinsic base region. This reduces
unnecessary current flow into the extrinsic base, thereby directing the bulk of the electrons
directly into the base beneath the collector and enabling high efficiency device
performance. To better appreciate the differences and impact of this emitter undercut on
device performance, detailed simulation results showing the performance of unetched and
etched emitter portions are presented in the subsequent chapter.
Figure 3.20 Proposed collector-up InGaP/GaAs HBT with unetched extrinsic emitter.
93
In this section, the simulation results of a typical collector-up structure, with unetched
extrinsic emitter (Fig. 3.20) are presented as a baseline for future comparison. The material
parameters and models discussed in section 3.2 were incorporated in these simulations
and are the same ones used in the emitter-up device configuration previously presented.
The epitaxial structure of the simulated InGaP/GaAs collector-up HBT is shown in Table
3.9.
Table 3.9 Epitaxial structure of GaInP/GaAs collector-up HBT.
Layer
Material
Doping (cm-3)
Thickness (nm)
Collector-cap
n+ In0.5Ga0.5As
4X1019
200
Collector
n GaAs
1X1017
300
Base
p+ GaAs
3X1019
50
Emitter
n In0.49Ga0.51P
5X1017
250
Sub-emitter
n+ GaAs
2X1019
200
The device performance parameters cutoff frequency (fT), maximum frequency of
oscillation (fmax), small signal current gain (β) and maximum unilateral power gain (Umax) are
each calculated as a function of collector current density and presented in Figs. 3.21-3.26.
Shown in Figure 3.21 is the Gummel plot of IC and IB vs VBE, which shows the device has a
current gain of around 2 (~6 dB). This very low gain is due to the fact that many electrons
injected into the base are lost due to recombination under the base contact so that the
emitter injection efficiency is low. In the next chapter we will show the improvement in the
current gain when etching is used to remove part of the extrinsic emitter. Shown in Fig.
94
3.22 is the fall off in current gain with increasing collector current density due to high
current effects. The frequency response of the current gain is shown in Fig. 3.23. The high
frequency parameter fT is extracted from this frequency response for different base-emitter
bias voltages and the results are shown in Fig. 3.24. A more closer look at this parameter
and its optimization for this structure is presented in the next chapter. Shown in Fig. 3.25 is
the unilateral power gain versus DC collector current density showing a similar fall off at
high collector current density. Fig. 3.26 shows Umax’s variation with frequency that can be
used to obtain fmax. The maximum frequency of oscillation (fmax) extracted from successive
bias voltages from curves akin to Fig. 3.26 is presented in Fig. 3.24 as a function of DC
collector current density.
10
C o lle c to r C u r r e n t ( m A )
B a s e C u rre n t (m A )
C
I ,I
B
(mA)
1
0 .1
0 .0 1
1 .2
1 .3
1 .4
1 .5
1 .6
1 .7
B a s e - E m itte r V o lta g e ( V )
Figure 3.21 Gummel-Poon characteristics of the simulated InGaP/GaAs
collector-up HBT.
95
6 .1
Current Gain (dB)
6
5 .9
5 .8
5 .7
5 .6
0 .0 0 1
0 .0 1
0 .1
1
10
2
C o lle c t o r C u r r e n t D e n s ity ( K A /c m )
Figure 3.22 Variation of AC current gain at a frequency of 2 GHz with collector current
density.
Log (Frequency)
Figure 3.23 AC response of the simulated collector-up InGaP/GaAs HBT.
96
120
Frequency (GHz)
100
80
60
40
20
0
0 .0 0 1
0 .0 1
0 .1
1
C o lle c t o r C u r r e n t D e n s ity ( K A /c m
10
2
)
Figure 3.24 fT(• ), fmax(♦ ) variation with collector current density.
27
26
U
max
(dB)
25
24
23
22
21
20
0 .0 0 1
0 .0 1
0 .1
1
10
2
C o lle c t o r C u r r e n t D e n s ity ( K A /c m )
Figure 3.25 Maximum unilateral power gain (at 2 GHz ) variation with collector current
density.
97
Unilateral Power Gain (dB)
Frequency (GHz)
Figure 3.26 Simulation of unilateral power gain’s frequency response for the
InGaP/GaAs collector-up extrinsic emitter unetched HBT.
The peak values of fT, fmax, β and Umax are 109 GHz, 77 GHz, 6.0 dB and 26.2 dB,
respectively. The very low value of small signal current gain is anticipated as emitter
injection efficiency is drastically reduced since only a third of the total electrons are actually
injected into the base beneath the collector if we assume uniform injection across the
emitter-base junction. The values of fT and fmax too are considerably smaller than for an
emitter-up HBT (fT=158 GHz, fmax=267 GHz). The reason behind this is quite clear. The
structures are quite different and to a common basis for comparison isn’t, therefore,
possible. In particular, base width (XB) is 50 nm for the collector-up HBT while it is 30 nm
98
2
X
for the emitter-up structure. Since the base transit time ( τ b = B ), the larger base width
v.DnB
would inevitably result in smaller values of cutoff frequency (fT). Further, collector doping is
larger for the collector-up structure (~ 1017 cm-3) than that of emitter-up structure (~ 2X1016
cm-3). So the collector junction capacitance would be augmented as it is directly
proportional to the square root of collector doping concentration. Hence, it also contributes
to the reduction of cutoff frequency. These two factors are independent of the nature of the
device configuration and therefore the collector-up configuration is not entirely responsible
for high frequency parameter degradation. Further, this collector-up configuration itself
hasn’t been optimized in accordance with practical considerations. It has an inactivated or
unetched extrinsic emitter region, the large junction area of which, serves to lower the
emitter junction capacitance significantly. Just like the collector junction capacitance, the
emitter junction capacitance plays a crucial role in deciding the value of cutoff frequency.
Hence the presence of extrinsic emitter raises the emitter and collector charging times and
so lowers the cutoff frequency. The cutoff frequency is, however, not insignificant and well
over 100 GHz. This can be attributed to the reduced collector junction area, which lowers
the collector junction significantly, thereby improving the cutoff frequency. This reduction in
collector junction capacitance alone cannot improve the maximum frequency of oscillation
(fmax). The following is a second order expression for fmax of an emitter-up HBT [12]
f max
1
=
4π
 rbi C jci ( RBB + RB ( epi ) C jc ) 


