ADVANCED TUNNELING DIODES FOR HIGH-FREQUENCY

ADVANCED TUNNELING DIODES FOR

HIGH-FREQUENCY APPLICATIONS AND

WIRELESS COMMUNICATION SYSTEMS

A thesis submitted to The University of Manchester for

the degree of

Doctor of Philosophy

In the Faculty of Science and Engineering

2022

AHMED KHALID A ALQURASHI

SUPERVISOR: MOHAMED MISSOUS

Department of Electrical and Electronic Engineering

 
 
1 
 
TABLE OF CONTENTS 
TABLE OF CONTENTS ................................................................................... 1 
LIST OF TABLES .............................................................................................. 5 
LIST OF FIGURES ............................................................................................ 6 
LIST OF SYMBOLS AND ABBREVIATIONS ......................................... 12 
ABSTRACT ...................................................................................................... 14 
DECLARATION .............................................................................................. 17 
COPYRIGHT STATEMENT ......................................................................... 17 
ACKNOWLEDGEMENT .............................................................................. 19 
DEDICATION ................................................................................................. 21 
PUBLICATIONS ............................................................................................. 22 
CHAPTER 1: INTRODUCTION .................................................................. 23 
1.1.  Overview of Terahertz Radiation Sources .......................................................... 23 
1.2.  mmWave and Terahertz Imaging Applications ................................................ 26 
1.3.  RTDs in 5G Wireless Communications systems ................................................ 26 
1.4.  Thesis Aims and Objectives .................................................................................. 27 
1.5.  Thesis Outline ......................................................................................................... 29 
CHAPTER 2: FUNDAMENTALS AND BACKGROUND OF 
RESONANT TUNNELLING DIODES (RTDs) ........................................ 31 
2.1.  Introduction ............................................................................................................ 31 
2.2.  Theory of Quantum Tunnelling ........................................................................... 31 
2.3.  Tunnelling Diodes .................................................................................................. 33 

 
 

 
4.  Double-Barrier Quantum-Well Resonant Tunnelling Diodes (DBQW RTDs)

4.1.  Epi-layers structures of DBQW RTD ....................................................................... 40 
4.2.  The operational principle of DBQW RTD ............................................................... 42 
4.3.  DC and RF characteristics of DBQW RTD .............................................................. 44 
5.  Effects of layer thickness on the performance of DBQW RTD ........................ 51 
5.1. Barrier thickness ............................................................................................................... 51 
5.2. Well thickness ................................................................................................................... 52 
5.3. Spacer thickness ............................................................................................................... 54 
6.  State of the art in InGaAs/AlAs RTDs ................................................................. 55 
7.  Summary ................................................................................................................. 56 
CHAPTER 3: PHYSICAL MODELLING OF ASYMMETRICAL 
SPACERS RESONANT TUNNELLING DIODES (RTDs) .................... 58 
1.  Introduction ............................................................................................................ 58 
2.  State of the art in Asymmetrical spacers RTDs .................................................. 58 
3.  Physical modelling of asymmetrical spacers RTDs Tunnelling Diodes by 
SILVACO ATLAS tool ...................................................................................................... 62 
3.1.  SILVACO ATLAS ....................................................................................................... 62 
3.2.  Model Validation........................................................................................................ 73 
4.  Asymmetrical spacers RTDs with a fixed quantum-well thickness ............... 76 
4.1.  DC characteristics ....................................................................................................... 76 
4.2.  RF Characteristics ....................................................................................................... 83 
5.  Asymmetrical spacers RTDs with varying quantum-well thickness ............. 89 
5.1.  DC characteristics ....................................................................................................... 91 
5.2.  RF Characteristics ....................................................................................................... 94 

 
 

 
6.  Asymmetrical spacers RTDs with deep and thin quantum-wells .................. 99 
7.  Summary ............................................................................................................... 108 
CHAPTER 4: DESIGN AND ANALYSIS OF 10 GHz RTD BASED 
AMPLIFIER FOR WIRELESS COMMUNICATIONS .......................... 110 
1.  Introduction .......................................................................................................... 110 
2.  Power amplifications using the resonant tunnelling diodes (RTDs) ............ 110 
3.  Principle operation of reflection-based RTD amplifier ................................... 111 
4.  Advanced Design System (ADS) software tool ............................................... 113 
5.  Modelling of Single branch coupler .................................................................. 116 
6.  Simulation of RTD amplifier .............................................................................. 121 
6.1.  Extraction of the RRTD and CRTD............................................................................... 121 
6.2.  Schematic circuit of the RTD amplifier ................................................................. 125 
6.3.  Modelling of circuit passive components ............................................................. 127 
6.4.  Layout design of RTD amplifier ............................................................................ 137 
7.  Summary ............................................................................................................... 139 
CHAPTER 5: DEVELOPMENT OF RTD OSCILLATORS FOR HIGH-
FREQUENCY APPLICATIONS ................................................................. 141 
1.  Introduction .......................................................................................................... 141 
2.  Conditions for the Design of RTDs Oscillators ................................................ 142 
3.  Oscillator Circuit's DC Stability ......................................................................... 144 
4.  Modelling of 100 GHz RTD oscillator ............................................................... 145 
5.  Modelling of passive components for the 100 GHz RTD oscillator .............. 156 
6.  Summary ............................................................................................................... 162 
CHAPTER 6: CONCLUSION AND FUTURE WORKS ........................ 163 

 
 
4 
 
6.1.  Conclusion ............................................................................................................. 163 
6.2.  Future works ......................................................................................................... 166 
APPENDICES ................................................................................................ 169 
A.  DC SIMULATION SCRIPTS FOR RESONANT TUNNELING DIODES 
(RTDs) ............................................................................................................................... 169 
i.  NEGF CODE ..................................................................................................................... 169 
ii.  SIS CODE .......................................................................................................................... 174 
B.  SUPPLEMENTARY FIGURES FOR SECTION 3.6 .......................................... 180 
REFERENCES ................................................................................................ 182 
 
   

 
 
5 
 
LIST OF TABLES 
Table 2.1. The lattice  constant, energy  bandgap,  and  the electron effective  mass of 
commonly used III-V compound semiconductors for RTDs at 300 K [45, 65-67]. ...... 40 
Table 3.1. The epi-layers and material parameters of the XMBE#300 sample [68]. ..... 75 
Table 3.2.The DC characteristics of the measured and modelled RTDs ....................... 76 
Table  3.3.  The  epi-layers  and  material  parameters  of  the  proposed  asymmetrical 
spacers RTDs with varying the thicknesses of the emitter spacer and the quantum well
.................................................................................................................................................. 90 
Table  3.4.  The  epi-layers  and  material  parameters  of  the  modified  asymmetrical 
spacers  RTDs  with  varying  the  thicknesses  of  the  emitter  spacer  and  Indium 
composition (x) in the quantum well ............................................................................... 101 
Table 4.1. Values of LC elements in the LC single branch coupler .............................. 120 
Table 4.2.Values of LC elements in the schematic RTD amplifier circuit ................... 126 
Table 4.3. The width and length of the MIM capacitors used in this work ................ 131 
Table 4.4. The parasitics inductances and capacitance of the MIM capacitors used in 
this work ............................................................................................................................... 133 
Table 4.5. The Equivalent  circuit’s components of the spiral inductors used in this 
work ...................................................................................................................................... 135 
Table 4.6. Comparison of RTD based amplifier and other device technologies ........ 139 
Table 5.1.The epi-layers and material parameters of the XMBE#300 sample ............ 146 
Table 5.2.The DC characteristics of the RTD sample XMBE#300 with a mesa area of 4 
μm
2
 at room temperature ................................................................................................... 147 
 
 
 
   

 
 
6 
 
LIST OF FIGURES 
Figure 1.1.  Comparison between several RTDs in terms of their output power [17, 19, 
21, 27, 28] ................................................................................................................................ 25 
Figure 1.2. The proposed steps of the thesis ..................................................................... 28 
Figure 2.1. The wave function of an electron tunnelling through a single barrier [46].
.................................................................................................................................................. 32 
Figure 2.2. The cross-section and the operation of the Esaki’ tunnel diode [51] ......... 34 
Figure 2.3. The I-V characteristics of a typical tunnel diode [51] ................................... 37 
Figure 2.4. The epi-layers and the current density of several RTDs with symmetrical 
spacers [68] ............................................................................................................................. 41 
Figure 2.5. The epi-layers of RTD with asymmetrical spacers [29] ............................... 41 
Figure 2.6. Typical energy band diagram of a DBQW RTD and the corresponding IV 
characteristics (where EC is the conduction band offset, EF is the Fermi level, and E1 
and E2 are the first and the second quantised energy levels inside the quantum-well) 
adapted from [57] .................................................................................................................. 43 
Figure  2.7.  The  IV  characteristics  with  clear  NDR  from  an  RTD  fabricated  at  the 
University of Manchester (sample XMBE#327) [68]. ....................................................... 45 
Figure 2.8. Schematic drawing for top and side views for the transmission line model 
(TLM) structure used in this work. .................................................................................... 46 
Figure 2.9. Cross-section of an RTD illustrating the epi-layers and contacts on a semi-
insulating InP substrate, as well as the lengths and depths used in equation 2.8. ...... 47 
Figure 2.10. Schematic of quantum-well with finite barrier height structure. (where E 
is the incident electron energy, EC is the conduction band, E1 and E2 are the first and 
second quantisation energies respectively, V0 is the barrier height, tw and tb are the 
quantum-well thickness and the barrier thickness respectively [57]. ........................... 53 
Figure 2.11. The band-diagram of RTD with the presence of the spacer layers on both 
sides of the barriers [54]. ...................................................................................................... 55 
Figure 3.1. The structure of the asymmetrical spacer RTD proposed by [88]. ............. 59 

 
 
7 
 
Figure  3.2.  The  oscillation  frequency  versus  the  spacer  thickness  with  the  I-V 
characteristics of asymmetrical spacers RTDs [88]. ......................................................... 59 
Figure 3.3. The structure of asymmetrical spacers RTDs reported and studied in [93]
.................................................................................................................................................. 61 
Figure 3.4. SILVACO ATLAS inputs and outputs [94]. .................................................. 63 
Figure 3.5. The electron effective mass, Dielectric constant, and the Energy bandgap at 
300K as a function of the composition fraction (x) ........................................................... 67 
Figure 3.6. In0.53Ga0.47As/AlAs conduction band diagram profile at zero bias. ............ 69 
Figure  3.7.  The  conduction  band  of  the  RTD  sample  XMBE#300  at  peak  voltage 
(0.177V). .................................................................................................................................. 74 
Figure 3.8. The Physical modelling results of the RTD sample XMBE#300 ................. 74 
Figure 3.9. Effect of Emitter and Collector spacers on the peak voltage ...................... 78 
Figure 3.10. The voltage span as the thickness of the collector and emitter spacers 
varies ....................................................................................................................................... 78 
Figure 3.11. Effect of Emitter and Collector spacers on the peak current ..................... 79 
Figure 3.12. Effect of Emitter and Collector spacers on the peak-to-valley current ratio
.................................................................................................................................................. 80 
Figure 3.13. The NDC as the thickness of the collector and emitter spacers vary ....... 81 
Figure 3.14. The effect of varying the thickness of emitter and collector spacers on the 
Maximum DC Output Power .............................................................................................. 82 
Figure  3.15.  Extraction  of  the  thickness  of  the  collector  depletion  region  from  the 
simulation results at peak voltage (0.177V). ..................................................................... 83 
Figure 3.16. The RTD transit time for RTDs with different thicknesses of emitter and 
collector spacers. ................................................................................................................... 84 
Figure 3.17. The effect of the emitter and collector spacers’ thicknesses on the RTD 
capacitance ............................................................................................................................. 85 
Figure  3.18.  The  effect  of  the  emitter  and  collector  spacers’  thicknesses  on  the 
maximum operating frequency .......................................................................................... 86 