+
2ω T
 ω Ti

−1 / 2
(3.18)
where rbi stands for intrinsic base resistance, ωTi corresponds to the angular cutoff frequeny
wherin all capacitive and resistive components are intrinsic, ωT is the angular cutoff
99
frequency including extrinsic components, Cjci is the intrinsic collector junction capacitance,
Cjc is the collector junction capacitance, RBB + RB(epi) is the extrinsic base resistance, which
is that component of total base resistance that lies outside the intrinsic base region. The
following figure (Fig. 3.27) helps to elucidate the physical origin of these parameters.
Figure 3.27 Illustration of intrinsic and extrinsic impedance and capacitive components for
an emitter-up HBT [12].
From the above figure and equation (3.18), it is clear that the presence of any extrinsic
collector region (or emitter region for the collector-up HBT) would only add to the capacitive
components that tend to lower the maximum frequency of oscillation. Though the extrinsic
resistive components would remain the same even when the extrinsic emitter region is
unetched, the emitter junction capacitance is substantially larger when the emitter region is
not reduced by etching. The increased emitter junction capacitance, therefore, significantly
reduces the maximum frequency of oscillation owing to the large emitter area associated
with the extrinsic emitter region.
100
3.5 Conclusions
In summary, it has been shown in this chapter that the material parameters and models
incorporated in the simulations have produced results in reasonable agreement with the
results reported for the emitter-up HBT by Oka et al. [10]. The degree of conformity was
reasonable keeping in view the fact that the lateral dimensions of the published structure
were not all given so that the simulated structure was not likely exactly the same, though
the epitaxial structure was the same as Oka et al. [10]. The peak values of fT and fmax that
were obtained from simulations for an emitter up HBT with SE1=0.5X4.5 µm2 are 158 GHz
and 267 GHz respectively. The published values for the same devices was 156 GHz and
255 GHz, respectively. Also, an InGaP/GaAs collector-up HBT with its extrinsic emitter
region unetched was proposed and simulated. Simulation results for this collector-up HBT
were presented. The fT and fmax values obtained were 109 GHz, 77 GHz respectively which
are substantially smaller than those obtained for the emitter-up structure discussed above.
However, differences from the emitter-up HBT were traceable to a larger base width and
higher collector doping in the collector-up HBT. The current gain for the collector-up HBT
was only around 2 (6dB) which can be explained reduced emitter injection efficiency as
there are significant losses due to injection and recombination beneath the base contacts.
Therefore, It is quite evident from these results that the performance of a collector-up
structure with unetched extrinsic emitter region is inferior to that of an emitter-up structure.
It will be shown in the subsequent chapter that, by undercutting the emitter region below
the extrinsic base contact, high frequency performance can be improved significantly and
the device can yield a performance that is comparable or superior to that of the emitter-up
HBT.
101
REFERENCES
[1] ATLAS User Manual, Vol. 1, Silvaco International, Santa Clara, CA, Feb’ 2000.
[2] Streetman, B., Solid State Electronic Devices, Prentice Hall Publications, New Delhi, pp.
119-146, 1995.
[3] Goldberg, Yu. A., “Gallium Indium Phosphide (GaxIn1-xP),” in Handbook Series on
Semiconductor Parameters, vol. 2, Ternary and Quaternary A3B5 Semiconductors,
Levinshtein, M., Rumyantsev, S. and Shur, M., ed., 2nd ed., World Scientific, Singapore, pp.
37-59, 1996.
[4] Levinshtein, M.E. and Rumyantsev, S.L., “Gallium Arsenide (GaAs),” in Handbook
Series on Semiconductor Parameters, vol. 1, Si, Ge, C (Diamond), GaAs, GaP, GaSb,
InAs, InP, InSb, Levinshtein, M., Rumyantsev, S. and Shur, M., ed., 2nd ed., World
Scientific, Singapore, pp. 77-103, 1996.
[5] Roulston, D.J., Arora, N.D. and Chamberlain, S.G., “ Modeling and Measurement of
Minority Carrier Lifetimes Versus Doping in Diffused Layers of n ±p Silicon Diodes”, IEEE
Trans. of Electr. Dev., pp. 284 –291, Feb. 1982.
[6] Caughey, D.M. and Thomas, R.E., “Carrier Mobilities in Silicon Empirically Related to
Doping and Field”, Proc. IEEE, vol. 55, pp. 2192-2193, 1967.
102
[7] Brennan, K.F. and Chiang, P.K., “Calculated Electron and Hole Steady State Drift
Velocities in Lattice Matched GaInP and AlGaInP,” J. Appl. Phys., vol. 71, no. 2, pp. 10551057, 1992.
[8] Blakemore, J.S., “Semiconducting and other Major Properties of Gallium Arsenide,” J.
Appl. Phys., vol. 53, no. 10, pp. R123-R181, 1982.
[9] Dalal, V.L., Drebeen, A.B. and Triano, A., “Temperature Dependence of Hole Velocity in
GaAs,” J. Appl. Phys., vol. 42, no. 7, pp. 2864-2867, 1971.
[10] Oka, T., Hirata, K., Suzuki, H., Ouchi, K., Uchiyama, H., Taniguchi, T., Mochizuki, K.,
Nakamura, T, “High-speed Small-scale InGaP/GaAs HBT Technology and its Application to
Integrated Circuits”, IEEE Trans. on Electr. Dev., vol. 48, no. 11, Nov. 2001, pp. 2625 –
2630.
[11] Kroemer, H. “Heterostructure Bipolar Transistors and Integrated Circuits”, Proc. Of the
IEEE, vol. 70, no. 1, Jan. 1982, pp. 13 -25.
[12] Liu, W., Handbook of III-V Heterojunction Bipolar Transistors, John Wiley and Sons
Inc., New York, pp. 755, 1998.
103
4. SIMULATION AND OPTIMIZATION OF InGaP/GaAs
COLLECTOR-UP HBTs
In the previous chapters we’ve begun this modeling study with the simulation of typical
InGaP/GaAs HBTs with collector and emitter up structures and their comparison. In this chapter, we
investigate the optimization of the collector-up InGaP/GaAs HBTs. Results are presented for a
collector-up structure where the extent of undercut of the base is varied to reduce the extrinsic
emitter. Subsequently, the design of the emitter, base and collector layers is investigated,
specifically the effects on the device’s high frequency performance including the power gain. We
conclude with simulation results for an optimized collector-up structure.
This chapter covers a number of aspects of InGaP/GaAs HBTs. After briefly reviewing the high
frequency performance parameters, the effects of undercut of the base layer on collector-up HBT’s
performance is examined with the aim of optimizing the device’s performance. The effects of the
device’s epitaxial structure are then investigated. Finally, the device modeling software is used to
simulate InGaP/GaAs collector-up HBT structures reported recently in the literature.
4.1 High Frequency Performance Parameters
This section reviews the various high frequency parameters that characterize the HBT’s
performance and provides a brief discussion of their importance and understanding to the device’s
structure.
104
4.1.1
Small Signal Current Gain (βac) and Cutoff Frequency (fT)
The Cutoff frequency, fT, is defined as the frequency at which the magnitude of h21 (hparameter forward current gain) decreases to unity. In particular, this discussion refers to h21e,
the gain for common emitter configuration, since the common base current gain is usually less
than unity and is of little practical interest. Symbolically, h21e is defined as:
h21e =
ic
ib
(4.1)
Vce = 0
where ic is the small signal collector current and ib is the corresponding base current. As the
frequency of device operation increases, internal capacitances associated with the device cause
the current gain to degrade. The parameter fT can also be defined as the frequency at which small
signal current gain |βac| becomes unity. It is this definition that is made use of in the current
simulations to extract this fT parameter.
The Cutoff frequency is mathematically related inversely to the collector-emitter transit time,
τec, which is defined to be a composite of the following transit time components [1]
fT =
1
2πτ ec
= τ e + τ b + τ sc + τ c
(4.2)
where τe is the emitter charging time, τb is the base transit time, τsc is the base-collector depletion
region transit time and τc is the collector charging time. This high frequency circuit fT can be
visualized in terms of the device capacitances and resistances as shown in the equivalent circuit
seen in Figure 4.1.
105
Figure 4.1 Equivalent circuit for HBT giving rise to the transit time components [1].
The emitter-charging time τe is defined as the time required to change the base potential by
charging up capacitances through the differential emitter-base junction resistance [1]
τe =
ηk B T
qI C
(C je + C jc )
(4.3)
where Cje and Cjc denote the base-emitter and base- collector junction capacitances respectively, IC
is the DC collector current, η is the ideality factor for the collector current and kBT/q is the voltage
equivalent of temperature. Clearly, this transit time has an inverse dependence on the collector
current, which explains why transistors designed for high frequencies must be operated at high
collector currents. The capacitance Cjc and Cje scale directly with the emitter and collector junction
areas, respectively. As a result, smaller devices give a smaller τe and a higher fT.
The base transit time τb is defined as the time required to discharge the excess minority
carriers in the base through the collector current. Mathematically, it is given by [1]
2
τb =
XB
vDnB
(4.4)
106
where XB is the width of the neutral base region, DnB is the electron diffusion constant in the base
and ν is a dimensionless parameter ~ 2, whose exact value depends on the extent of electron drift
and diffusion in the base. This component is quite significant for p-n-p HBTs as the low minority
diffusion coefficient of holes results in a significant base transit time. For n-p-n HBTs, it can be
negligible when compared to other transit time components, except at the optimum DC bias point
where fT is a maximum and τb may be important.
The space charge transit time τsc is the time required for carriers to drift through the depletion
region of the base-collector junction. It is given by [1]
τ SC =
X dep
(4.5)
2υ sat
where Xdep is the depletion region thickness of the base-collector junction and υsat is the electron
saturation velocity at high electric fields. This component is a strong function of the base-collector
junction bias VCB since Xdep is proportional to the square root of VCB.
Finally, the collector charging time τc is defined as the time taken to charge the base-collector
junction capacitance. This depends on parasitic emitter and collector resistances and is given by [1]
τ c = ( RE + RC )C jc
(4.6)
where RE is the emitter series resistance and RC is the collector series resistance, both of which
include the metal-semiconductor contact resistances.
The Overall transit time is therefore given by [1]
τ ec =
ηκT
qI C
(C je + C jc ) +
X B2 X dep
+
+ ( RE + RC )C jc
vDn 2v sat
107
(4.7)
The impact of each of the above terms in influencing fT will be seen in more detail while discussing
the optimization procedure for each layer of the device’s epitaxial structure.
4.1.2 Unilateral Power Gain (U) and Maximum Frequency of Oscillation (fmax)
A transistor whose output is completely isolated from its input, is said to be unilateral and the
process by which a lossless feedback network is added to the transistor such that the overall twoport is unilateral is called unilateralization [1]. The unilateral power gain is defined as the power gain
after the transistor as well as the lossless network is made unilateral. In terms of the device’s yparameters, it is given by [1]
U=
y12 y 21
−
∆y ∆y
2
 y  y 
 y   y 
4 Re 22  Re 11  − Re 21  Re 12 
 ∆y   ∆y 
  ∆y   ∆y 
(4.8)
where ∆y is defined as
∆y = y11 y 22 − y12 y 21
(4.9)
Similar to the device’s current gain, the power gain degrades at high frequencies due to the
presence of capacitances within the transistor. The maximum frequency of oscillation fmax is the
frequency at which unilateral power gain of the transistor rolls off to unity. It is the frequency that
marks the boundary between an active and passive network. It depends upon the value of fT as [1]
f max =
fT
8πrbC jc
(4.10)
where rb is the base series resistance, Cjc is the collector junction capacitance and fT is the cutoff
frequency discussed earlier. However, due to the significant tradeoff between base resistance and
fT, the value of fmax doesn’t usually directly vary with fT and optimizing one of them doesn’t
108
necessarily maximize the other. If we incorporate second order effects, however, the value of fmax
can be written as [1]
f max
1
=
4π
 rbi c jci ( RBB + RB ( epi ) )C jc 


+
w
2
w
T
 Ti

−1 / 2
(4.11)
in which rbi is the a.c. base resistance, Cjci is the intrinsic collector junction capacitance, RBB & RB(epi)
are the extrinsic resistive components of the total base resistance, and, ωTi is the angular cutoff
frequency with Cjc replaced by Cjci. Fig. 4.2 provides an equivalent circuit for the HBT showing
these components.
Figure 4.2 HBT model showing distributed resistances and base-collector capacitances [1].
The frequencies fT and fmax for a particular device are not single numbers but functions of
various parameters. The most important parameter that affects both fT and fmax is the collector
current density JC. An example of the variation of these parameters with JC is presented in Figure
4.3 for an N-p-n AlGaAs/GaAs HBT.
109
Figure 4.3 fT and fmax variation with collector current density for a fixed base-collector
bias [1].
In the above figure, when JC is small the emitter charging time, τe and so τec starts decreasing
as JC increases as τe is inversely proportional to collector current (see (4.3)). Hence, from (4.7), fT
starts increasing as JC increases. Similarly, from (4.10), fmax also increases as it is dependent upon
fT. At higher values of collector current density, the depletion width on the collector side Xdep starts
increasing, which increases τbc. In addition, base pushout and other high current effects occur,
which more than compensates the decrease of τe. This increase in τc can be explained by the
following expressions for Xdep [1]
1/ 2
X dep =
J  
J 
2ε s (VCB + φCB ) 
1 − C  1 − C 
qN C
J2  
J1 

−1 / 2
(4.12)
where J1 and J2 are constants that depend upon the device structure and collector junction bias and
given by [1]
J 1 = qυ sat N C
(4.13)
110
J2 =
(VCB + φCB )
ρ C ( X C − X dep )
(4.14)
where φCB is the built-in potential for the base-collector junction, ρC is the resistivity of the
undepleted collector material, Xdep is the depletion width inside the collector and XC is the designed
collector thickness. As JC approaches a threshold such that JC/J1 approaches unity, the square root
term of (4.12) starts increasing rapidly. This causes Xdep to increase sharply. As stated earlier, this
increase more than compensates for the reduction in τe and hence fT decreases as JC increases. In
addition, base pushout can simultaneously begin causing XB and τB to increase contributing to
further degradation in fT. The fmax similarly goes through a maximum, though it may be delayed to a
higher JC. Therefore, both fT and fmax are crucially affected by DC collector current density chosen
for device operation.
4.2 Effect of Base Undercut on Device Performance
In this section, the effect of gradually etching away the region beneath the extrinsic base
region, which is the extrinsic emitter, is investigated for the collector-up HBT. The extrinsic emitter
region is that portion of the emitter that is not directly beneath the collector. The lateral etching there
is important because it reduces the emitter-base junction area and so the capacitance cjc which
impact τe, fT and so fmax. This is expected to lead to performance enhancement of the high
frequency parameters fT and fmax. Simulation results are presented to illustrate the extent of this
effect on the GaInP/GaAs HBT’s performance. Shown in Figure 4.4 below is the collector-up HBT
with the extent of the partial removal of the extrinsic emitter in the undercut of the base contact
shown. This lateral undercut can be achieved by selective etching and other fabrication techniques
[2].
111
Collector
Base
Lateral Undercut
Emitter
Figure 4.4 Simulated collector-up InGaP/GaAs HBT with partially etched extrinsic emitter
4.2.1 Theoretical Basis for Extrinsic Base Undercut
The effect of undercutting the extrinisic base is theoretically expected to augment the device
performance by reducing Cje. This idea was central to the concept of collector-up HBTs from the
inception of that concept itself [3]. It was initially suggested by Kroemer [3] that, if the portion of
emitter-base junction that is not immediately opposite to the collector-base junction is “inactivated”,
efficient charge collection as well as other advantages would entail. This concept is better illustrated
in Fig. 4.5 below by the reversing arrows at the outer edges of the emitter. The central idea here is
that electron injection across the emitter-base junction is limited to the central region beneath the
collector.
112
Figure 4.5 Original concept behind collector-up HBTs illustrating the importance of
having an “inactivated” extrinsic emitter region [3].
Theoretically, the following are considered to be advantages of having a collector-up HBT with
an inactivated or etched extrinsic emitter configuration [3]:
(1) Without removal of the extrinsic emitter, the region below the base contact, i.e. the extrinsic
base, leads to excessive recombination that kills the emitter injection efficiency. As a result,
only a fraction of the total electron current injected into the base from the emitter can now
reach the collector. This leads to very small values of current gain. Blocking electron
injection into the extrinsic base region, therefore, would substantially improve the current
gain.
(2) By making inactive (or etching away) the area underneath the extrinsic base, the emitterbase junction area and its capacitance Cje could be reduced significantly. This would
improve the cutoff frequency as this capacitance forms an important component of emitter
charging time τe (see (4.3)).
113
(3) By removing the extrinsic emitter, the emitter resistance may also be reduced, which would
lower the collector charging time τc (see (4.6)). This forms an important component of total
transit time, so, the frequency performance of the device could benefit from inactivation or
removal of the extrinsic emitter.
These advantages are illustrated by recent research findings showing significant performance
enhancement for the collector-up GaInP/GaAs HBT with undercut. For example, for a 120 nm base,
doped with carbon at 5X1019 cm-3, Girardot et al. [4] achieved a peak fmax value of 110 GHz. They
used low a boron dose ion implantation to “isolate” the extrinsic emitter and prevent parasitic
current injection into the base. Using the same concept of low dose boron ion implantation to
achieve inactivation of extrinsic emitter region, Henkel et al. [5] recently obtained 115 GHz for a
similar base width and doping of 6X1019 cm-3. Similarly, while investigating the performance of
collector-up Ge/GaAs HBTs, boron implantation of the extrinsic emitter was shown to be a crucial
factor in obtaining high performance 112-GHz fmax devices [6]. In addition, some collector undercut
techniques have also been investigated for emitter-up HBTs. In fact, experimental reports indicate
fmax can be improved to well over 200 GHz in InP/InGaAs SHBTs using a collector undercut [7].
4.2.2 Simulation Results for GaInP/GaAs Collector-up HBT with Extrinsic Base
Undercut
In this section, the simulation results of the collector-up HBT whose epi-structure is shown in
Table 3.9 are presented. Specifically, contact resistivities have been incorporated into the
simulations whose values for base layer is 5X10-7 Ω/cm2 and for emitter/collector layers is 5X10-8
Ω/cm2. The results are obtained for structures that have various degrees of undercut such as that
114
shown in Figure 4.4. For this purpose, a parameter called the percentage undercut is introduced.
This percentage undercut is defined as the percentage of etched emitter underneath the extrinsic
base to the total extrinsic emitter width under the extrinsic base. Hence, a 100% undercut would
correspond to a complete etch removal of the extrinsic emitter region underneath the extrinsic base.
In this case, the emitter region width would exactly equal the collector width.
A comparison of the DC characteristics of the extrinsic emitter unetched structure with those of
the 100% undercut structure is shown in Figures. 4.6 and 4.7. The significant improvement in
current gain is quite evident from these figures.
Figure 4.6 Gummel Poon Characteristics for the extrinsic emitter unetched collector-up
InGaP/GaAs HBT.
115
Figure 4.7 Gummel Poon Characteristics for the extrinsic emitter completely etched
collector-up InGaP/GaAs HBT.
The performance parameters are now presented as a function of base-emitter voltage for
various percentages of undercuts. This is done in order to emphasize the gradual improvement in
all aspects of the device performance due to the degree of undercut. Experimentally, the larger the
degree of undercut to be performed, the greater is the technical difficulty in achieving the same.
Figure 4.8 shows the impact of increasing undercut on the collector current density. Since the
collector current is a function of emitter injection efficiency, which is quite poor when the extrinsic
base region is present, a gradual increase of this parameter with increasing undercut is theoretically
anticipated and seen in the figure. At the highest bias, the increase is more than five-fold from 0%
to 100% undercut, so the effect of the emitter undercut is significant.
Figure 4.9 shows the impact of emitter undercut on the small signal AC current gain. Owing to
increased emitter efficiency due to undercut of the extrinsic base, this parameter increases
116
significantly with increased undercut. For no undercut, the current gain is only around 6 dB,
whereas for 100% undercut, the current gain is around 30 dB. This corresponds to an increase in
gain from ~ 2 to ~32, a factor of 16 increase. This results from an increase in the collector current
(as seen in Fig. 4.6), but is also likely due to a decrease in the base recombination current.
14
0 %
20 %
12
2
Collector Current Density (KA/cm )
40 %
60 %
10
80 %
100 %
8
6
4
2
0
1 .2
1 .3
1 .4
1 .5
1 .6
1 .7
B a s e - E m it te r V o l t a g e ( V )
Figure 4.8 Collector current density as a function of base-emitter voltage for various percentages of
base undercut for VCE=2 V.
3 5
0
Current Gain (dB)
3 0
2 5
%
2 0
%
4 0
%
6 0
%
8 0
%
1 0 0
%
2 0
1 5
1 0
5
1 .2
1 .3
1 .4
1 .5
B a s e - E m it te r V o lta g e
1 .6
1 .7
(V )
Figure 4.9 Current Gain as a function of base-emitter voltage for various percentages of base
undercut for VCE=2 V.
117
A brief comparison of the AC characteristics of the extrinsic emitter unetched and completely
etched cases is presented here with the help of Figures 4.10 and 4.11. It is clearly evident from
them that the small signal AC gain is increased manifold, from a meager value of ~6 dB when the
extrinsic emitter is unetched to around 30 dB when the extrinsic emitter is completely etched.
Figure 4.10 AC Characteristics for the unetched extrinsic emitter collector-up
InGaP/GaAs HBT.
118
Figure 4.11 AC Characteristics for the extrinsic emitter etched collector-up
InGaP/GaAs HBT.
Figure 4.12 shows the impact of undercut on the cutoff frequency, fT. It can be easily seen that
increasing undercut improves fT and for 100% undercut, the maximum cutoff frequency reaches a
high of around 144 GHz. This value is significantly higher than that obtained with no undercut (~109
GHz). The origin of this improvement is clear from the reduction in the emitter-base junction
capacitance Cje, and the corresponding decrease in τe and τec from (4.7). From Fig. 4.8, the
increased undercut also increases the collector current, which reduces the ratio Cjc/Ic in (4.7), which
further contributes to the decrease in τe and τec and the enhancement in fT seen in Fig. 4.12.
119
150
0%
20 %
40 %
80 %
100 %
100
T
Cutoff Frequency f (G Hz)
60 %
50
0
1.2
1.3
1.4
1.5
1.6
1.7
Base-Em itter Voltage (V)
Figure 4.12 fT as a function of base-emitter voltage for various percentages of base
Undercut for the GaInP/GaAs HBT for VCE=2 V.
The most significant impact of undercut is seen clearly in the values of fmax which show a
tremendous increase from ~75 GHz to close to 200 GHz, for the 100% etched configuration as
seen in Figure 4.13. For the GaInP/GaAs HBT, the increase in fmax with increased undercut is due in
part to the previously discussed increase in fT. However, (4.10) is an approximate relationship
between fT and fmax that does not explain all of the observed increase in fmax seen in Figure 4.13
since rb and Cjc seen in (4.10) are not modified by the degree of base undercut. For the Silvaco
120
software used here, fmax is not calculated from fT using (4.10). But rather, the power gain is
calculated as a function of frequency and the intercept at 0 dB is used to determine fmax.
200
M aximum Frequency of Oscillation f
m ax
(G Hz)
0%
20 %
40 %
60 %
150
80 %
100 %
100
50
0
1.2
1.3
1.4
1.5
1.6
1.7
Base-Emitter Voltage (V)
Figure 4.13 fmax as a function of base-emitter voltage for various percentages of base undercut for
VCE=2 V.
Similarly, the maximum unilateral power gain at a frequency of 2 GHz, also shows substantial
improvement with undercut as seen in Figure 4.14. As in the fT and fmax data, the improvement is
largest at a VBE ≈ 1.5 V where the device performance is at its best before high current effects
produce degradation.
121
55
M aximum Unilateral Power G ain (dB)
0 %
20 %
50
40 %
60 %
80 %
45
100 %
40
35
30
25
20
1 .2
1 .3
1 .4
1 .5
1 .6
1 .7
B a s e - E m it te r V o lta g e ( V )
Figure 4.14 UMAX at a frequency of 2 GHz as a function of base-emitter voltage for various
percentages of base undercut for VCE=2 V.
These results can also be summarized in a more comprehensible form by picking out the peak
parametric values and presenting their variation with the percentage undercut. Figures. 4.15-4.18
show the variations of peak collector current density, current gain, fT and fmax and Umax with
percentage undercut. The base emitter voltage at which these comparisons were made was 1.47 V.
In each case, it is clearly observed that the impact of undercut is to substantially improve the overall
device performance, both AC and DC characteristics, with the added advantage of not requiring any
trade-offs in other parametric values.
122
Collector Current Density (KA / cm
2
)
2
1 .5
1
0 .5
-2 0
0
20
40
60
80
100
120
P e rc e n t U n d e rc u t (% )
Figure 4.15 Collector current density as a function of undercut percentage for a fixed
VBE=1.47 V and VCE= 2 V.
35
Current Gain (dB)
30
25
20
15
10
5
-2 0
0
20
4 0
60
8 0
100
P e rc e n ta g e U n d e rc u t (% )
Figure 4.16 Current gain as a function of percentage undercut for a fixed
VBE=1.47 V and VCE= 2 V.
123
120
180
F t, G H z
Fm ax. G H z
160
(G Hz)
140
T
f ,f
m ax
120
100
80
60
-2 0
0
20
40
60
80
100
120
P e rc e n t U n d e rc u t (% )
Figure 4.17 fT, fmax as a function of percentage undercut for VBE=1.47 V and VCE=2 V.
38
36
34
30
U
m ax
(dB)
32
28
26
24
22
-2 0
0
20
40
60
80
100
120
P e rc e n t U n d e rc u t (% )
Figure 4.18 Umax at 2 GHz as a function of percentage undercut for VBE=1.47 V, VCE=2 V.
124
4.3
Optimization of the Collector-up HBT structure (SR)
It is imperative to investigate the effects of doping and layer thickness variations on device
performance to ensure high efficiency performance. An efficient device design is one that would
provide maximization of the key high frequency parameters, namely fT and fmax. Keeping this
perspective in mind, an optimization procedure has been carried out such that it jointly maximizes fT
and fmax. In the case of a tie, fmax is deemed a more practically useful parameter to optimize than fT.
The other parameters, small signal current gain and unilateral power gain, are not specifically
optimized as more interest has been placed on the high frequency performance of the etched
collector up HBT rather than its high power performance.
4.3.1 Optimization of the Base layer
Optimization of the base layer involves the most conspicuous compromise between maximizing
fT or fmax. fT depends on base transit time while fmax depends critically on base resistance as seen in
(4.7). The base transit time (τb) is not a strong function of the base doping and is proportional to the
square of base thickness and inversely proportional to the minority carrier diffusion constant. In
fact, fT increases initially very slowly with increasing doping due to the dependence of the minority
diffusion constant electrons on the base doping as follows [8]
DnB