 
 
8 
 
Figure  3.19.  The  intrinsic  limit  frequency  as  the  emitter  and  collector  spacers’ 
thicknesses vary .................................................................................................................... 87 
Figure 3.20. The actual output power as a function of the frequency for three different 
RTD structures ....................................................................................................................... 88 
Figure 3.21. The peak voltage (VP) of 1X2μm
2
 asymmetrical spacers RTDs with varying 
the thickness of the emitter spacer and the quantum well ............................................. 91 
Figure  3.22.  The  peak  current  (IP)  as  the  thickness  of  the  emitter  spacer  and  the 
quantum well vary ................................................................................................................ 92 
Figure 3.23. Effect of varying the thickness of the Emitter spacer and the quantum well 
on the peak-to-valley current ratio ..................................................................................... 92 
Figure 3.24. The effect of varying the thickness of the emitter spacer and quantum well 
on the NDC with 1X2μm
2 
RTD mesa area. ........................................................................ 93 
Figure 3.25. The effect of varying the thickness of the emitter spacer and quantum well 
on the Maximum DC Output Power with 1X2μm
2 
RTD mesa area. ............................. 94 
Figure 3.26. The change in the RTD transit time as the thickness of the emitter spacer 
and the quantum well change ............................................................................................. 95 
Figure 3.27. The effect of thinning the quantum well and thickening the emitter spacer 
on the RTD capacitance ........................................................................................................ 95 
Figure 3.28. The effect of varying the thickness of the quantum well and the emitter 
spacer on the maximum operating frequency .................................................................. 96 
Figure 3.29. The effect of thinning the quantum well and thickening the emitter spacer 
on the intrinsic frequency limit ........................................................................................... 97 
Figure 3.30. The actual output power as a function of the frequency for thin quantum 
well RTDs with very thick emitter spacers and 1X2μm
2
 RTD mesa area ..................... 98 
Figure 3.31. The epi-layer structure and the band diagram of the asymmetrical spacers 
RTD with deep and thin quantum well reported in [108]. ........................................... 100 
Figure 3.32. The effect of increasing the Indium composition in the quantum well on 
the peak voltage of RTDs with various quantum well thicknesses ............................. 102 

 
 
9 
 
Figure 3.33.  The  peak  current  of asymmetrical  spacers  RTDs as  the  quantum  well 
thickness and the Indium composition vary ................................................................... 102 
Figure 3.34. The change in the RTD transit time as the thickness of the quantum well 
and the Indium composition change ............................................................................... 104 
Figure 3.35. The RTD capacitance of asymmetrical spacers RTDs as the quantum well 
thickness and the Indium composition vary ................................................................... 105 
Figure 3.36. The effect of varying the thickness of the quantum well and the Indium 
composition on the maximum operating frequency ..................................................... 106 
Figure 3.37. The calculated actual RF power of RTDs with different quantum well 
thicknesses and different Indium compositions............................................................. 107 
Figure 4.1. Schematic circuit of the RTD reflection-based amplifier model ............... 112 
Figure 4.2. The model of a single branch coupler with ideal transmission lines ....... 117 
Figure 4.3. The result of S-parameter simulation for single branch coupler modelled in 
ADS using ideal transmission lines at 10 GHz ............................................................... 117 
Figure 4.4. The LC model of single branch coupler operating at 10 GHz using ADS 
software ................................................................................................................................ 118 
Figure 4.5. The result of S-parameter simulation for single branch coupler modelled in 
ADS using LC components at 10 GHz ............................................................................. 119 
Figure 4.6. The equivalent circuit of the intrinsic RTD .................................................. 122 
Figure  4.7.  Measured  and  fitted  forward  I-V  characteristics  as  well  as  extracted 
junction resistance of the RTD XMBE#300 with a 16μm
2
 mesa size ............................ 123 
Figure 4.8. Extraction of the RTD capacitance from the measured S-parameters ..... 123 
Figure 4.9. Left and right sides: measured S11 for intrinsic device sample #300 with a 
mesa area of 4×4μm2 biased in the NDR region plotted in smith chart and x-y graph, 
respectively. ......................................................................................................................... 124 
Figure 4.10. The result of S-parameter simulation for single branch coupler modelled 
in ADS using LC components with a resistance of 100Ω and a capacitance of 100fF at 
10 GHz .................................................................................................................................. 125 

 
 
10 
 
Figure 4.11. The schematic circuit of the reflection-based amplifier built-in ADS shows 
two RTDs with an LC branch coupler ............................................................................. 126 
Figure 4.12. The gain and return loss of the RTD amplifier schematic circuit using RTD 
sample XMBE#300 with a mesa area of 4X4 μm
2 
over the X-band .............................. 127 
Figure 4.13. The schematic of the MIM capacitor: (a) a top view and (b) a cross-section 
view ....................................................................................................................................... 129 
Figure 4.14. The equivalent circuit model of the MIM capacitor [125]. ...................... 130 
Figure 4.15.EM simulation (red lines) and Equivalent circuit (blue dots) S-parameters 
response of 80fF, 243fF, and 261fF MIM capacitors in the frequency range of 0.1-40GHz 
plotted on a Smith chart along with the layout of the MIM capacitors depicted in ADS-
schematic .............................................................................................................................. 132 
Figure 4.16. Spiral inductor cross-section and equivalent circuit model including both 
primary and parasitic components................................................................................... 135 
Figure 4.17.EM simulation (red lines) and Equivalent circuit (blue dots) S-parameters 
response of 510pH and 610pH spiral inductors in the frequency range of 0.1-40GHz 
plotted on a Smith chart along with the layout of the spiral inductor depicted in ADS-
schematic .............................................................................................................................. 136 
Figure 4.18. The layout of the 10 GHz reflection-based RTD amplifier ...................... 137 
Figure 4.19. The gain and return loss of the RTD amplifier layout using RTD sample 
XMBE#300 with a mesa area of 4x4 μm
2 
over the X-band ............................................. 138 
Figure  5.1.  A  single  RTD  oscillator  topology  with  stabilizing  circuit  components: 
decoupling capacitor and shunt resistor ......................................................................... 142 
Figure 5.2. I-V characteristic of the InGaAs/AlAs RTD device sample XMBE#300 with 
a mesa area of 4 μm
2
 ........................................................................................................... 148 
Figure 5.3.The Measured I-V characteristics of the RTD XMBE#300 with 4 m
2
 device 
size in comparison with a 6
th
 order polynomial fitting equation modelled in Keysight-
ADS. ...................................................................................................................................... 150 
Figure 5.4.The schematic of  the RTD  oscillator  circuit in ADS software  using RTD 
sample XMBE#300 with 4 μm
2
 .......................................................................................... 153 

 
 
11 
 
Figure 5.5. The output voltage signal across the load resistor for the simulation of 
100GHz RTD oscillator a) over 5 ns time span b) over 100 ps time span ................... 154 
Figure 5.6. The output power spectrum across the load of the RTD oscillator modelled 
in ADS using RTD XMBE#300 with 4 m
2
 device size .................................................. 155 
Figure 5.7. The results of the S-parameters simulation for the 19 pF MIM capacitor
................................................................................................................................................ 157 
Figure 5.8. The thin-film NiCr resistor's geometry [57]. ................................................ 159 
Figure 5.9. The equivalent circuit of NiCr resistor [141]. .............................................. 160 
Figure 5.10. The S-parameters results for 16  NiCr resistor ....................................... 161 
   

LIST OF SYMBOLS AND ABBREVIATIONS

εr

Relative Permittivity

Γ-Γ

Gamma to Gamma

Γ-X

Gamma to X

μm

Micrometre

μW

Microwatts

Ohms

Electron Affinity

ℎ

Planck Constant

Φm

Metal Work Function

One Dimensional

Two Dimensional

2-DEG

Two-Dimensional Electron Gas

Three Dimensional

Fifth Generation

A/Amp

Ampere (Current Unit)

ADS

Advanced Design System

AlAs

Aluminium Arsenide

Junction Capacitance

Centimetre

CMOS

Complementary Metal-Oxide Semiconductor

CPW

Coplanar Waveguide

DBQW

Double-Barrier Quantum Well

Direct Current

Conduction Band

Bandgap

Electromagnetic

Valence Band

Electron Volt

FFT

Fast Fourier Transform

Femto- Farad

GaAs

Gallium Arsenide

GHz

Gigahertz

Conductance

HBT

Heterojunction Bipolar Transistor

HEMT

High Electron Mobility Transistor

I-V

Current Voltage

I.E.

For example

Integrated Circuit

InAs

Indium Arsenide

InGaAs

Indium Gallium Arsenide

InP

Indium Phosphide

Peak Current

Valley Current

Kelvin

MBE

Molecular Beam Epitaxy

MIM

Metal Insulator Metal

Millimeter

MMIC

Monolithic Microwave Integrated Circuit

MOCVD

Metal Organic Chemical Vapour Deposition

MOSFET

Metal Oxide Semiconductor Field Effect Transistor

MOVPE

Molecular Organic Vapour Phase Epitaxy

Electron Effective Mass

me,t

Tunnelling Effective Mass

Milli-Siemens

n-Doped

NDC

Negative Differential Conductance

NDR

Negative Differential Resistance

NEGF

Non-Equilibrium Green Function

Nanometre

Pico Farad

Pico- Henry

PVCR

Peak to Valley Current Ratio

QCL

Quantum Cascade Lasers

Resistance and Capacitance

Radio Frequency

Junction Resistance

RTD

Resonant Tunnelling Diode

S-parameter

Scattering Parameter

Silicon

Semi-Insulating

SIS

Semiconductor-Insulator-Semiconductor

SiO2

Silicon Dioxide

SRF

Self-Resonant Frequency

Temperature

TCAD

Technology Computer Aided Design

THz

Terahertz

TIA

Transimpedance Amplifier

Transmission Line

TLM

Transmission Line Model

Tes

Collector Spacer Thickness

Tcs

Emitter Spacer Thickness

Quantum Well Thickness

Volt (Voltage Unit)

Peak Voltage

Valley Voltage

ABSTRACT

The research was focused on developing and enhancing a critical InP-based

technology, namely the Resonant Tunnelling Diode (RTD). This development was

initially established through a detailed modelling investigation of Double Barrier

Quantum Well (DBQW) InGaAs/AlAs RTDs to optimise the diode's DC and RF

characteristics by utilising asymmetrical spacer structures that target low peak

voltages and short transit times for use in high frequency and low dc power

consumption applications. The results of the asymmetrical spacer RTDs indicated that

thickening the emitter spacer significantly decreased the peak voltage and current,

while thickening the collector spacer increased the peak voltage and current. A few

modifications were made to the asymmetrical spacers RTDs to increase their negative

differential conductance (NDC) and output power while maintaining low peak

voltages. Reduced quantum well thickness aided in increasing the NDC, output

power, and operating frequency, but at the expense of significantly increased peak

voltage. The structure was then further modified by increasing the Indium content of

the quantum well. This step enabled the achievement of NDC values in the range of

20 mS and 50 mS and output power in the range of 200 μW and 450 μW while

maintaining a low peak voltage (i.e. 0.14 V to 0.35 V) and a high operating frequency

(i.e. 575 GHz to 700 GHz). This work demonstrated that RTDs are suitable for high

output power radio frequency (RF) applications and low power or ultra-low power

radio frequency (RF) applications.

This project also involved the modelling and theoretical analysis of an X-band

reflection-based amplifier using InGaAs/AlAs RTD sample #300 with a 16 μm

mesa

size. The model was constructed using a lumped element branch-line coupler with

two active RTD loads. The analysis included component extraction from the RTD

equivalent circuit and passive component modelling. By constructively combining the

amplified in-phase electromagnetic waves at the output port, it was possible to predict

a simulated gain of 13.5 dB at 10 GHz while consuming only 3.2 mW of DC power.

This gain results in a figure of merit of 4.22 dB/mW, confirming the amplifier's

superior performance compared to other X-band amplifiers using other technologies

(e.g. 65nm CMOS, GaN transistors). Due to the high gain and low dc power

consumption of the RTD amplifiers compared to other semiconductor technologies

such as CMOS and GaN transistors, they could be an excellent candidate for 5G/6G

wireless communication systems.

A 2D electromagnetic model of an RTD oscillator based on a 4 μm

InGaAs/AlAs RTD

(sample #300) coupled to a CPW resonator predicts an output power of 83 μW at 100

GHz fundamental frequency. The spectrum also shows that the first harmonic occurs

at 200.4 GHz with extremely low power of 0.09 μW. The RTD oscillator's passive

components, such as NiCr resistors, parallel plate capacitors, and CPW transmission

lines, were all modelled. Due to the rapidly increasing data rates for 5G/6G wireless

communication systems, implementing an ultra-high-speed RTD transmitter capable

of operating at speeds exceeding 20 Gb/s becomes critical. Thus, the RTD oscillators

developed in this thesis may aid 5G/6G technologies in overcoming the speed

limitations of CMOS and GaN technologies.

DECLARATION

No portion of the work referred to in the thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institutes of learning.

i. The author of this thesis (including any appendices to this thesis) owns

certain copyright or related rights in it (the "Copyright"), and he has given

The University of Manchester certain rights to use such Copyright,

including for administrative purposes.

ii. Copies of this thesis, either in full or in extracts and whether in hard or

electronic copy, may be made only in accordance with the Copyright,

Designs and Patents Act 1988 (as amended) and regulations issued under

it or, where appropriate, in accordance with licensing agreements which

the University has from time to time. This page must form part of any

such copies made.

iii. The ownership of certain Copyright, patents, designs, trademarks and

other intellectual property (the "Intellectual Property") and any

reproductions of copyright works in the thesis, for example graphs and

tables ("Reproductions"), which may be described in this thesis, may not

be owned by the author and may be owned by third parties. Such

Intellectual Property and Reproductions cannot and must not be made

available for use without the prior written permission of the owner(s) of

the relevant Intellectual Property and/or Reproductions.

iv. Further information on the conditions under which disclosure, publication

and commercialisation of this thesis, the Copyright and any Intellectual

Property and/or Reproductions described in it may take place is available

in the University IP Policy, in any relevant Thesis restriction declarations

deposited in the University Library, The University Library's regulations

and in The University's policy on Presentation of Theses.

ACKNOWLEDGEMENT

First, I would like to express my gratitude and appreciation to Allah for blessing me

with the strength necessary to complete this work. All praise is due to Allah for

bestowing upon me the honour of assisting humanity by contributing to its

knowledge enrichment.

I want to express my heartfelt appreciation to everyone at the University of

Manchester who has assisted me in achieving my academic goals. Additionally, I

would like to express my heartfelt gratitude and appreciation to my esteemed

supervisor, Professor Mohamed Missous, for his unwavering support, assistance, and

guidance throughout my PhD journey. The knowledge and experience I gained while

working with Professor Missous helped develop my academic career and develop my

personality. Without the assistance of numerous friends, this thesis would not exist in

its current form.

Without a doubt, I owe my parents, brothers, and sisters my deepest gratitude and

appreciation for their support, prayers, and patience, and I would not have reached

this stage without you. Special thanks to my great mother, Fawziah, for providing me

with motivation, inspiration, and love during some of the most challenging times in

the research.

I want to express my heartfelt gratitude and appreciation to my beloved wife and

children, Seba, Fawz, and Abdurrahman. They have always been encouraging and

patient.

Additionally, I would like to express my gratitude to Umm Al-Qura University for

providing me with this opportunity to earn a PhD and for financially supporting me

throughout my journey.

DEDICATION

This thesis is dedicated to my lovely parents, sisters, brothers, wife, and gorgeous daughters.

PUBLICATIONS

A. Alqurashi, J. Sexton, and M. Missous, "Design and Performance Analysis of X band

Reflection-based amplifier utilizing large RTDsʺ, UK Semiconductors 2022

A. Alqurashi, J. Sexton, and M. Missous, "Development of 100 GHz resonant tunnelling

diodes based oscillatorʺ, IEEE Latin America Electron Devices Conference (LAEDC)

2022, doi: 10.36227/techrxiv.21369729.v1

A. Alqurashi, S. G. Muttlak, J. Sexton, and M. Missous, "Narrow-band Amplifier for 5G

New Radio Standard Applications Utilizing Tunneling Based Devicesʺ, EEE PGR Poster

Conference 2021, Manchester, Poster Presentation

A. Alqurashi and M. Missous, "Physical Modeling of Asymmetric Spacers Resonant

Tunneling Diodes (RTDs)", IEEE Latin America Electron Devices Conference (LAEDC)

2021, pp. 1-4, doi: 10.1109/LAEDC51812.2021.9437970

A. Alqurashi and M. Missous, "InGaAs/AlAs Asymmetric Spacers RTDs for THz Imaging

Applications", Semiconductor and Integrated OptoElectronics (SIOE) Conference 2021,

Cardiff, Oral Presentation

A. Alqurashi and M. Missous, "Asymmetrical Spacer Resonant Tunneling Diodes (RTDs)

for THz Imaging Applicationsʺ, EEE PGR Poster Conference 2020, Manchester, Poster

Presentation

1. CHAPTER 1: INTRODUCTION

1.1. Overview of Terahertz Radiation Sources

High-speed, low-power, high-frequency electronic devices have become increasingly

popular over the last four decades, and semiconductor technology has been thrust to

the forefront of the industry as the most cost-effective solution for a broad range of

applications. New electronic device concepts, such as resonant tunnelling diodes

(RTDs), asymmetric spacer tunnel diodes (ASPAT), and other innovations, have been

made possible by advances in the Molecular Beam Epitaxy (MBE) growth technique.

Terahertz radiation can be generated in various ways; however, the compactness,

room-temperature operation, coherent nature, and high power of a coherent Terahertz

radiation source may make Terahertz radiation most advantageous in real-life

applications. The Terahertz band (30 GHz – 300 GHz) meets the requirements of

modern systems, including high data rates. As a result, numerous researchers and

companies across various industries, including medical science, semiconductor

technologies, and others, have developed devices capable of operating at these

frequencies [1-3].

Quantum Cascade Lasers (QCL) are the most common lasers operating at frequencies

greater than 1 THz while delivering a high output power level [1-9]. However, they

require a cooling system because of the low temperatures they need to operate [1, 10].

Several researchers have attempted to improve the performance of QCLs by

increasing their operating temperature. According to their findings [10], Fathololoumi

et al. achieved 199.5 K operation at a wavelength of 91μm by increasing the oscillator

strength. Another higher temperature (225 K) was recorded by applying electrical and

magnetic fields [11]. However, these temperatures still require significant cooling, and

the resulting output power is usually much lower.

Another type of terahertz radiation generator is the Gunn diode [12, 13]. The Gunn

diode is constructed from n-doped semiconductor materials elements (i.e. GaAs, InP).

When the applied voltage increases, the carrier drift velocity in the semiconductor

material reaches its maximum value; subsequent increases in the electric field cause

the carrier drift velocity to decrease. The electric field pushes electrons with sufficient

energy up to a separate conduction band with a lower drift velocity than the current

band. Although the Gunn diode exhibits a negative differential resistance (NDR)

property, it cannot operate at frequencies greater than 200 GHz [14, 15].

The NDR feature of the Resonant Tunnelling Diode (RTD) makes it a potential THz

source for high-frequency operation [16]. In addition, RTDs can operate at room-

temperature. Due to RTDs' quick switching speed, many structures have been created

to improve their performance in circuit implementations. The highest oscillation

frequency of 1.98 THz was obtained by increasing the antenna electrode thickness.

However, the output power was exceedingly low [17] (i.e. on the scale of nano-W).

The RTD's low output power is one of its most critical disadvantages [18]. Historically,

the output power of the RTD was in the microwatt (μW) range; consequently,

researchers attempted to increase the output power of the RTD, particularly at high

frequencies [19-21]. It was established that by integrating power circuits that

incorporate several RTD devices [22-26], the output power of the RTD could be

significantly increased. Thus, a high output power (i.e. 0.61 mW) at 624 GHz was

attained by combining synchronised two-element arrays [27]. A 0.73 mW output

power at 1 THz was also achieved with an 89 elements array [28]. Another way to

increase the output power of the RTD is using a slot antenna and controlling the

lengths of the short and long parts of the slot antenna [21, 27, 29]. In their research,

Suzuki and colleagues demonstrated a high output power of around 0.4 mW at 550

GHz, utilising a single RTD and an offset antenna [21].

Figure 1.1. Comparison between several RTDs in terms of their output power [17, 19, 21, 27, 28]

The authors of [30] predicted that a rectangular cavity resonator would produce

approximately 2 mW at 1 THz with a single RTD. This is due to the fact that the

conduction loss of the cavity resonator is less than that of the slot, allowing the

inductance to be decreased and the RTD area to be increased. In a conventional slot

100

200

300

400

500

600

700

800

0 0.5 1 1.5 2 2.5

output power (

μW)

Oscillation Frequency (THz)

[17] Single RTD

[19] Single RTD

[21] Single RTD

[27] Two-element array

[28] 89-element array

resonator, it is difficult to achieve 1 THz oscillations with a mesa area greater than 10

μm

. Additionally, it was projected that a cylindrical cavity resonator might

theoretically operate at a greater oscillation frequency (i.e. 2 to 3 THz) [31]. Figure 1.1

illustrates several reported RTDs with various oscillation frequencies and output

powers.