KT
NB

83001 +
≈
q
 3.98 X 1015 + N B 


641 

−1 / 3
(4.15)
Fig. 4.19 shows the effects of base doping on fT. The peak fT increases and shifts to higher VBE
bias with increased base doping up to 1X1019 cm-3. This is due largely to an increase in τb due to a
reduced DnB as seen in (4.7). However, for NB ≈1X1019 cm-3, fT decreases.
125
Further simulations show that fmax increases with increasing base doping as the increased
doping significantly lowers base resistance rb as seen from (4.10). In addition, the peak shifts to a
higher VBE. This could imply that increasing base doping to the maximum solubility limits of the
material (GaAs) would yield maximum values of fmax and fT. However, current simulations show that
there is an optimum value of base doping beyond which fT decreases significantly. This optimum
value is ~ 3X1019 cm-3. The following figures (Fig. 4.20) depicts the effects of increased base doping
on fmax.
Nb=7e18
Nb=1e19
Nb=2e19
Nb=3e19
Nb=4e19
Nb=7e19
Nb=1e20
cm-3
cm-3
cm-3
cm-3
cm-3
cm-3
cm-3
100
T
Cutoff Frequency f (G Hz)
150
50
0
1.2
1.3
1.4
1.5
1.6
1.7
Base-Emitter Voltage (V)
Figure 4.19 fT versus base-emitter voltage for various base doping levels for VCE=2 V.
126
300
N b = 7 e 1 8 c m -3
N b = 1 e 1 9 c m -3
250
N b = 2 e 1 9 c m -3
N b = 3 e 1 9 c m -3
N b = 4 e 1 9 c m -3
N b = 7 e 1 9 c m -3
N b = 1 e 2 0 c m -3
150
f
m ax
(G Hz)
200
100
50
0
1 .2
1 .3
1 .4
1 .5
1 .6
1 .7
B a s e - E m it t e r V o l t a g e ( V )
Figure 4.20 fmax vs base-emitter voltage for various base doping levels for VCE=2 V.
The same epi-structure (Table 3.9) based collector-up HBT is now investigated for the impact
of base width on high frequency parameter values. For fixing base width, there is less discrepancy
with theory about the nature of its behavior. It has been predicted theoretically that the effect of
reducing base width would be detrimental to fmax while augmenting fT [8]. For fT, the base transit
time τb ∝ XB2, so τb and τec increase with increasing XB so that fT decreases. For fmax, because of the
direct dependence of fmax on the reciprocal of base resistance (rb), which decreases with increasing
base thickness, fmax is expected to decrease with increasing XB according to (4.10). Hence a
suitable tradeoff between fmax and fT is solicited. However, as specified in the beginning of this
section, the key aim of the optimization procedure was to achieve sufficiently high values of both
fmax and fT. Hence, as presented in the results below (Figs. 4.21 and 4.22), a base width of 30 nm
was considered most suitable as it could yield peak values of 146 GHz at an IC of 1.2 mA and 206
GHz at an IC of 2.5 mA.
127
Figure 4.21 shows the observed improvement in fT with decreasing base width as the base
transit time is reduced. The improvement in peak fT is approximately a factor of 2 for XB reduced
from 60 nm to 10 nm. However, each small base widths may pose significant fabrication problems.
Figure 4.22 shows the observed behavior for fmax as the base width is varied. Its peak value rises
and then falls as XB is decreased from 60 nm to 10 nm. Initially, the improvement in fT seen in Fig.
4.21 causes fmax to rise as XB decreases. However, as XB decreases further, the increase in the
base resistance rb dominates and the peak fmax decreases from (4.10).
200
W b=10 nm
W b=20 nm
W b= 30nm
W b=40 nm
W b=50 nm
W b=60 nm
100
T
f (GHz)
150
50
0
1 .2
1 .3
1 .4
1 .5
1 .6
1 .7
B a s e - E m itte r V o lta g e ( V )
Figure 4.21 fT vs base-emitter voltage as a function of the base width for VCE=2 V.
128
250
M aximum Frequency of O scillation f
m ax
(G Hz)
Wb=10
Wb=20
Wb=30
Wb=40
Wb=50
Wb=60
200
nm
nm
nm
nm
nm
nm
150
100
50
0
1.2
1.3
1.4
1.5
1.6
1.7
Base-Emitter Voltage (V)
Figure 4.22 fmax vs base-emitter voltage as a function of the base width for VCE=2 V.
4.3.2 Optimization of the Emitter layer
The impact of etching the emitter region beneath the base has been previously discussed in
the last section. The main impact of the emitter thickness along the direction of current flow, on the
other hand, is quite minimal on both fT and fmax. The following plot (Fig. 4.23) shows the impact of
total emitter resistance, which increases with emitter thickness, on fT and fmax from the results
reported by Liu [8] for AlGaAs/GaAs HBTs.
129
Figure 4.23 Variation of fT, fmax and emitter charging time (τe) as a function of total emitter
resistance RE[8].
For the InGaP/GaAs HBTs under study, assuming similar bias conditions, fT and fmax show very
little decrease with increasing emitter thickness and resistance. This shows that small signal
performance of the device is nearly unaffected by changing emitter resistance, however,
experimental results indicate that substantial degradation of large signal performance can occur [8].
A high emitter resistance is known to degrade large signal performance while small signal
performance is hardly affected. But since the scope of this work is confined to investigating the
small signal behavior of this device, it hasn’t been considered an important factor in optimization
and a typical value of emitter thickness (XE=0.25 µm) from published papers has been chosen.
A more significant factor in determining device’s performance is emitter doping. The emitter
doping affects fT by its impact on the emitter junction capacitance and emitter charging time where
the emitter charging time is given by [8]
130
τe =
kT
qJ C  2ε
s