1.2. mmWave and Terahertz Imaging Applications

THz frequencies can be used in various imaging fields, including security imaging

and medical imaging. Terahertz waves can pass through clothing and be absorbed by

the human body [32]. As a result, these frequencies may be advantageous for airport

safety [33]. Terahertz imaging equipment has higher image resolution and less

Rayleigh scattering [34]. THz radiation has been used in various imaging applications,

including security scanning [35, 36] and medical imaging [37]. Terahertz imaging

requires further advancement in penetration depth and imaging system cost [34].

1.3. RTDs in 5G Wireless Communications systems

Wireless communications are one of the most critical applications of THz radiation.

Fifth-generation (5G) technology is the future of wireless communication networks.

Current 5G communication systems operate at frequencies less than 6 GHz; however,

these frequencies are crowded and fragmented [38]. As a result, researchers have been

interested in 5G communication systems that can function at a higher frequency range,

known as the new radio millimetre wave (NR mmWave) [39]. The NR mmWave has

frequencies ranging from 24 GHz to 100 GHz and has a high data rate and low latency

[40]. RTDs were utilised to create a 30 Gb/s modulated terahertz source [41]. In terms

of system coverage and overall power efficiency, power amplifiers are critical

components of 5G wireless communications [42]. To be used in 5G wireless

communication systems, the power amplifier must be efficient in output power and

power consumption [43]. As the power working frequency increases, the power

efficiency and output power decrease with large parasitic and limited supply voltage.

Thus, various designs, such as the Wilkinson power combiner based on transmission

lines, have been proposed to increase the output power. However, this type of power

combiner is bulky and inefficient. Due to their ability to minimise chip size and noise

performance, reflection-based amplifiers appear superior to transmission-line-based

amplifiers. This project aims to analyse reflection-based RTD power amplifiers

operating at 10 GHz to determine their suitability for use in the range of mm-wave 5G

wireless communication systems.

1.4. Thesis Aims and Objectives

One of the key objectives of this thesis is to explore the physics and principles of

Resonant Tunnelling Diodes (RTDs) and investigate the DC and RF properties of new

InGaAs/AlAs RTD oscillators’ structures. Additionally, the other goal of this thesis is

to investigate the potential uses of RTDs in mmWave/Terahertz imaging and wireless

communications. The steps outlined in the thesis are depicted in Figure 1.2. Because

of the effects of Covid19 on laboratory operations, steps 3 and 5 were not carried out

in this thesis.

This work simulates RTDs with varying spacer thicknesses and asymmetrical spacer

thicknesses using the SILVACO ATLAS tool to optimise the RTDs' performance based

on their DC and RF characteristics. Prior to this phase, a symmetrical RTD structure

was first modelled and compared to measured values to validate and calibrate the

simulator. The initial PhD plan was that the asymmetrical designed RTDs would then

be manufactured. However, the fabrication step was unable to be completed due to

the Covid19's effect on laboratory operations.

Figure 1.2. The proposed steps of the thesis

The RTDs were used to design and simulate integrated circuits (ICs) for specific

applications, in this case, narrow-band amplifiers and mm-Wave oscillators, via

Advanced Design System (ADS) software. Due to the difficulty of fabricating the

needed RTDs during the pandemic, the amplifier and oscillator circuits were designed

utilising RTDs formerly fabricated at the University of Manchester. Again, the

fabrication of integrated circuits was practically impossible because of the pandemic.

Thus, the fabrication of novel RTDs and integrated circuits are considered future

works for this thesis.

Additionally, this project aims to develop a high-performance RTD oscillator circuit

capable of operating at 100GHz at room temperature, including modelling of passive

components. This study aims to determine the performance of these oscillators and

their passive components in high-frequency applications and to determine how to

satisfy the conditions necessary for proper circuit operation.

1.5. Thesis Outline

This thesis consists of five chapters. The first chapter provides an overview of THz

sources and their uses in imaging and wireless communication systems. Additionally,

it includes the thesis's purpose and objectives and the thesis structure.

The second chapter discusses quantum tunnelling theory before discussing the

operation of double-barrier quantum-well resonant tunnelling diodes (DBQW RTDs).

A detailed review of the literature on RTDs is presented.

The physical modelling of novel RTD structures is covered in Chapter 3, followed by

each design's DC and RF characteristics. It also provides performance optimisation for

RTDs based on the application.

The design of narrow-band amplifiers employing double barrier quantum well RTDs

is presented in Chapter 4. The RTD-based amplifiers and reflection-based amplifiers

are explored first. The passive components of the RTD amplifier are next modelled

and simulated, followed by the modelling of the RTD device's DC characteristics. The

final section shows the circuit and layout of the RTD amplifier operating at 10 GHz.

Chapter 5 discusses the modelling of a high-performance oscillator using double

barrier quantum well RTDs. The conditions for designing an RTD-based oscillator and

the DC stability of the oscillator circuit are discussed first. The DC characteristics of

the RTD device are then modelled, followed by the design of the coplanar waveguide

line. The RTD oscillator operating at 100 GHz is then presented, followed by the model

of the RTD oscillator's passive components.

Chapter 6 summarises some of the significant accomplishments made in this thesis. It

also suggests some potential enhancements to the project that could be implemented

in the future. The final chapter offers the thesis conclusion and recommendations for

future works.

2. CHAPTER 2: FUNDAMENTALS AND BACKGROUND OF

RESONANT TUNNELLING DIODES (RTDs)

2.1. Introduction

This chapter describes the foundational basis of the theory and physics of resonant

tunnelling diodes. It explores the fundamental operation of double barrier resonant

tunnelling diodes (DBRTDs). This chapter also provides an overview of the pertinent

literature on resonant tunnelling diodes. Prior to delving into the physical modelling

of such a device, it is critical to understand the fundamental operating principle and

heterostructure design of double barrier resonant tunnelling diodes.

Theory of Quantum Tunnelling

Classical mechanics, which is limited to massive objects, describes the motion of

macroscopic objects. According to classical physics, a particle with energy E cannot

overcome a potential barrier with potential V unless its energy is equal to or greater

than the potential barrier's energy (E > V). As a result, classical mechanics cannot

account for phenomena such as tunnelling. Quantum mechanics was proposed in the

last century to represent the behaviour of atomic and subatomic worlds. According to

quantum mechanics, tiny particles (electrons) act as both waves and particles [44, 45].

According to quantum physics, if a barrier is sufficiently thin, a particle has a finite

probability of passing through it without overcoming or breaking it. This is referred

to as quantum tunnelling. Quantum tunnelling is dominant in the radioactive decay

of nuclei and electron field emission [44].

Because the probability of an electron passing through a thin barrier is not equal to

zero, the tunnelling probability and tunnelling current were devised working as

concepts. Solving the one-dimensional Schrödinger equation yields the tunnelling

probability. The wave function (Ψ), which is the solution to the Schrödinger equation,

can be used to calculate the electron current density:

























 







  (2.1)

where 



is the effective mass of the electron, is Planck’s constant divided by 2π, E

is the total energy of the electron, and V(x) is the potential energy of the electron at a

point x in the electric field.

Figure 2.1 depicts the quantum tunnelling theory for an electron passing through a

barrier with height V and thickness tb.

Figure 2.1. The wave function of an electron tunnelling through a single barrier [46].

When only one barrier exists, the wave function () in the barrier has the general form

[47] 







where the wave number (















Because the electron energy E is less than the barrier height V, k is imaginary because

the term contained within the square root is negative. Based on the solution of the

wave function, the transmission coefficient for a single barrier tunnelling is written as

follows [47]:













































(2.2)





































 (2.3)

where 



is the barrier thickness and 





is the effective electron mass.

If the effective mass and height of the barrier are minimal and the barrier thickness is

sufficiently thin, a finite transmission coefficient for a given energy value (E) can be

determined [48]. Most tunnelling devices have non-ohmic behaviours due to the

quantum tunnelling phenomenon. Tunnelling periods of carriers travelling through a

potential barrier, which is dominated by the quantum transition probability per unit

time, are very short (of the order of picoseconds), making tunnelling devices very

suitable for millimetre and sub-millimetre wave applications [45].

Tunnelling Diodes

An Esaki tunnel diode is a p-n junction with substantially doped semiconductor

materials in the p-type and n-type regions (doping concentrations of







to







). In 1958, Leo Esaki found that quantum tunnelling could occur in such

a device which was subsequently called after him [49, 50]. The Esaki diode was the

first device to use the quantum tunnelling phenomenon. Tunnelling diodes are

promising candidates for THz applications and wireless communication systems due

to their fast transit time, which allows for high-speed switching.

Figure 2.2 (a) depicts a cross-section of Esaki's diode (a).

Figure 2.2. The cross-section and the operation of the Esaki’ tunnel diode [51]

In this device, the two regions of the PN junction are heavily doped. As a result, the

qualities of the materials will differ from their intrinsic properties. The Fermi level is

an important material property. The intrinsic semiconductor's Fermi level, the energy

level where the probability of free states being occupied by electrons is equal to 0.5, is

located at the centre of the bandgap [44, 51].

In contrast, the Fermi level in heavily-doped n-type materials is above the conduction

band edge and below the valence band edge in heavily-doped p-type materials [44,

51]. The extent of the barrier (i.e. depletion region) is very thin as a result of the

substantial doping in the p-n junction, as according to [45]:





































(2.4)

where 



is the width of the tunnel diode barrier,





is the permittivity of the

semiconductor,  is the electron charge, 



is the barrier height, 



is the acceptor

impurity concentration, and 



is the donor impurity concentration.

The barrier height in a traditional p-n junction prohibits electron diffusion from the n-

type zone into the p-type region and vice versa; however, narrowing the barrier width

allows electrons to tunnel through the barrier [51]. If the following criteria are met [44,

51], electrons can tunnel through a potential barrier:

1) Because electron energy must be preserved, electron tunnelling from the n-type

area into the p-type region must take a horizontal path.

2) The occupied states in the n-type area must exist, as must the empty permissible

states in the p-type region, and they must have the same energy levels.

3) The tunnelling probability is finite because the barrier width must be sufficiently

thin. In contrast, the barrier height must be sufficiently low.

When no bias voltage is applied, no current flows through the junction, as shown in

Figure 2.2. (b). Then, with a slight applied forward bias, many electrons in the n-type

side's conduction band edge tunnel across the barrier to the p-type side's valence band

edge. The current flow through the junction increases as the forward voltage increases

because the Fermi level of the n-type area overlaps with the valence band edge of the

p-type region. The Fermi level of the p-type region overlaps with the conduction band

edge of the n-type region. The bands nearly completely overlap when the forward

voltage hits the peak voltage. The tunnelling current achieves its most significant

value when the overlapping reaches its highest value, which shows the peak value of

the forward voltage (Figure 2.2. (c)). Because of the availability of empty states in the

p-type region, the current falls as the voltage increases after this point. As a result, a

negative differential resistance (NDR) is formed. The p-type region has no empty

states for tunnelling. As a result, the current approaches its minimal value (see Figure

2.2. (d)). As the forward voltage increases, the thermal current will flow after the valley

current point. The I-V characteristics of the tunnelling diode seen in Figure 2.2 are

depicted in Figure 2.3.

Although alternative RTD structures have been proposed (e.g., a triple barrier

structure) [52], the double-barrier quantum-well structure has been the conventional,

most frequently used RTD structure since Tsu and Esaki proposed resonant tunnelling

in a finite double barrier structure [53] shortly after the introduction of the molecular

beam epitaxy (MBE) technique in the field of compound semiconductor crystal

growth [54].

Figure 2.3. The I-V characteristics of a typical tunnel diode [51]

Double-Barrier Quantum-Well Resonant Tunnelling Diodes (DBQW RTDs)

The double-barrier resonant tunnelling diode (RTD) is a two-terminal device made up

of three components:

1. An emitter region that serves as an electrons source

2. A double-barrier quantum-well (DBQW) structure consisting of a quantum-well

material with a narrow band gap sandwiched between two barriers made of a wide

band gap material, and

3. A collector region that captures electrons tunnelling through the DBQW structure.

The emitter and collector areas are n-type semiconductors that have been heavily

doped. The double-barrier construction was established to implement the resonant

energy levels in the quantum-well area. When carrier energies in the emitter are

aligned with quasi-confined energy levels in the quantum well region between the

barriers, tunnelling is likely to be at its highest level.

Numerous material systems, such as those containing Sb [55] or Si/SiGe [56], have

been employed; however, their usage has been limited due to the complexity of their

growth method [57]. As a result, most structures are composed of group III-V

compound semiconductors. Another advantage of employing group III-V compound

semiconductors is the ability to modify the bandgaps of these materials to increase

electron mobility [48, 54].

To generate a heterostructure composed of two different materials, their lattice

constants must be extremely close; otherwise, broken bonds will develop, disrupting

the heterojunction contact. The mismatch between the two materials caused by the

significant disparity in their lattice constants results in crystalline flaws. Thus,

dislocations will be generated at the interface, acting as undesired trapping centres

within the device.

GaAs/Al0.7Ga0.3As RTDs were the first to be demonstrated [53, 58]. These early RTDs

exhibited no NDR at room temperature until Shewchuk et al. altered the aluminium

composition from 0.7 to 0.25 [58]. The leakage current would climb to the upper

resonant level because the GaAs/AlxGa1-xAs conduction band offset is small.

Additionally, the high effective mass of GaAs/AlxGa1-xAs has limited electron

mobility, resulting in a low current density. As a result, GaAs/AlxGa1-xAs have been

phased out, favouring GaAs/AlAs to raise barrier height and attain high current

density [18, 59]. In 1985, the first GaAs/AlAs RTD capable of operating at room

temperature was demonstrated [59, 60]. Then, for an RTD with a mesa area of 5 m

a high current density (250 kA/cm

) was produced [61].

Numerous efforts have led to novel semiconductor materials with significantly larger

conduction band offsets and lower electron effective masses than GaAs/AlAs. Thus,

in 1986, an In0.53Ga0.47As/In0.52Al0.48As RTD with lattice matching was presented on an

InP substrate [62]. In 1987, a novel pseudomorphic In0.53Ga0.47As/AlAs heterostructure

was demonstrated [63]. In0.53Ga0.47As are better candidates for RTDs than GaAs due to

their lower electron effective mass, as demonstrated in Table 2.1. Furthermore, the

band discontinuity between In0.53Ga0.47As and AlAs is significantly larger than

between GaAs and AlAs.

In 2002, a novel heterostructure material for RTD was introduced (i.e. In0.8Ga0.2As) [64].

Metal-organic Vapour-Phase-Epitaxy (MOVPE) was used to grow the novel material.

Indium-doped quantum wells produce a peak current density at a lower voltage bias

than other materials [57]. The RTDs in this thesis are all made of In0.8Ga0.2As/AlAs.

Table 2.1. The lattice constant, energy bandgap, and the electron effective mass of commonly used III-

V compound semiconductors for RTDs at 300 K [45, 65-67].

Material

The lattice constant, a0

(Å)

Energy gap, Eg

(eV)

Electron effective

mass, me

GaAs

Al0.7Ga0.3As

5.653

5.659

1.42 (direct)

2.059 (indirect)

0.067m0

0.125m0

GaAs

AlAs

5.653

5.661

1.42 (direct)

2.9 (direct)

0.067m0

0.15m0

In0.53Ga0.47As

In0.52Al0.48As

5.868

5.852

0.75 (direct)

1.44 (direct)

0.041m0

0.075m0

In0.53Ga0.47As

AlAs

5.868

5.661

0.75 (direct)

2.9 (direct)

0.041m0

0.15m0

In0.8Ga0.2As

AlAs

5.977

5.661

0.494 (direct)

2.9 (direct)

0.032m0

0.15m0

InP

5.869

1.35 (direct)

0.077m0

2.4.1. Epi-layers structures of DBQW RTD

The DBQW RTD comprises three components: the emitter, the collector, and the

DBQW area. Numerous epi-layers variations of DBQW RTD have been reported;

however, they differ only in their thickness. Figure 2.4 illustrates an epilayer structure

of DBQW RTD with symmetrical spacer layers [57, 68]. Figure 2.5 illustrates another

structure with asymmetrical spacers [29]. The current in this study flowed from the

substrate to the top layer. They claimed that using a thick collector spacer with spiking

doping resulted in a lower peak voltage, despite the fact that the main cause of the

decreased peak voltage is the use of the spike doping structure. Because the emitter

region is heavily doped, a structure was reported in [20] that grades the emitter

doping levels to lower the collector's transit time.

Figure 2.4. The epi-layers and the current density of several RTDs with symmetrical spacers [68]

Figure 2.5. The epi-layers of RTD with asymmetrical spacers [29]

2.4.2. The operational principle of DBQW RTD

Figure 2.6 demonstrates the operation of a typical DBQW RTD, which can be

summarised in six steps:

a) The emitter's Fermi level, above the conduction band edge due to the strong

doping and lack of external bias, is lower than the quantum-lowest well's

quantised energy level. As a result, there is no current flow in this state.

b) As the external bias increases, the number of electrons with sufficient energy to

overcome the barrier grows. Additionally, the lowest quantised energy level

will be decreased to match the emitter's Fermi level, allowing a small amount

of current to flow through the diode.

c) As the bias voltage increases, the lowest quantised energy level decreases. As

a result, the diode will conduct many electrons until the diode current reaches

its maximum value. When the first resonant energy hits the bottom of the

conduction band, the maximum current, referred to as the peak current IP, is

reached. The voltage at which the highest current occurs is called the peak

voltage VP.

d) After reaching the maximum voltage point, the initial resonant energy level

falls below the conduction band offset. As a result, the current rapidly

decreases as the number of electrons traversing the double barrier decreases.

e) The current will continue to decrease until it reaches its minimal value, referred

to as the valley current IV. When the valley current is reached, the voltage value

is the valley voltage VV. Following this, another mechanism will operate.

f) As the voltage increases, the proportion of electrons with sufficient kinetic

energy to overcome the barrier grows proportionately. Thus, the current

increases until the energy of the second resonance fall below the Fermi level.

Thus, the following resonance condition enhances the current flow. Following

the second resonance, the current flow is dominated by thermionic emission

over the barriers.

Figure 2.6. Typical energy band diagram of a DBQW RTD and the corresponding IV characteristics

(where EC is the conduction band offset, EF is the Fermi level, and E1 and E2 are the first and the

second quantised energy levels inside the quantum-well) adapted from [57]

2.4.3. DC and RF characteristics of DBQW RTD

The RTD is a negative differential resistance (NDR) device, as illustrated in Figure 2.7.

As a result, three essential parameters should be considered when evaluating the

RTD's performance: the peak voltage VP, the peak current IP, and the peak-to-valley

current ratio (PVCR). The peak voltage (VP) is where the peak current (IP) occurs. The

PVCR is the ratio between the peak and the valley currents (IP and IV). The peak

current must be sufficient to guarantee that the RTD produces sufficient RF output

power and suffers minimum losses. Additionally, the high peak-to-valley-current

ratio (PVCR) would imply that the valley current must be kept to a minimum. PVCR

is denoted as follows:











(2.5)

However, a very high peak current might result in excessive power dissipation, which

a low peak voltage can minimize.

Another key DC parameter is the absolute value of the negative differential

conductance (GRTD). This parameter can be expressed as follows [69]:















(2.6)

where  and  are the difference between the peak and the valley current and

voltage, respectively. The primary reason for the appearance of the factor 3/2 is the

derivation of the absolute value of the negative differential conductance at the centre

of the NDR from the average power balance between the NDR and the load

conductance.

While the DC properties of resonant tunnelling diodes are critical in determining

their eligibility for high-frequency operation, the RF characteristics are more useful

for adapting the devices to specific applications. This is because the equivalent

circuit components of tunnelling devices are often frequency sensitive, reducing the

switching speed and expected RF output power of the RTD oscillators. Three critical

metrics can assess the RTD's RF characteristics: series resistance RS, RTD capacitance

CRTD, and oscillation frequency.

Figure 2.7. The IV characteristics with clear NDR from an RTD fabricated at the University of

Manchester (sample XMBE#327) [68].

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Current Density (mA/µm

)

Voltage (V)

XMBE 327

NDR

region

The RTD's series resistance comprises the ohmic resistance, resistance due to the epi-

layer contacts, and resistance due to the wafer substrate spreading resistance.

Figure 2.8. Schematic drawing for top and side views for the transmission line model (TLM) structure

used in this work.

The specific contact and sheet resistances can be evaluated using the transmission line

model (TLM) structure, as shown in Figure 2.8. Their values can be utilised to

determine quality of current flow in the device. The device's contact resistance can be

determined using the TLM technique; hence, the device's specific contact resistance is

provided by [70]:





































 (2.7)

where 



is the contact resistance (i.e. 













, 



is the transfer length (effective

length) where most of the current flow out of the metal into the semiconductor or vice

versa, 



is the sheet resistance under the metal electrode, and W and d are the width

and the length of the contact pad, respectively.

The spreading resistance can be approximated as follows [71]:



























 (2.8)

where  is the conductivity of the bottom contact, ddepth is the thickness of the bottom

ohmic layer, 



is the horizontal distance between the top and bottom metal

electrodes and 



is length of the bottom ohmic layer as shown in Figure 2.9.

Figure 2.9. Cross-section of an RTD illustrating the epi-layers and contacts on a semi-insulating InP

substrate, as well as the lengths and depths used in equation 2.8.

The resistance due to the epi-layer contacts is expressed as follows [72]:













(2.9)

Where ρ, ARTD and l are the material resistivity, the cross-section area, and material

length of the RTD, respectively.