qN
 E
εs
JC


kT
 φ BE − 1.23 ln(
)
−17  
q
2.69 X 10


1/ 2
(4.16)
From this expression it is clear that emitter charging time directly depends on the square root of
emitter doping. However, at lower doping values, the high current effects become prominent. Fig
4.24 shows that an optimum value of fT could be obtained at higher values of doping, provided
current density is sufficiently high to ensure smaller values of τe.
Figure 4.24 Emitter charging time (τe) as a function of collector current density (Jc) for
various emitter doping values for an AlGaAs/GaAs HBT [8].
Hence, in this study the emitter design is done such that the transistor operates at a higher
current density. The doping value chosen is highly dependent on the nature of the application. fmax,
on the other hand, depends on emitter doping only through its dependence on fT as seen in (4.10).
Hence, once fT is optimized with a given emitter layer design, fmax is automatically optimized. The
current simulations show that the most suitable value of emitter doping is 5X1017 cm-3. At this
optimized value, the maximum values of fT and fmax are both maximized. As previously stated in
chapter 3, this particular emitter doping has been previously assumed in that simulation. Figures
131
4.25 and 4.26 show the simulations carried out during optimization process for fT and fmax,
respectively.
150
(GHz)
100
Cutoff Frequency
N e = 3 e 1 7 c m -3
N e = 5 e 1 7 c m -3
N e = 7 e 1 7 c m -3
50
0
1 .2
1 .3
1 .4
1 .5
1 .6
1 .7
B a s e - E m it te r V o lta g e ( V )
Figure 4.25 fT vs base-emitter voltage for various emitter doping levels for VCE=2 V.
250
Maximum Frequency of Oscillation
(GHz)
N e = 3 e 1 7 c m -3
N e = 5 e 1 7 c m -3
N e = 7 e 1 7 c m -3
200
150
100
50
0
1 .2
1 .3
1 .4
1 .5
1 .6
1 .7
B a s e - E m it t e r V o l t a g e ( V )
Figure 4.26 fmax vs base-emitter voltage for various emitter doping levels for VCE=2V.
132
4.3.3 Optimization of the Collector Layer
Optimization of the collector involves optimization of not only the layer thickness and doping but
also, the collector-emitter voltage. An increase in VCE results in an increase of the base-collector
depletion width (Xdep) that the collector charging (τc), which in turn reduces the collector junction
capacitance Cjc [8]. This would lead to the emitter-collector transit time to be limited by the collector
charging time (τc), which becomes the most important component of total emitter-collector transit
time (τec) at lower VCE values. As VCE increases, the space charge component (τsc) becomes more
prominent as the collector depletion width (Xdep) increases. This produces an increase that not only
compensates for the decrease in collector current charging time (τc) but also increases the total
transit time by manifold leading to gradual decrease in Cutoff frequency (fT). However, the value of
fmax continuously increases with increase in VCE as it is independent of Xdep and monotonously
increases until Xdep equals the collector thickness Xc. Therefore an optimum value of VCE depends
on not compromising the cutoff frequency if it is intended to achieve substantial values of both fT
and fmax. Therefore, the value of VCE has been chosen to be 2 V, a typical value, based on the
above considerations.
Optimization of the collector thickness is comparatively difficult when compared with the emitter
layer design. As is seen from the expression for the emitter to collector delay time given in (4.7), the
space charge transit time (τsc) and collector charging time (τc) are directly influenced by the space
charge width of the collector since the collector capacitance is given by Cjc=Acεs/Xdep assuming the
collector layer is completely depleted. But they have opposite dependencies on the Xdep. Therefore,
a minimization of their sum ,i.e.,
τ sc + τ c =
X dep
2v sat
+ ( RE + RC ).
AC ε s
X dep
133
(4.17)
is needed rather than minimizing each one of them individually. Subsequently, we show both
graphically and experimentally that lowering collector thickness would augment cutoff frequency
(fT), i.e., the space charge transit time would prove decisive in deciding the optimum value.
However, increasing the transit frequency at the expense of lowering collector thickness is not a
suitable option for various RF and high power applications. That is because a smaller value of Xdep
and Xc, collector thickness, would lead to very low values of breakdown voltage, typically less than
2 V for collector thicknesses of a few tens of nanometers. Since it is intended to obtain overall
optimization of the device, a moderate value of Xc is chosen without particular emphasis on
maximizing fT at the expense of breakdown voltage. Thus, Xc is selected as 0.4 µm on the basis of
simulation results shown below for three collector widths : 0.2 µm, 0.3 µm and 0.4 µm in Figures
4.27 and 4.28. These figures provide adequate reason for the choice of the collector thickness as
0.4 µm that would yield fT and fMAX values of 145 GHz at 1.2 mA and 227 GHz at 3.2 mA.
160
W c = 0 .2 m ic r o n
W c = 0 .3 m ic r o n
Cutoff Frequency (GHz)
140
W c = 0 .4 m ic r o n
120
100
80
60
40
20
0
1 .2
1 .3
1 .4
1 .5
1 .6
1 .7
B a s e - E m it te r V o l ta g e ( V )
Figure 4.27 fT vs base-emitter voltage for several collector widths for VCE=2 V.
134
25 0
Maximum Frequency of Oscillation (GHz)
W c = 0 .2 m ic r o n
W c = 0 .3 m ic r o n
20 0
W c = 0 .4 m ic r o n
15 0
10 0
5 0
0
1 .2
1 .3
1 .4
1 .5
1 .6
1 .7
B a s e - E m it te r V o lta g e ( V )
Figure 4.28 fmax vs base-emitter voltage for several collector widths for VCE=2V.
Another important collector design concern is Kirk Effect [8]. This is the effect associated with
base pushout, which can be defined as a gradual increase in effective base width at high collector
densities due to electric field reversal at the base-collector junction, that causes holes to be spilled
over into the collector. It is highly detrimental to the device’s current gain and fT and frequently
accounts for the fall off in these parameters as VBE and IC are raised to high values. In order to
delay the onset of Kirk effects, the collector doping can be increased to a larger value. This would
cause effective electron concentration due to the collector current flow to be smaller than the
ionized dopant concentration until higher collector current densities tend to make depletion width
equal to collector thickness. However, in order to maximize fmax it is essential to have lower collector
doping since the collector junction capacitance Cjc is directly proportional to the square root of
collector doping concentration. Hence, an optimum value of collector doping must be chosen that
doesn’t compromise on fmax without allowing Kirk Effects to degrade the device performance at
lower collector current densities. Figures 4.29 and 4.30 depict the collector doping impact on cutoff
frequency and the maximum frequency of oscillation, respectively. As expected from (4.7), the peak
135
fT decreases as the collector doping increases due to Cjc and fmax decreases according to (4.10)
since fT decreases and Cjc increases. In conclusion, the collector doping level is set to as low a
value as possible consistent with breakdown voltage requirements.
250
N c = 7 e 1 6 c m -3
N c = 9 e 1 6 c m -3
N c = 1 e 1 7 c m -3
Cutoff Frequency (GHz)
200
N c = 2 e 1 7 c m -3
N c = 3 e 1 7 c m -3
150
100
50
0
1 .2
1 .3
1 .4
1 .5
1 .6
1 .7
B a s e -E m itte r V o lta g e (V )
Figure 4.29. fT vs base-emitter voltage for various collector doping levels for VCE=2 V.
M aximum Frequency of Oscillation f
m ax
(GHz)
2 5 0
2 0 0
N c = 7 e 1 6
c m -3
N c = 9 e 1 6
c m -3
N c = 1 e 1 7
c m -3
N c = 2 e 1 7
c m -3
N c = 3 e 1 7
c m -3
1 5 0
1 0 0
5 0
0
1 .2
1 .3
1 .4
1 .5
B a s e - E m it te r V o lta g e
1 .6
1 .7
(V )
Figure 4.30 fmax vs base-emitter voltage for various collector doping levels for VCE=2 V.
136
It can be inferred from the above figures, that for a mode of optimization consistent with the
procedure for obtaining suitable fT and fmax values that have been jointly optimized, it is quite logical
to chose Nc as 9X1016 cm-3 or 1X1017 cm-3. The corresponding high frequency parameters for these
two final optimized structures are presented below. From these values, it appears that the goal of
joint optimization of fT and fmax is efficiently met by the Nc=9X1016 cm-3 owing to slightly better values
of the more practically useful parameters, fmax and Umax, and a very small difference in the other two
parameters. Therefore, the final optimized value of collector doping is taken to be 9X1016 cm-3.
Table 4.1 Peak parametric values for the final optimized structures.
Peak parameter values
Nc=9e16 cm-3
Nc=1e17 cm-3
fT(IC), GHz
139 (0.8 mA)
145 (1.2 mA)
fMAX(IC), GHz
233 (2.5 mA)
227 (3.2 mA)
CG(IC), dB
53 (2.5 mA)
53 (2.6 mA)
UMAX(IC), dB
59 (3.2 mA)
56 (3.3 mA)
4.3.4 Optimization of the Sub-collector Layer
Optimization of the Sub-collector layer is discussed in this section. The Sub-collector region
design involves the sole purpose of minimizing the epitaxial resistance it imposes in the cutoff
frequency expression seen in (4.7). It can be minimized by doping the layer to its solubility limit.
Further, from experimental studies, the sheet resistance and parasitic series resistance are known
to decrease with increasing thickness. However, this steady increase of doping cannot be done
indefinitely, as practical concerns make it quite important to isolate the sub-collector. Hence, a
practically typical value of 0.2 µm was taken at 4X1019 cm-3 for an InGaAs sub-collector.
137
4.4
Final Optimized Structure
The final, optimized structure of the extrinsic emitter etched (100% extrinsic base undercut)
InGaP/GaAs collector up HBT is presented in this section. The optimized thickness values of all the
layers along with their corresponding doping concentrations are incorporated into this structure. A
TONYPLOT layout of this structure is shown in Figure 4.31. The Gummel-Poon characteristics and
frequency response of this final structure are presented in Figures 4.32 and 4.33, respectively, for a
base-emitter bias voltage of 1.61 V.
Figure 4.31 Simulated InGaP/GaAs fully optimized collector-up HBT structure with 100% extrinsic
base undercut.
138
Table 4.2 Final Optimized Epitaxial Structure for GaInP/GaAs Collector-up HBT
Material
Function
Doping (cm-3)
Thickness (µm)
InGaAs
Sub collector
n+- 4e19
0.2
GaAs
Collector
n- 9e16
0.4
GaAs
Base
p- 3e19
0.03
InGaP
Emitter
n- 5e17
0.25
GaAs
Sub emitter
n+- 5e18
0.2
Figure 4.32 Gummel-Poon characteristics of fully optimized InGaP/GaAs collector-up HBT
structure.
139
Figure 4.33 AC response of the fully optimized InGaP/GaAs collector-up HBT structure.
The final results of this optimized structure can be tabulated as under:
Table 4.3 Final Simulation Results for the optimized GaInP/GaAs collector-up HBT.
Peak parameters
Parametric values
fT (IC), GHz
139 (0.8 mA)
fMAX (IC), GHz
233 (2.5 mA)
CG (IC), dB
53 (2.5 mA)
UMAX (IC), dB
59 (3.2 mA)
BV, Volts
~5.5 V (estimated)
140
4.5
Typical Collector up Structure
In this section, a novel collector-up structure is investigated for high frequency performance. A
practically realizable nine-layered structure, which is actually an off-shoot of the tunneling collector
HBT structure proposed by Mochizuki et al. [8], is investigated in this section. The simulations are
run with similar models as used in the previous structure to facilitate meaningful comparison of
results with the previously optimized structure (SR).
4.5.1 Structure with 9 Layers (SR1)
This GaInP/GaAs HBT structure is an offshoot of the structure conceived by Mochizuki et al.
[8], which was designed for minimizing the offset voltage VCE,sat and the knee voltage Vk. The base
width was, however, reduced to a reasonably optimum value of 50 nm rather than the 70 nm
structure used by Mochizuki et al. [8]. This was done to make the high frequency performance
results obtained from these simulations more meaningful for comparison with the optimized
collector-up structure (SR). The structure investigated here, named SR1 for convenience, is
presented in the following table:
Table 4.4 Epitaxial structure of GaInP/GaAs HBT identified as SR1.
Material
Function
Thickness (µm)
Doping (cm-3)
InGaAs
Collector Cap –1
0.1
n+-2e19
InGaAs
Collector Cap –2
0.1
n+-2e19
GaAs
Collector Cap –3
0.05
n-5e18
GaAs
Collector
0.3
n-3e16
GaAs
Spacer
0.03
n-5e17
GaAs
Base
0.05
p-3e19
InGaP
Emitter
0.25
n-5e17
InGaP
Sub-emitter
0.04
n+-3e19
GaAs
Substrate
0.3
n+-5e18
141
The structure is shown as a TONYPLOT presentation in Fig. 4.34. The DC and High frequency
characteristics are shown in subsequent Figs. 4.35 and 4.36. It is evident that the high frequency
characteristics are highly distorted at very low frequencies. However, they do serve the purpose of
enabling the extraction of fT, fmax at higher frequencies.
Figure 4.34 Simulated collector-up structure of SR1.
142
Figure 4.35 Gummel Poon characteristics of SR1.
Figure 4.36 AC response of SR1. Note the distortion at lower frequencies.
143
Parameters extracted from these plots are presented in Figs. 4.37-4.40 as a function of
collector current density. Current gain as a function of collector current density doesn’t improve
much with the inclusion of a spacer layer at the base-collector junction that is moderately doped,
which could prevent a spilling of holes into the collector and increase electron injection efficiency
into the collector. Figs. 4.37 and 4.38 present a graphical comparison between the current gains of
the structures conceived by Mochizuki et al. [8] and the one used in this simulation (SR). The graph
compared to the doped-spacer structure in Fig. 4.37 compares favorably with the current gain graph
simulated in Fig. 4.38 establishing the accuracy of the results. A peak value of about 35 dB at a
collector current density of about 5 KA/cm2 is observed in the plot shown in Mochizuki et al. [8],
while a peak value of 32 dB at around 4 KA/cm2 is obtained from the simulation results for SR1.
Figure 4.37 Current gain vs collector current density for the collector-up structure designed by
Mochizuki et al. [8].
144
35
Current Gain (dB)
30
25
20
15
10
5
0
0
5
10
15
20
C o lle c to r C u r r e n t D e n s ity ( K A /c m
25
2
)
Figure 4.38 Current gain vs collector current density for SR1.
The most important high frequency parameters, fT and fmax, are shown as a function of collector
current density in Fig 4.39. Both values are decently high, considering the fact that base has been
doped only at 3X1019 cm-3 and is 50 nm thick. fmax is slightly lower than that of SR because of
smaller collector depletion width owing to the presence of a moderately spacer region. This would
slightly increase the junction capacitance, thereby lowering the value of fmax. The high values of fT,
on the other hand, could be explained by the lowered values of lead resistances, owing to collector
caps being doped to the solubility limits of respective materials and also being slightly thicker (0.25
µm), which significantly lowers the collector charging time (τc). The peak fT and fmax values were in
the upper 170 GHz range at a collector current density of a few KA/cm2. A comparison of these
parameters with those corresponding to the structure designed by Mochizuki et al. [8] wasn’t
possible as these parameters were not extracted by his team.
145
180
Cutoff Frequency (GHz)
160
140
120
100
80
C u to ff F r e q u e n c y (G H z )
M a x im u m F r e q u e n c y o f O s c illa t io n ( G H z )
60
0 .1
1
10
100
C o lle c to r C u r r e n t D e n s ity ( K A /c m
2
)
Figure 4.39 fT, fmax vs collector current density for SR1.