The general form of the series resistance can be given by:













 



 



(2.10)

As demonstrated by equation 2.10, as the device mesa area increases, the series

resistance decreases, but the operating frequency decreases due to the increase in

depletion region capacitance. Additionally, the series resistance is mainly determined

by the device contact resistance in the metal electrodes, which is caused by the metal-

semiconductor contact. This resistance can be reduced significantly by doping the

ohmic layers substantially.

For RTDs, the term CRTD refers to both the depletion region (Cdep) and quantum

capacitances (CQ), as theoretically defined by 











[71]. 

















 can be used to calculate the capacitance of the depletion region (as a

parallel plate), where 



, 



, and d denote the free space permittivity, the relative

dielectric constant, and the thickness of the double barriers quantum well region,

including emitter and collector spacers, respectively [73]. The primary reason for

adopting such an associated quantum capacitance is to raise the negative charge in the

accumulation region and quantum well, balancing the positive charge in the depletion

region [74, 75]. 

















is the quantum capacitance formula, where 



is the

transit time across the double barriers quantum well (



) and collector depletion

region (



). The carrier transit time in a resonant tunnelling diode is expressed as

[71]:

















(2.11)

In the analysis of transistors, the







term for collector depletion region transit time

has been mathematically derived [76]. The 1/2 term used to differentiate between

signal delay time and carrier transit time in the collector region.

The carrier transit time across the collector depletion region has been mathematically

derived in the theoretical analysis of the RTD as follows [77]:















(2.12)

where 



is the thickness of the collector depletion layer, and 



is the saturation

velocity.

The calculations of the dwell time (i.e. the transit time across the quantum well region)

is given by [77]:













(2.13)

where is the reduced Planck’s constant, and 



is the width of the resonant level.

The full-width at half-maximum (FWHM), which is an approach of the Wentzel-

Kramers-Brillouin (WKB) approximation as given by [59, 78]:



































 (2.14)

where 



and 



are denoted as the electron effective mass in the barrier and the

barrier thickness, respectively.

The quantisation energies in the case of quantum-well with finite barrier height are

calculated as follows:





























(2.15)

where 



and 



are the electron effective mass and the thickness of the quantum –

well, respectively.

The upper operating frequency limit can be theoretically expressed as follows [79]:





































  (2.16)

It might be important to emphasise that fmax is the frequency at which the RTD's net

negative differential resistance equals zero. As shown in equation (2.16), it is critical

to minimise passive elements, including Rs and other parasitic components, to reach

as close to the theoretical maximum frequency as possible and to ensure efficient

operation in the mm-wave/THz areas. Regardless of the high-frequency operation

limitations imposed by parasitic elements on the diodes, the intrinsic high-frequency

limit imposed by tunnelling and depletion region delay periods is given by [69]:















(2.17)

In Equation 2.17, the absolute value of the negative differential conductance without

the tunnelling and transit times reaches zero after approaching 1 in the low frequency

limit. The frequency in this instance is 









Summarizing, the difference between the peak and valley voltages (∆V) is critical in

optimising the RF output power of an efficient THz RTD emitter as is minimizing the

series resistance. Keeping this in mind, it is also critical to achieve a peak resonance at

a lower bias voltage for low dc power consumption. The dc output power (i.e. 











has a maximum when 









, where 









and 







. Because the I-V curve

in the NDC region is typically unstable and challenging to measure directly, a and b

are expressed approximatively with the current and voltage widths of the NDC

region. The maximum dc output power the electron delay time parasitic elements are

neglected can be calculated as 









 [80]. However, the output power

is reduced due to the frequency-dependent decrease in GRTD (i.e. a transit delay time).

So the formula mentioned above becomes [16]:















(2.18)

Effects of layer thickness on the performance of DBQW RTD

2.5.1. Barrier thickness

The current density is proportional to the barrier thickness and the resonant state

energy width, and the analysis should be explained from a quantum mechanical

perspective. The resonant tunnelling current via a double barrier quantum-well

device is proportional to the transmission probability, defined as [54]:





 (2.19)

where the wave vector inside the barrier is expressed as follows:















(2.20)

where 



is the electron effective mass in the barrier at the energies close to the

conduction band edge of the emitter,  is the reduced Planck’s constant, and V is the

potential barrier height.

Therefore, the reduction in the barrier thickness leads to an exponential increase in the

transmission probability and the peak current density, as stated in equation 2.19.

Although a small decrease in the barrier thickness leads to an enormous improvement

in the current density, the PVCR reduces.

2.5.2. Well thickness

Quantisation energy or resonant energy level (with respect to the CB edge) in the

quantum-well increases when both the electron effective mass and the quantum-well

thickness decrease. The example of a quantum well with a limited barrier height is

illustrated in Figure 2.8, where the quantisation energies are determined using

equation 2.15.

Figure 2.10. Schematic of quantum-well with finite barrier height structure. (where E is the incident

electron energy, EC is the conduction band, E1 and E2 are the first and second quantisation energies

respectively, V0 is the barrier height, tw and tb are the quantum-well thickness and the barrier

thickness respectively [57].

As a result of the decline in quantum-well thickness, the following implications occur:

1) Increases in the first resonant energy level increase the peak voltage required

to generate the peak current.

2) Nonetheless, the increase in the first resonant energy level has the beneficial

effect of lowering the barrier (



 



). As a result, the full-width at half-

maximum (FWHM) value will grow [78]. This approach to the Wentzel-

Kramers-Brillouin (WKB) approximation as described in equation (2.14). As a

result, as stated in equation (2.21), the transmission coefficient increases,

increasing the tunnelling current [59].

































  

















(2.21)

where 



and 



are the transmission coefficients of the left barrier and the right

barrier, respectively

3) The distance between adjacent resonant energy levels increases as the width of

the quantum well decreases. As a result of the reduction in leakage current

components at the second resonant energy level, the PVCR is projected to

increase.

2.5.3. Spacer thickness

Primary thinking behind the inclusion of the emitter and collector spacers is to reduce

dopant diffusion into the subsequent layer during growth; for example, dopant

diffusion from strongly doped n-InGaAs into the AlAs barrier. The band diagram of

an RTD with a spacer layer on both sides of the barriers under bias is shown in Figure

2.10. Due to an undoped or low-doped spacer layer between the emitter and the

barrier, and when a high applied voltage bias is applied, a triangular well forms at the

emitter barrier [54]. The confinement of this triangular well will generate a population

of 2D electron gas (2DEG) electrons in quasi-bound states. This population results in

resonant tunnelling between the quantised states in the triangle well and the resonant

state in the quantum well, a phenomenon referred to as 2D-2D resonant tunnelling.

As a result of the improved PVCR, a sharper resonance is noticed at a reduced current

density and often seen as a bump in the otherwise smooth I versus V characteristic

below resonance [54].

Figure 2.11. The band-diagram of RTD with the presence of the spacer layers on both sides of the

barriers [54].

State of the art in InGaAs/AlAs RTDs

THz radiation is most beneficial when it is generated from a coherent source and can

operate at room temperature. As a result, numerous studies have generated various

RTD architectures with varying oscillation frequencies and output powers. The best

candidate would be resonant tunnelling diodes due to their fast speed and small size.

In 1984, one of the earliest attempts to show an RTD experimentally occurred, and it

functioned at 18 GHz with a 5 μW output power [81]. The oscillation frequency was

increased numerous times until it reached several hundred GHz [59, 61]. In 1991, it

was claimed that an RTD with a fundamental oscillation of 712 GHz had been

developed [55]. A 64-element arrayed oscillator with RTDs was proposed with an

oscillation frequency of 650 GHz [82]. A harmonic oscillation frequency greater than

1 THz has been observed [83]. A fundamental oscillation of 650 GHz and a harmonic

oscillation of 1 THz were reported, while the output power at 1 THz was 60 μW [69].

The fundamental oscillation frequency climbed to 831 GHz in 2009 [84] and exceeded

1 THz in 2010 [85]. The fundamental oscillation frequency has been demonstrated by

numerous examples and exceeded 1.1 THz [19, 71, 86, 87]. The highest oscillation

frequency achieved is 1.98 THz, which was accomplished by increasing the antenna

electrode thickness to 2μm [17].

Summary

This chapter discussed quantum tunnelling theory and the development of the first

tunnelling diode using the Molecular Beam Epitaxy (MBE) technology and later

Metal-Organic Chemical Vapour Deposition (MOCVD). The essential operation of

Esaki's diode was then described. Since Esaki and Tsu established the concept of

resonant tunnelling in a finite double barrier structure, the double-barrier quantum-

well RTD structure has been the most often employed. The most useful RTD material

systems have been those using group IIIV compound semiconductors because of their

capacity to enhance electron mobility through band-gap engineering. The structure of

the epi-layers and the operating concept of the DBQW RTD have been described in

depth.

Additionally, this chapter discussed the DC and RF properties and how to extract or

compute them. Additionally, the implications of layer thickness on RTD performance

have been discussed. Finally, the state of the art has been discussed in the

InGaAs/AlAs RTD. The following chapter will examine the physical modelling of the

RTD's new structures.

3. CHAPTER 3: PHYSICAL MODELLING OF ASYMMETRICAL

SPACERS RESONANT TUNNELLING DIODES (RTDs)

3.1. Introduction

This chapter presents a detailed numerical investigation of asymmetrical spacers

resonant tunnelling diodes (RTDs). It optimises device performance by varying layer

thicknesses. This chapter also provides an overview of the relevant literature on

asymmetrical spacers resonant tunnelling diodes (RTDs). It is critical to validate the

physical model of formerly fabricated devices before proceeding with the

optimisation analysis of such a device. This chapter used the SILVACO ATLAS

software tool to conduct all physical modelling and analysis.

3.2. State of the art in Asymmetrical spacers RTDs

The oscillation frequency was the primary focus of previous research on RTDs. Thus,

various methods for increasing the oscillation frequency were proposed. One method

is to reduce the mesa area; however, this method may decrease the absolute value of

the negative differential conductance (NDC) and increase the series resistance [84].

Another technique for increasing the oscillation frequency is to decrease the RTD's

capacitance by thickening the collector spacer [88]. As Figure 3.1 below shows,

Professor Asada's group fabricated RTDs with varying collector spacer thicknesses.

They discovered that increasing the collector thickness increased the peak voltage and

voltage width ∆V of the NDR region. They also found that the current density is

independent of the collector spacer thickness as it is determined by the amount of

electron concentration in the emitter and the transmission coefficient of the double

barrier region.

Figure 3.1. The structure of the asymmetrical spacer RTD proposed by [88].

Figure 3.2. The oscillation frequency versus the spacer thickness with the I-V characteristics of

asymmetrical spacers RTDs [88].

They observed an increase in oscillation frequency from 325 GHz to 425 GHz when

the collector spacer thickness was increased from 5nm to 45nm, as illustrated in Figure

3.2 [86]. The oscillation frequency was increased to 831 GHz by decreasing the barrier

thickness from 1.5nm to 1.4nm and increasing the collector and emitter spacer

thicknesses to 20nm and 2nm, respectively [82]. Additionally, the peak and valley

voltage points increased as the collector spacer thickness increased. More oscillation

frequency improvement has been achieved by optimising the collector spacer

thickness alone [89] or the slot antenna length and thickness [17, 90]. While this

method increases the oscillation frequency by lowering the RTD capacitance, it also

increases the intrinsic delay time of the RTD by increasing the transit time in the

collector depletion region, making the RTD slower [91].

Additionally, increasing the collector spacer may increase the peak voltage point,

resulting in increased power dissipation. Consequently, the peak voltage point has to

be lowered, reducing power dissipation. Thus, by increasing the thickness of the

emitter spacer, the capacitance of the RTD can be reduced, increasing the oscillation

frequency without increasing the transit time across the collector depletion region

[90].

The authors of [92] investigated the effect of emitter spacer thickness on peak current

density using the numerical solution to the Schrödinger equation. They discovered

that an optimal emitter spacer thickness results in a high current density with a low

peak voltage. The collector spacer was 10nm thick. Two asymmetrical spacers RTDs

(mesa area= 3µm

and 5µm

) with the structure depicted in Figure 3.3 below have been

demonstrated theoretically and experimentally. The authors discovered that high

output power of 3.1 mW at 300 GHz and 1.8 mW at 600 GHz is possible [93].

Figure 3.3. The structure of asymmetrical spacers RTDs reported and studied in [93]

Additionally, the voltage span of the NDR region increases as the emitter spacer

thickness increases. There are only a few theoretical studies on RTDs with

asymmetrical spacers and thick emitter spacers. However, most of them focus

exclusively on the emitter spacer, omitting the collector spacer from the structure,

which is not the case with our devices.

3.3. Physical modelling of asymmetrical spacers RTDs Tunnelling Diodes by

SILVACO ATLAS tool

Due to the lengthy and expensive fabricating of semiconductor devices, it is frequently

faster and more cost-effective to explore new device concepts using physical

modelling and simulation. Physical modelling has been utilised extensively

throughout this research to assist and advise the development of new device

structures and to optimise device performance. This process has been simplified over

time using technology-computer-assisted design (TCAD) software such as SILVACO

ATLAS. This section will begin with a brief overview of the SILVACO ATLAS TCAD

software's features. This will include a discussion of how ATLAS defines devices as

part of the physical model. Additionally, this work discusses the utilised material

models, the incorporation of traps and defects, the physical simulation models, the

specification of doping levels, and the incorporation of contacts. The physical

modelling of RTDs will then be discussed.

3.3.1. SILVACO ATLAS

SILVACO is a simulator developed for the physical modelling and characterisation of

electronic devices. Numerous semiconductor fabrications and in-house designs have

benefited from the contribution of the SILVACO simulator to the development of the

"technology behind the chip". SILVACO expanded its simulator operation to include

analogue, mixed-signal, and RF circuit simulation and design as its presence in the

Electronic Design Automation (EDA) and Technology Computer-Aided Design

(TCAD) fields expanded. This simulator consists of a Virtual Wafer Fabrication (VWF)

simulator capable of simulating two-dimensional and three-dimensional physical

devices [94]. SILVACO allows users to model devices in a wide range of

environments, including electrical, thermal, and optical, under various bias

conditions. This robust simulator has the ability to generate precise and accurate

analysis of results, which is a significant advantage. ATLAS is a product from

SILVACO that is used to simulate devices. ATLAS is primarily composed of a

command file named Deckbuild, which refers to the location of the program's source

code. It includes syntax and commands for defining or modelling any specified

structure, material, or physical feature of electronic devices. ATLAS solves all

structures automatically by analysing log and structure files. TonyPlot is then used to

visualise both the statistical and model analyses. TonyPlot is a tool that visualises the

simulation output graphically. The SILVACO ATLAS flowchart is depicted in Figure

3.4.

Figure 3.4. SILVACO ATLAS inputs and outputs [94].

During the device simulation process, the device is defined in the device structure

command file, which contains the parameters and execution instructions of the device.

The simulator outcome consists of three distinct file types: 1) Runtime Output, which

shows the program's progress, error, and alerts to the user; 2) A Log File, which stores

all node voltage and current measurements from the device analysis; and 3) Solution

Files, which store 2D and 3D data relating to solution values at the applied bias point

across devices.

The 2D structure of the studied device is defined in DeckBuild using the ATLAS

syntax. The Region statement is used to define the structure in ATLAS Deckbuild,

isolating the selected location of the device. It accomplishes this by dividing the initial

mesh statement into different blocks. Afterwards, the Region number is used to set

the initial material parameters, which can be referred to later. The mesh should be

appointed to a region, with the region numbers arranged in ascending order. The

Region statement introduces the tunnel structure into the device modelling. This

assertion is contingent upon the solver used in the SILVACO modelling. The tunnel

structure region is defined as qtregion (i.e. quantum tunnelling region) in the

Semiconductor-Insulator-Semiconductor (SIS) solver. In contrast, the tunnel structure

region is defined using the Model statement in the Non-Equilibrium Green Function

(NEGF) solver.

Typically, the device structure is defined using 2D or 3D geometric grids. In spite of

this, the current tunnelling model implemented in SILVACO ATLAS emerged to be

quasi-one-dimensional and was therefore analysed on a sequence of parallel or

roughly parallel slices through the insulator. The type of mesh determines the

specifics of the implementation. Since the simulation employs a two-dimensional

structure, the mesh was defined in the x and y planes, with the x-plane denoting the

horizontal plane and the y-plane denoting the vertical plane. All coordinates were

given in microns. The spacing parameter was utilised to improve the accuracy and

precision of the analysis at a particular location. The mesh statement then created a

rectangular mesh on which all aspects of quantum tunnelling were computed. In

addition to Region and Mesh, the structure specification also includes a Doping

statement. This statement establishes the doping levels within the previously

designated regions. By default, the simulator simulates with silicon materials

parameters as a base material. The electrode command is the final command in the

structure specification that implements a comprehensive model structure. Based on

an electrically analysed device area, this statement is defined. In this study, anode and

cathode designations were assigned to all tunnel structure electrodes. The anode was

positioned at the high point of the epitaxial layer. Concurrently, the cathode is situated

directly above the device collector ohmic contact. Contact corresponds to the physical

property of an electrode. By default, an ohmic contact is assumed to exist between an

electrode and a semiconductor material. If a workfunction is defined, the electrode is

regarded as a Schottky contact. A Schottky Barrier (SB) contact's metal workfunction

was specified using the contact statement.

To improve the fitting of experimental data for materials with a high indium (In)

content, material parameters were determined. The materials used in physical

parameters were linked to the materials used in the mesh system. For standard

semiconductors such as silicon, GaAs, and AlAs, the parameters in ATLAS Deckbuild

were set to default values. As the database of material parameters gathered by our

group at the University of Manchester over the years became more accurate and

precise, the modelling for the lattice-matched system appeared quite progressive.

Typically, new materials require user-defined parameters, particularly for energy

bandgap, conduction and valence effective masses, and effective density of states at

300 K. In addition, it was essential to validate and precisely define each of the

necessary parameters in the section for material parameters [92].

The difference in bandgaps created an abrupt discontinuity in the valence and

conduction bands. At equilibrium, the energy band diagram of a modelled device

illustrates data on various parameters, such as barrier height, the width of the

quantum well formed between the two barriers, the degree of band bending in the

emitter and collector regions, and the spacer layers formed following the heavy

doping in the doped layer. The material parameters have the most significant

influence on the band diagram (i.e. electron affinities, energy bandgaps, effective

masses, and permittivity). As a result, the following sections present and discuss

additional details on physical device models and parameters that govern the model.

- Indium Gallium Arsenide (InGaAs) Material Parameters

Unlike the binary material GaAs, the tertiary material definition for InGaAs used the

Gallium composition fraction x in In(1-x)Ga(x)As. Due to the fact that the composition of

the compound semiconductors utilized in this structure differed from the ATLAS

configuration (In0.5Ga0.5As), the user was required to define a number of parameters.

Because of the unusual composition, the parameters were computed based on the

semiconductor parameter definition [93]. As a result, the effective electron mass,

dielectric constant, electron affinity, and bandgap energy of this ternary alloy were

defined using equations (3.1) to (3.4). Figure 3.5 shows these parameters for different

fractions such as In0.53Ga0.47As and GaAs.

Figure 3.5. The electron effective mass, Dielectric constant, and the Energy bandgap at 300K as a

function of the composition fraction (x)













   



(3.1)





   



(3.2)

   (3.3)





    



(3.4)

- Aluminium Arsenide (AlAs) Material Parameters

The indirect bandgap of thick (or bulk) AlAs is typically 2.16 eV. However, when the

barrier thickness is 10 ML (28.3 Å), the - direct tunnelling with a 3.15 eV energy barrier

is dominant [95]. The -X current made a negligible contribution and thus was omitted

from the physical model. In terms of AlAs tunnelling effective mass (me,t), the Γ-valley

effective mass was lower than the X-valley effective mass due to the steeper curvature.

The effective mass of the electron, me*, was determined to be 0.15m0 in this work, in

accordance with [96].

The electron affinity of the barrier material is another critical parameter. The energy

difference between an electron's vacuum level and the bottom of the conduction band

edge is defined as its electron affinity [57]. This determines the band discontinuities at

semiconductor hetero-interfaces, specifically at the ΔEC and ΔEV interfaces. The

discontinuities in the conduction band (ΔEC) can be defined as follows:









 



(3.5)

The value of Δ for In0.53Ga0.47As/AlAs RTD was fixed at 1.69 eV in the command

file, consistent with the SILVACO ATLAS results shown in Figure 3.6. Thus, the

electron affinity of AlAs and In0.53Ga0.47As/AlAs were fixed at 2.91 eV and 4.6 eV,

respectively.

Figure 3.6. In0.53Ga0.47As/AlAs conduction band diagram profile at zero bias.

The Model statement specifies the model flags that indicate the inclusion of various

physical mechanisms, models, and other parameters in the simulation, such as global

temperature. To accurately model a specific phenomenon, the Model statement

parameters should be accurate, as flag setting requires differing mathematical models,

physical mechanisms, and other global parameters, such as substrate temperature.

Indeed, this simulator incorporates a variety of numerical methods for resolving

semiconductor device problems. The numerical method specification was

incorporated into the Method statements of the input file. The solution is defined in

the final section of this physical modelling. Obtaining solutions is comparable to

setting up a laboratory's parametric test equipment for device measurement. The user

-1

-0.5

0.5

1.5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Electron Energy (eV)

Thickness (μm)

must specify the voltages at each electrode. The simulation output is displayed in a

log and a solution file format. The user must first define the log and solve and save

the statement in the ATLAS simulation to run this file. Together, these statements offer

data for other functions to analyse. This study analysed the I-V characteristics, energy

band diagram, and other outputs of the device using three statements. Once the

simulator reached the solve statement, the problem-solution was enabled. Later, the

log statement was used to save any DC, transient, or AC data generated by the solve

statement. The saved statement assigned all data points in the output file to a node.

Before proceeding to the next section, the solvers associated with the model used in

this work, namely SIS and NEGF, are discussed.