Fig. 4.40 shows that the Maximum unilateral power gain also shows some decent performance.
As anticipated, the values of Umax roll off at higher current densities. Prominent reasons for higher
values of Umax would be the lightly doped and substantially thick collector and lower base resistance
due to a larger base thickness (50 nm) than our previous optimized structure (SR).
M aximum Unilateral Pow er Gain (dB)
5 1
5 0
4 9
4 8
4 7
4 6
1 0
-5
0 .0 0 0 1
0 .0 0 1
0 .0 1
0 .1
C o lle c t o r C u r r e n t D e n s ity
1
( K A /c m
Figure 4.40 Umax vs collector current density for SR1.
146
1 0
2
)
1 0 0
4.5.2 Performance Comparison
In this section the two device structures described in this chapter are compared for high
frequency performance. Table 4.5 shows the high frequency parameters at their respective collector
current bias points. From this table, it is evident that the first structure has significantly better values
of fmax, current gain and Umax. The characteristics of SR1 was slightly distorted and need further
optimization to improve its high frequency performance. Some significant factors contributing to
such results include the smaller base width of the optimized structure (SR) and also the thicker
collector thickness. The transit frequency has an inverse dependence on base width as well as
collector thickness. The maximum frequency of oscillation, on the other hand, directly depends on
the collector width and increases steadily with increasing width. Since the optimized structure (SR)
has a much thicker collector and smaller base width, it is expected to have a moderately high value
of fT while the smaller collector width and moderate value of base thickness yields a comparatively
higher value of this parameter for SR1. For fmax, however, the larger collector thickness
dramatically increases the value for SR when compared to SR1.
Table 4.5 Comparison of small signal AC characteristics of the two collector-up structures (SR) and
(SR1).
Parameter
SR
SR1
fT (IC)
139 (0.8 mA)
177 (2.0 mA)
fmax (IC)
233 (2.5 mA)
179(3.8 mA)
CG (IC)
53 (2.5 mA)
32 (2.0 mA)
UMAX (IC)
59 (3.2 mA)
49 (2.0 mA)
147
4.6
Conclusions
In this chapter, the DC and high frequency characteristics of two typical InGaP/GaAs collector
up HBTs were discussed. The impact of undercutting the extrinsic base region on device
performance and the subsequent improvements were verified by simulation results from ATLAS.
Subsequently, the undercut structure was optimized by vary the emitter, base and collector doping
levels and thicknesses. The results for the optimized structure were compared for high frequency
performance with a typical collector-up structure similar to the one reported by Mochizuki et al. [8].
Our results suggest that the device’s performance can be further enhanced over reported device
performances by carefully optimizing the device’s epitaxial layer design.
148
REFERENCES
[1] Liu, W., “Small Signal Properties”, Handbook of III-V Heterojunction Bipolar Transistors, John
Wiley & Sons Inc., New York, pp.632-760, 1998.
[2] Massengale, A.R., Larson, M.C., Dai, C., Harris, J.S., Jr., “Collector-up AlGaAs/GaAs HBTs
using oxidized AlAs”, Device Research Conference Digest, 54th Annual , pp. 36 –37, 1996 .
[3] Kroemer, H. “Heterostructure Bipolar Transistors and Integrated Circuits”, Proc. Of the IEEE, vol.
70, no. 1, pp. 13 –25, Jan. 1982.
[4] Girardot, A., Henkel, A., Delage, S.L., diForte-Poisson, M.A., Chartier, E., Floriot, D., Cassette,
S. and Rolland, P.A., “High Performance Collector-up InGaP/GaAs Heterojunction Bipolar
Transistor with Schottky Contact”, IEEE Electron. Lett., vol. 35, no. 8, pp. 670-672, Apr. 1999.
[5] Henkel, A., Delage, S.L., diForte-Poisson, M.A., Chartier, E., Blanck, H. and Hartnagel, H.L.,
“Collector-up InGaP/GaAs Double Heterojunction Bipolar Transistors with High fmax”, IEEE Electron.
Lett., vol. 33, no. 7, pp. 634-636, Mar. 1997.
[6] Kawanaka, M., Iguchi, N. and Sone, J., “112-GHz Collector-up Ge/GaAs Heterojunction Bipolar
Transistors with Low Turn-on Voltage”, IEEE Trans. Electron. Dev., vol. 43, no. 5, pp. 670-675,
May. 1996.
[7] Lee, K., Yu, D., Chung, M., Kang, J. and Kim, B., “New Collector Undercut Technique Using a
SiN Sidewall for Low Base Contact Resistance in InP/InGaAs SHBTs”, IEEE Trans. Electron. Dev.,
vol. 49, no. 6, pp. 1079-1082, Jun. 2002.
149
[8] Liu, W., “Epitaxial Layer Design”, Handbook of III-V Heterojunction Bipolar Transistors, John
Wiley & Sons Inc., New York, pp.761-817, 1998.
[9] Mochizuki, K., Welty, R.J., Asbeck, P.M., Lutz, C.R., Welser, R.E., Whitney, S.J. and Pan, N.,
“GaInP/GaAs Collector-up Tunneling Collector Heterojunction Bipolar Transistors (C-up TC- HBTs):
Optimization of Fabrication Process and Epitaxial Layer Structure for High-Efficiency High-Power
Amplifiers”, IEEE Trans. Electron. Dev., vol. 47, no. 12, pp. 2277-2283, Dec. 2000.
150
5. Conclusions and Future Work
5.1 Conclusions
In this work, the primary focus of investigation was the impact of removal of the extrinsic emitter
by etching on the high frequency device performance of collector-up InGaP/GaAs HBTs. This was
accomplished by characterizing each high frequency parameter as a function of percentage of
undercut under the base. Each of the performance parameters were studied as a function of the DC
bias from the onset of the active region to the edge of the saturation region for various degrees of
base undercut. The maximum frequency of operation fmax was found to be more significantly
impacted by the degree of undercut than the other high frequency parameters.
To ensure the validity of the simulations, material parameter verification was given utmost
importance. Most of the simulation parameters were obtained from references provided in a review
article by Goldberg [1]. For mobility modeling, Caughey-Thomas mobility models for electrons in
InGaP and for electrons and holes in GaAs were derived on the basis of experimental studies by
Masselink et al. [2], Shitara et al. [3] , Quigley et al. [4], Rode [5] and Wiley [6].
An emitter-up InGaP/GaAs HBT structure designed by Oka et al. [7] was simulated initially with
the material parameters and mobility models extracted as described above. The simulation results
closely conformed to the published results, validating the usage of those models and material
parameters in collector-up structure simulations.
For the collector-up InGaP/GaAs HBT simulation, a conventional 5 layered structure consisting
of a sub-collector, collector, base, emitter and sub-emitter was chosen and the simulations were
carried out for the case where the extrinsic emitter, which is the region underneath the extrinsic
151
base, was not removed. As expected, the results were quite poor and a maximum current gain of 6
dB was obtained. The fT and fMAX values were of the order of 109 GHz and 76 GHz, which are far
less than what a superior heterojunction like GaInP/GaAs could yield.
Subsequently, the improvement in high frequency and DC performance of the same structure
as a function of the percentage of extrinsic emitter undercut was investigated. For successive
stages of undercut, the improvement is consistent, gradual and quite significant. For the case where
the extrinsic emitter was completely etched resulting in an emitter size equal to the collector’s, the
current Gain (β), maximum unilateral power gain (Umax), cutoff frequency (fT) and maximum
frequency of operation (fmax) were found to be 30 dB, 38 dB, 140 GHz and 160 GHz, respectively.
This indicates a clear improvement over the unetched extrinsic emitter case, inspite of the fact that
the device’s epitaxial structure was not yet optimized for maximizing high frequency and DC
performance.
The device’s epitaxial structure was then optimized for enhancing both fT and fmax by optimizing
each layer’s doping and thickness. The improvement in all the high frequency and DC parameters
was evaluated after optimizing each layer. The theoretical basis for this procedure was obtained
from Liu [8]. The epitaxial structure of the final optimized structure (named SR for convenience)
and the simulation results are tabulated in Tables 5.1 and 5.2, respectively.
152
Table 5.1 Final Optimized Structure of the Collector-up InGaP/GaAs HBT.
Material
Function
Doping (cm-3)
Thickness (µm)
InGaAs
Sub collector
n+- 4X1019
0.2
GaAs
Collector
n- 9X1016
0.4
GaAs
Base
p- 3X1019
0.03
InGaP
Emitter
n- 5X1017
0.25
GaAs
Sub emitter
n+- 5X1018
0.2
Table 5.2 Simulation Results for Optimized InGaP/GaAs Collector-up HBT.
Peak parameters
Parametric values
fT (IC), GHz
139 (0.8 mA)
fMAX (IC), GHz
233 (2.5 mA)
Current Gain (IC), dB
53 (2.5 mA)
UMAX (IC), dB
59 (3.2 mA)
Breakdown Voltage, V
~5.5 (estimated)
Finally, a novel collector-up InGaP/GaAs HBT structure (SR1), based on a published structure
by Mochizuki et al. [9] was investigated. The results were compared with the optimized structure
(SR) discussed previously. The following tabulation (Table 5.3) depicts a comparison of these
results. It was found that the optimized structure, SR, provided better frequency and current gain
values than the nine-layered collector-up HBT (SR1). The performance of SR1 was modest, and an
efficiently optimized structure of the same can match SR in many crucial parameters. The primary
reason for the superior performance of the SR structure was its smaller base width (30 nm) as
compared with the 50 nm base width of SR1 structure.
153
Table 5.3 Comparison of Simulation Results for the Two Investigated Structures.
Parameter
SR
SR1
fT (IC)
139 (0.8 mA)
177 (2.0 mA)
fMAX (IC)
233 (2.5 mA)
179 (3.8 mA)
CG (IC)
53 (2.5 mA)
32 (2.0 mA)
UMAX (IC)
59 (3.2 mA)
49 (2.0 mA)
5.2 Future Work
In this section, we discuss work that could be done to extend the current thesis as well as the
direction of research in this field. At first, we present future work that could be done to improve
upon the progress made in this thesis. In this work, the DC and high frequency simulations carried
out for three collector-up HBT structures have been presented and analyzed. The simulations could
be made more practicable by incorporating device self-heating effects. It would also be useful to
have additional features in the modeling software that facilitate the inclusion of different varieties of
dopants like Sn, C, etc. The processing power of the workstations could also be upgraded to
facilitate faster 3-D simulations that allow a more holistic visualization and generate more accurate
results. Finally, it is desirable to fabricate the optimized collector-up HBT (SR) to assess its practical
performance for comparison.
As regards the future of collector-up GaInP/GaAs HBTs, as such, the concept of having a
collector-up configuration is still in its infancy, though research that is being done in a handful of
laboratories across the world has shown promising results. To facilitate this device’s development,
154
the incentives for working with this configuration must be made more recognized. These include
high speed of operation, high breakdown voltage and low power dissipation. Only an application
specific research aimed at maximizing these qualities can succeed in commercializing this toplogy.
155
REFERENCES
[1] Goldberg, Yu. A., “Gallium Indium Phosphide (GaxIn1-xP),” in Handbook Series on
Semiconductor Parameters, vol. 2, Ternary and Quaternary A3B5 Semiconductors, M. Levinshtein,
S. Rumyantsev and M. Shur, ed., 2nd ed., Singapore: World Scientific, pp. 37-59, 1996.
[2] Masselink, W.T., Zachau, M., Hickmott, T.W. and Hendrickson, K., “Electronic and Optical
Characterization of InGaP grown by Gas-Source Molecular-beam Epitaxy,” J. Vac. Sci. Technol. B,
vol. 10, no. 2, pp. 966-968, Mar/Apr. 1992.
[3] Shitara, T. and Eberl, K., “Electronic Properties of InGaP Grown by Solid-source MBE with a
GaP Decomposition Source,” Appl. Phys. Lett., vol. 65, no. 3, pp. 356-361, 1994.
[4] Quigley, J.H., Hafich, M.J., Lee, H.Y., Stave, R.E. and Robinson, G.Y., “Growth of InGaP on
GaAs using Gas-source Molecular-beam Epitaxy,” J. Vac. Sci. Technol. B, vol. 7, no. 2, pp. 358360, Mar/Apr. 1989.
[5] Rode, D.L., “Low-Field Electron Transport,” Semiconductors and Semimetals, Willardson, R.K.
and Beer, A.C., eds., Academic Press, New York, vol. 10, 1975, p.1.
[6] Wiley, J.D., “Mobility of Holes in III-V Compounds,” Semiconductors and Semimetals,
Willardson, R.K. and Beer, A.C., eds., Academic Press, New York, vol. 10, 1975, p.91.
[7] Oka, T., Hirata, K., Suzuki, H., Ouchi, K., Uchiyama, H., Taniguchi, T., Mochizuki, K.,
Nakamura, T, “High-speed small-scale InGaP/GaAs HBT technology and its application to
156
integrated circuits”, IEEE Transactions on Electron Devices, Vol. 48, no. 11, Nov. 2001, pp.
2625 –2630.
[8] Liu, W., Handbook of III-V Heterojunction Bipolar Transistors, John Wiley & Sons, Inc., New
York, 1998.
[9] Mochizuki, K., Welty, R.J., Asbeck, P.M., Lutz, C.R., Welser, R.E., Whitney, S.J. and Pan, N.,
“GaInP/GaAs Collector-up Tunneling Collector Heterojunction Bipolar Transistors (C-up TC- HBTs):
Optimization of Fabrication Process and Epitaxial Layer Structure for High-Efficiency High-Power
Amplifiers”, IEEE Trans. Electron. Dev., vol. 47, no. 12, pp. 2277-2283, Dec. 2000.
157
APPENDIX A
In this appendix, the derivation of Caughey-Thomas doping dependent mobility parameters for
GaInP is elaborated. The ATLAS version of the Caughey Thomas model is given by [1]
µ n 0 = MU 1N .CAUG.(
TL ALPHAN .CAUG
+
)
300 K
T
TL BETAN .CAUG
− MU 1N .CAUG.( L ) ALPHAN .CAUG
)
300 K
300 K
TL GAMMAN .CAUG
N
DELTAN .CAUG
1+ (
)
.(
)
NCRITN .CAUG
300 K
MU 2 N .CAUG.(
µ p 0 = MU 1P.CAUG.(
TL ALPHAP.CAUG
+
)
300 K
T
TL BETAP.CAUG
− MU 1P.CAUG.( L ) ALPHAP .CAUG
)
300 K
300 K
TL GAMMAP .CAUG
N
DELTAP .CAUG
1+ (
)
.(
)
300 K
NCRITP.CAUG
MU 2 P.CAUG.(
(A-1)
(A-2)
For GaInP, the mobility model for electrons is alone considered as no experimental data on the
determination of hole mobility is available in literature. Further, the use of GaInP solely in the
emitter region of most devices precludes the necessity of having hole mobility modeled in
accordance with (A-2). Therefore, an inbuilt model is used for hole Mobility values.
The parameters that need to be determined for the electron mobility model of (A-1) are:
MU1N.CAUG, MU2N.CAUG, NCRITN.CAUG and DELTAN.CAUG. The other parameters like
ALPHAN.CAUG, BETAN.CAUG and GAMMAN.CAUG are trivial as simulations are run at room
temperature that causes the TL/300 factor to become unity.
158
The experimental values are initially compiled from various sources including Masselink et al.
[2], Quigley et al. [3] and Shitara et al. [4] by reading off values from the published results. The
composite mobility model now contains a set of disparate values of mobility for each doping
concentration. To extract the Caughey-Thomas mobility parameters from this composite set of data,
the following procedure is used.
The experimental data is initially grouped in such a fashion that it forms a monotonously
decreasing set of mobility values with increasing doping concentration. This eliminates certain
values that do not conform to the Caughey-Thomas mobility model. Also, the ambiguity of having
multiple values for the same doping concentration is also minimized. From this select chunk of data,
the minimum and maximum values are tentatively assigned to the MU1N.CAUG and MU2N.CAUG
parameters respectively. This is justified, as these parameters correspond to minimum and
maximum mobility values. These values are 300 cm2/V-s and 2000 cm2/V-s respectively.
The Caughey-Thomas expression is presented here once again for the sake of convenience in
nomenclature [5]
µ ( N ) = µ min +
( µ max − µ min )
 N
1 + 
 NC



α
(A-3)
It is now required to derive the critical doping concentration (NC) and exponential parameter (α).
Now, two experimental mobility values are randomly chosen and substituted for µ(N) in the above
expression at two doping concentration values (N). The two randomly chosen values are:
159
µ(N=3.5X1015 cm-3)=1570 cm2/V-s and µ(N=7.2X1015 cm-3)=1428 cm2/V-s. Substituting the values
of µ(N), N, µmin and µmax, we obtain two equations in NC and α, which are given as follows:
1570 = 300 +
⇒ 1270 =
( 2000 − 300)
 3.5 X 1015 

1 + 
 NC 
α
1700
 3.5 X 1015 

1 + 
 NC 
(A-4)
(A-5)
α
α
 3.5 X 1015 
43
 =
⇒ 
127
 NC 
(A-6)
Similarly for the second set of mobility and doping values:
1428 = 300 +
⇒ 1128 =
( 2000 − 300)
 7.2 X 1015 

1 + 
 NC

α
1700
 7.2 X 1015 

1 + 
 NC

(A-7)
(A-8)
α
α
 7.2 X 1015 
 = 0.507
⇒ 
 NC

(A-9)
160
Solving (A-6) and (A-9) simultaneously, we obtain the values of NC and α as 2.25X1016 cm-3
and 0.59 respectively. These parameters correspond to NCRITN.CAUG and DELTAN.CAUG
discussed earlier.
161
REFERENCES
[1] ATLAS User Manual, Vol. 1, Silvaco International, Santa Clara, CA, Feb’2000.
[2] Masselink, W.T., Zachau, M., Hickmott, T.W. and Hendrickson, K., “Electronic and Optical
Characterization of InGaP grown by Gas-Source Molecular-beam Epitaxy,” J. Vac. Sci. Technol. B,
vol. 10, no. 2, pp. 966-968, Mar/Apr. 1992.
[3] Quigley, J.H., Hafich, M.J., Lee, H.Y., Stave, R.E. and Robinson, G.Y., “Growth of InGaP on
GaAs using Gas-source Molecular-beam Epitaxy,” J. Vac. Sci. Technol. B, vol. 7, no. 2, pp. 358360, Mar/Apr. 1989.
[4] Shitara, T. and Eberl, K., “Electronic Properties of InGaP Grown by Solid-source MBE with a
GaP Decomposition Source,” Appl. Phys. Lett., vol. 65, no. 3, pp. 356-361, 1994.
[5] Caughey, D.M. and Thomas, R.E., “Carrier Mobilities in Silicon Empirically Related to Doping
and Field”, Proc. IEEE, vol. 55, pp. 2192-2193, 1967.
162
APPENDIX B
In this appendix, the derivation of Caughey-Thomas doping dependent mobility parameters for
GaAs is elaborated. As stated in the previous appendix, the ATLAS version of the Caughey
Thomas model is given by [1]
µ n 0 = MU 1N .CAUG.(
TL ALPHAN .CAUG
+
)
300 K
T
TL BETAN .CAUG
− MU 1N .CAUG.( L ) ALPHAN .CAUG
)
300 K
300 K
TL GAMMAN .CAUG
N
1+ (
)
.(
) DELTAN .CAUG
NCRITN .CAUG
300 K
MU 2 N .CAUG.(
µ p 0 = MU 1P.CAUG.(
TL ALPHAP.CAUG
)
+
300 K
T
TL BETAP.CAUG
)
− MU 1P.CAUG.( L ) ALPHAP .CAUG
300 K
300 K
T
N
1 + ( L ) GAMMAP .CAUG .(
) DELTAP.CAUG
300 K
NCRITP.CAUG
MU 2 P.CAUG.(
(B-1)
(B-2)
For GaAs, mobility models for both electrons and holes are abundantly provided in literature
facilitating the derivation of both the mobility models.
The parameters that need to be determined for the electron mobility model of (B-1) are:
MU1N.CAUG, MU2N.CAUG, NCRITN.CAUG and DELTAN.CAUG. The other parameters like
ALPHAN.CAUG, BETAN.CAUG and GAMMAN.CAUG are trivial as simulations are run at room
temperature which causes the TL/300 factor to become unity.
163
The experimental values are initially compiled from various sources including Levinshtein and
Rumyanstev [2] and Rode et al. [3], by reading off values from the published results. The composite
mobility model now contains a set of disparate values of mobility for each doping concentration. To
extract the Caughey-Thomas mobility parameters from this composite set of data, the following
procedure is used.
The procedure is similar to the one described previously for GaInP. The experimental data is
initially grouped in such a fashion that it forms a monotonously decreasing set of mobility values
with increasing doping concentration. This eliminates certain values that do not conform to the
Caughey-Thomas mobility model. Also, the ambiguity of having multiple values for the same doping
concentration is also minimized. The minimum and maximum values are tentatively assigned to the
MU1N.CAUG and MU2N.CAUG parameters respectively. These values are 0 and 7200 cm2/V-s
respectively. They’ve been documented in many literature findings including Levinstein and
Rumyanstev [2].
The Caughey-Thomas expression is presented here once again for the sake of convenience in
nomenclature [4]
µ ( N ) = µ min +
( µ max − µ min )
 N
1 + 
 NC



α
(B-3)
It is now required to derive the critical doping concentration (NC) and exponential parameter (α).
Now, two experimental mobility values are randomly chosen and substituted for µ(N) in the above
expression at two doping concentration values (N). The two randomly chosen values are:
164
µ(N=9.0X1017 cm-3)=2880.316 cm2/V-s and µ(N=9.0X1019 cm-3)=989.6942 cm2/V-s. Substituting the
values of µ(N), N, µmin and µmax, we obtain two equations in NC and α, which are given as follows:
2880.316 = 0 +
⇒ 2880.316 =
(7200 − 0)
 9.0 X 1017 

1 + 
 NC

α
7200
 9.0 X 1017 

1 + 
 NC

(B-4)
(B-5)
α
α
 9.0 X 1017 
 = 1.4997
⇒ 
 NC

(B-6)
Similarly for the second set of mobility and doping values:
989.6942 = 0 +
⇒ 989.6942 =
(7200 − 0)
 9.0 X 1019 

1 + 
 NC

7200
 9.0 X 1019 

1 + 
 NC

α
α
(B-7)
(B-8)
α
 9.0 X 1019 
 = 7.2749
⇒ 
 NC

(B-9)
165
Solving (B-6) and (B-9) simultaneously, we obtain the values of NC and α as 2.443X1017 cm-3
and 0.3108 respectively. These parameters correspond to NCRITN.CAUG and DELTAN.CAUG
discussed earlier. After obtaining these values, a plot is obtained for various doping concentrations
and its conformation to the experimental values can be used as a validation for the extracted
values.
The Values of hole mobility parameters are obtained in a similar fashion. That is, the values of
NCRITP.CAUG and DELTAP.CAUG. The values of MU1P.CAUG and MU2P.CAUG are chosen as
0 and 380 cm2/V-s respectively. The two random values chosen for forming simultaneous equations
are: µ(N=9X1017 cm-3)=154.36 cm2/V-s and µ(N=9X1019 cm-3)=45.75 cm2/V-s. Substituting these
values in (B-3):
154.36 =
380
 9 X 1017 

1 + 
 NC 
(B-10)
α
α
 9 X 1017 

 = 1.4617
 NC 
(B-11)
Similarly for the second set of values:
45.75 =
380
 9 X 1019 

1 + 
 NC 
(B-12)
α
α
 9 X 1019 
 = 7.306

N
C


(B-13)
166
Solving (B-11) and (B-13) simultaneously, we obtain the values of Nc and α as 3.0363X1017 cm-3
and 0.3494 respectively.
167
REFERENCES
[1] ATLAS User Manual, Vol. 1, Silvaco International, Santa Clara, CA, Feb’ 2000.
[2] Levinshtein, M.E. and Rumyantsev, S.L., “Gallium Arsenide (GaAs),” in Handbook Series on
Semiconductor Parameters, vol. 1, Si, Ge, C (Diamond), GaAs, GaP, GaSb, InAs, InP, InSb,
Levinshtein, M., Rumyantsev, S. and Shur, M., ed., 2nd ed., World Scientific, Singapore, pp. 77-103,
1996.
[3] Rode, D.L., “Low-Field Electron Transport,” Semiconductors and Semimetals, Willardson, R.K.
and Beer, A.C., eds., Academic Press, New York, vol. 10, 1975, p.1.
[4] Caughey, D.M. and Thomas, R.E., “Carrier Mobilities in Silicon Empirically Related to Doping
and Field”, Proc. IEEE, vol. 55, pp. 2192-2193, 1967.
168
APPENDIX C
In this appendix, a sample code used for simulating the collector-up structure and obtaining its
DC and high frequency response. The extrinsic emitter portion of the collector-up HBT is completely
etched. The mesh definition is done very carefully as elaborated in section 3.1. Important material
and mobility parameters of InGaP and GaAs were obtained as described in chapter 2. The input file
set up has been planned to generate fewer bias steps to avoid convergence problems. The
parameter extraction was done manually by reading off values from TONYPLOT simulations. The
code is given as follows:
go atlas
title GaInP/GaAs HBT simulation with DD model
#
#
# SILVACO International 1993, 1994
#
# SECTION 1: Mesh Specification
#
mesh space.mult=1.0
#
x.mesh loc=0.0 spac=0.05
x.mesh loc=0.5 spac=0.05
x.mesh loc=1.0 spac=0.05
x.mesh loc=1.5 spac=0.05
#
#
#
y.mesh loc=0 spac=0.02
y.mesh loc=0.2 spac=0.02
y.mesh loc=0.5 spac=0.01
y.mesh loc=0.55 spac=0.02
y.mesh loc=0.8 spac=0.05
y.mesh loc=1.0 spac=0.05
#
#
#
# SECTION 2: Structure Definition
#
region num=1 material=air x.min=0.0 x.max=1.5 y.min=0.0 y.max=1.0
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region num=2 material=InGaAs x.min=0.0 x.max=0.5 y.min=0.0 y.max=0.2 x.comp=0.47
region num=3 material=GaAs x.min=0.0 x.max=0.5 y.min=0.2 y.max=0.5
region num=4 material=GaAs x.min=0.0 x.max=1.0 y.min=0.5 y.max=0.55
region num=5 material=InGaP x.min=0.0 x.max=0.5 y.min=0.55 y.max=0.8 x.comp=0.5
region num=6 material=GaAs x.min=0.0 x.max=1.5 y.min=0.8 y.max=1.0
#
#
elec num=1 name=collector x.min=0.0 x.max=0.5 y.min=-0.02 y.max=0.0
elec num=2 name=base x.min=0.6 x.max=1.0 y.min=0.48 y.max=0.5
elec num=3 name=emitter x.min=1.1 x.max=1.5 y.min=0.78 y.max=0.8
#
CONTACT NAME=emitter CON.RESIST=5E-8
CONTACT NAME=base CON.RESIST=5E-7
CONTACT NAME=collector CON.RESIST=5E-8
#
#
#
doping uniform region=2 n.type conc=4.0e19
doping uniform region=3 n.type conc=1.0e17
doping uniform region=4 p.type conc=3.0e19
doping uniform region=5 n.type conc=5.0e17
doping uniform region=6 n.type conc=4.0e19
#
#
#
# SECTION 3: Set models and define material parameters
#
material material=InGaP eg300=1.849 nc300=6.5e17 nv300=1.45e19 affinity=4.1
material material=GaAs affinity=4.07 eg300=1.424 nc300=9.2e17 nv300=1.286e19
#
# Recombination parameters
#
material region=3 taun0=5.0e-9 taup0=3.0e-6 vsatn=2.0e7 vsatp=1.8e7
material region=4 taun0=5.0e-9 taup0=3.0e-6 vsatn=2.0e7 vsatp=1.8e7
material region=5 taun0=9.0e-11 taup0=9.0e-11 vsatn=1.0e7 vsatp=1.0e7
material region=6 taun0=5.0e-9 taup0=3.0e-6 vsatn=2.0e7 vsatp=1.8e7
#
# Mobility models
#
mobility material=InGaP analytic.n mu1n.caug=300 mu2n.caug=2000 ncritn.caug=2.25e16
deltan.caug=0.59
mobility material=GaAs analytic.n mu1n.caug=0 mu2n.caug=7200 ncritn.caug=2.443e17
deltan.caug=0.3108
mobility material=GaAs analytic.p mu1p.caug=0 mu2p.caug=380 ncritp.caug=3.0363e17
deltap.caug=0.3494
models srh analytic fldmob evsatmod=1 temperature=300 fermidirac print
#
#
170
#
# SECTION 4: Initial Solution
#
output con.band val.band
solve init
#
# Calculate Gummel plot and AC parameters versus Vbe (Vce) at 1 # MHz
solve prev
solve local v1=0.01 ac freq=1e6 direct
solve v1=0.025 vstep=0.025 nstep=2 electr=1
solve v1=0.1 vstep=0.1 nstep=19 electr=1
#
#
#
# SECTION 5: Input Voltage specification and frequency analysis
#
# 3 - emitter 2 - base 1 - collector
log outf=sslash_bas100UC_GasSESMC_24_1.log
#
solve v2=0.01 ac freq=10 direct
solve v2=0.025 vstep=0.025 electr=2 nstep=2 ac freq=1e6 direct
solve v2=0.1 vstep=0.1 electr=2 nstep=5 ac freq=1e6 direct
solve v2=0.65 vstep=0.05 electr=2 nstep=6 ac freq=1e6 direct
solve v2=0.975 vstep=0.025 electr=2 nstep=3 ac freq=1e6 direct
solve v2=1.05 vstep=0.02 electr=2 nstep=3 ac freq=1e6 direct
solve v2=1.14 vstep=0.025 electr=2 nstep=4 ac freq=1e6 direct
solve v2=1.24 vstep=0.025 electr=2 nstep=4 ac freq=1e6 direct
solve v2=1.34 vstep=0.025 electr=2 nstep=2 ac freq=1e6 direct
solve v2=1.39 vstep=0.02 electr=2 nstep=6 ac freq=1e6 direct
solve v2=1.51 vstep=0.02 electr=2 nstep=4 ac freq=1e6 direct
#
save outf=sslash_bas100UC_GasSESMC_24_2.str
tonyplot sslash_bas100UC_GasSESMC_24_2.str
#
# Frequency domain AC analysis up to 100 GHz
#
log outf=sslash_bas100UC_GasSESMC_24_3.log s.param gains inport=base outport=emitter
width=50
#
load inf=sslash_bas100UC_GasSESMC_24_2.str master.in
#
solve previous ac freq=1 direct
solve ac freq=10 fstep=10 mult.f nfstep=8 direct
solve ac freq=2e9 direct
solve ac freq=5e9 direct
solve ac freq=1e10 direct
solve ac freq=2e10 fstep=2e10 nfstep=4 direct
solve ac freq=1e11 fstep=1e11 nfstep=5 direct
#
#
#
171
# SECTION 5: Output Extraction
#
# Gummel Plot
tonyplot sslash_bas100UC_GasSESMC_24_1.log -set hbtex06_1_log.set
#
# AC current gain versus frequency
tonyplot sslash_bas100UC_GasSESMC_24_3.log -set hbtex06_4_log.set
#
quit
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