- Non-Equilibrium Green Function (NEGF) Solver

The ATLAS model includes the charge associated with the quantisation effect in

strong quantum confinement. Thus, the NEGF solver would enable the Schrodinger-

Poisson solver to evaluate the tunnelling current, resulting in the current being

calculated as a sum over eigenstates. Using the following equation, the SILVACO

NEGF solver computed the current density through the barrier and quantum

confinement:



















 

























































(3.6)

where , q, k, and  denote the semiconductor's effective mass, electron charges,

Boltzmann constant, and the reduced Plank constant, respectively. Meanwhile, EFr and

EFl are the quasi-fermi levels on the barrier's right and left sides, respectively.

NEGF was used in the ATLAS simulator to determine carrier tunnelling in the

Negative Differential Region (NDR) through imposing quasi-equilibrium

requirements on the device's emitter and collector regions [97]. To incorporate this

model into the simulator, the user must define the NEGF modes in the model

statement using either N.NEGF PL or P.NEGF PL to activate planar NEGF solver for

electrons or for holes. The N.NEGF PL was used because the investigated structure

was based on the electrons.

Additionally, three conditions had to be met for this model to function correctly. First,

the device's quasi-equilibrium region was defined by defining Equil.NEGF on both

the emitter and collector sides. Following that, the ETA.NEGF parameter was

included in the model statement to set the broadening for characterising the Quasi-

equilibrium regions. Finally, Esize.NEGF was used to configure the NEGF solver's

energy grid points. In the case of insufficient convergence, the energy grid's size (i.e.

Esize.NEGF in the Model statement) and the magnitude of the broadening in quasi-

equilibrium regions were increased.

- Semiconductor-Insulator-Semiconductor, SIS Solver

The probability that an electron with energy E tunnels through the barrier was

determined by solving the Schrodinger equation using the transfer matrix method

(TMM) [94]. TMM [98-100] found the solution to the equation by discretizing the

device band profile and computing the transfer matrix, which contained potential

energy and effective mass. Regarding quantum mechanical tunnelling, because it is

treated as a wave, the tunnelling process can be assumed to be elastic. The current

density through the barrier was calculated using the equation 3.6 by SILVACO's SIS

solver.

The Non-local Quantum Barrier Tunnelling Model demonstrated SIS in SILVACO

ATLAS. Using SIS, the simulator calculated the tunnelling current between two

semiconductor regions separated by a potential barrier [101-103]. Previously, it was

assumed that the charge passed through the entire barrier with the source or sink at

the semiconductor regions' interface. To incorporate the model into the simulator, the

Model statement required the definition of "sis.el sis.ho" to enable direct electron

quantum tunneling through an insulator between two semiconductor regions.

Because the devices under investigation were doped with n-type carriers, SIS.EL was

used to simulate electron tunnelling. In the event of insufficient convergence, the

Model statement flag SIS.NLDERIVS was activated. This resulted in the incorporation

of non-local couplings into the system matrix. After creating the model, the user must

inform the simulator of the barrier structure's location. The most straightforward

technique is to specify the quantum tunnelling region by including the qtregion

parameter in each Region statement that defines a quantum barrier. It injects

tunnelling current at the interface's precise location and its lower carrier energy side.

The current after the NDR region, where thermal diffusion occurs, was calculated

using the SIS model.

3.3.2. Model Validation

Prior to designing a new structure for an RTD, it is necessary to validate that the

results of physical modelling are consistent with actual RTD measured results. Thus,

physical modelling and validation of fabricated RTD samples should be undertaken.

The RTD sample XMBE#300, fabricated at the University of Manchester [68], has a

mesa size of 1x2 μm

. Its epi-layer structure and material parameters are listed in Table

3.1. As illustrated in Table 3.1, XMBE#300 contains symmetrical spacers. Figure 3.6

illustrates the conduction band of the DBQW RTD sample XMBE#300 at zero bias, and

it is obvious that the emitter and collector regions are heavily doped. The conduction

band at the peak voltage is depicted in Figure 3.7. (0.177V).

The modelled and measured data for the XMBE#300 with a mesa size of 1x2 μm

are

shown in Figure 3.8. The peak current density of the simulated data was 1.2 mA/μm

at 0.175 V. In comparison, the measured data had a peak current density of 1.17

mA/μm

at 0.177 V. The simulated data had a valley current density of 0.191 mA/μm

at 0.295 V. In contrast, the measured data had a valley current density of 0.31 mA/μm

at 0.423 V. PVCR of simulated data was 6.3, which was greater than that of measured

data (i.e. 3.8). The I-V characteristics of the measured and modelled RTDs are shown

in Table 3.2.

Figure 3.7. The conduction band of the RTD sample XMBE#300 at peak voltage (0.177V).

Figure 3.8. The Physical modelling results of the RTD sample XMBE#300

The difference between the measured and simulated valley currents was due to the

software tool's inability to account for the parasitics of the measuring equipment. In

addition, the discrepancy between the modelled and measured values prior to the

peak voltage suggests that the formation of the 2D states in the emitter spacers may

-1

-0.5

0.5

1.5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

Electron Energy (eV)

Thickness (μm)

0.5

1.5

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Current (mA)

Voltage (V)

Measured data

Modelled data

not have been modelled accurately. Another explanation for the difference between

the modelled and measured data could be the self-heating of the device during

processing. Although there was a difference between the physical model and the

measurement of valley current and voltage, which affected the NDC, PVCR, and

maximum output power values, the physical model could be an excellent fit for circuit

design and investigation of other RTD structures.

Table 3.1. The epi-layers and material parameters of the XMBE#300 sample [68].

Layer

Material

Doping

(cm

-3

)

Thickness

(nm)

Bandgap (eV)

Ohmic layer

In0.53Ga0.47As(n++)

2E+19

0.75

Emitter

In0.53Ga0.47As(n+)

3E+18

0.75

Spacer

In0.53Ga0.47As

undoped

0.75

Barrier

AlAs

undoped

1.2

3.15 (direct)

Quantum Well

In0.8Ga0.2As

undoped

4.5

0.5

Barrier

AlAs

undoped

1.2

3.15 (direct)

Spacer

In0.53Ga0.47As

undoped

0.75

Collector

In0.53Ga0.47As(n+)

3E+18

0.75

Ohmic layer

In0.53Ga0.47As(n++)

1E+19

400

0.75

Substrate

InP

Table 3.2.The DC characteristics of the measured and modelled RTDs

(mA)

(V)

(mA)

(V)

|ΔI|

(mA)

|ΔV|

(V)

PVCR

(mS)

max

(μW)

Measured

2.34

0.177

0.619

0.423

1.7

0.246

3.8

Modelled

2.41

0.175

0.381

0.295

2.03

0.12

6.3

3.4. Asymmetrical spacers RTDs with a fixed quantum-well thickness

After validating the physical model of sample XMBE#300, the same structure as in

Table 3.1 was used but with emitter and collector spacer thicknesses ranging from

1nm to 10nm to investigate the effects of asymmetrical spacers on the RTD's DC and

RF characteristics. Only the thickness of the emitter spacer was varied in [104], and

only in 2.5nm steps. Both spacers' thicknesses were varied in this study, with a 1nm

step. This step was performed in small steps to demonstrate clearly that increasing the

thickness of the emitter spacer decreases peak voltage while maintaining the

oscillation frequency and increasing the thickness of the collector spacer increases

peak voltage while decreasing the oscillation frequency.

3.4.1. DC characteristics

This section will demonstrate how the thickness of the emitter and collector spacer

affects RTD performance in terms of peak voltage, peak current, peak-to-valley

current ratio, negative differential conductance, and maximum dc output power.

- Peak Voltage (VP)

Increasing the thickness of the emitter spacer while maintaining a thin collector spacer

resulted in a low peak voltage. In contrast, RTDs with a thick collector spacer and a

thin emitter spacer had a high peak voltage. As illustrated in Figure 3.9, the peak

voltage of the RTDs with symmetric spacers would be in the moderate range. When

the collector spacer was thicker than the emitter spacer, it appeared that the peak

voltage was increasing, which would result in a significant increase in power

dissipation. This work aims to present RTDs suitable for low DC power consumption

applications; thus, increasing the peak voltage by thickening the collector spacer

would not aid in accomplishing this goal.

Additionally, the voltage span, defined as the difference between the peak and valley

voltages, increased with the thickness of the emitter and collector spacers, but at a

greater rate for thick emitter spacer RTDs than thick collector spacer RTDs. The

voltage span was maximum when both spacers were thick and symmetrical, as shown

in Figure 3.10. When the collector spacer was significantly thinner than the emitter

spacer (e.g. tcs=1nm, tes=10nm), the peak voltage was extremely low, which could result

in low NDC and DC output power. The RTD would not generate enough current to

operate in the NDR region in this case.

Figure 3.9. Effect of Emitter and Collector spacers on the peak voltage

Figure 3.10. The voltage span as the thickness of the collector and emitter spacers varies

- Peak Current (IP)

While thickening the emitter spacer resulted in a lower peak voltage, it also resulted

in a reduction in peak current due to the thickening of the triangular well formed

between the emitter region and the quantum well. As a result, electrons would have

more direct tunnelling into the quantum well than with the thin emitter spacer RTDs.

The Peak current was extremely high when the collector spacer was thicker than the

emitter spacer. However, this condition probably applied until the emitter spacer

thickness reached 3nm. When the thickness of the emitter spacer reached 3nm, the

peak current reached the moderate range, as shown in Figure 3.11. A significant peak

current resulted in increased power dissipation, conceptually similar to a high peak

voltage.

Figure 3.11. Effect of Emitter and Collector spacers on the peak current

- Peak-to-Valley Current ratio (PVCR)

The PVCR varies according to the peak and valley currents. Because the peak current

for thick collector spacer RTDs was high, the PVCR was very high, which could be

due to a decrease in the valley current. On the other hand, RTDs with emitter spacer

thicknesses greater than 2nm would maintain a moderate or slightly higher PVCR.

Such an RTD characteristic demonstrates how critical it is to maintain a moderate or

high PVCR when designing RF circuit amplifiers with microwatt DC power

consumption [105]. Figure 3.12 depicts the PVCR as the thickness of the emitter and

collector spacers changes.

Figure 3.12. Effect of Emitter and Collector spacers on the peak-to-valley current ratio

- Negative Differential Conductance (|Gn|)

NDC was determined by the difference between the peak and valley voltages and

currents; thus, a thick emitter spacer resulted in a low NDC, whereas a thick collector

spacer resulted in a high NDC. As illustrated in Figure 3.13, RTDs with symmetric

spacers of up to 3nm thickness exhibited a high NDC. However, symmetric spacer

RTDs with thicknesses of 8nm exhibited an extremely low NDC. As a result,

asymmetrical spacer RTDs with thicknesses ranging from 3 to 7nm would provide a

moderate NDC, allowing the RTD to operate with a low peak voltage and a moderate

peak current.

Figure 3.13. The NDC as the thickness of the collector and emitter spacers vary

- Maximum DC Output Power (PDC-MAX)

Similarly to NDC, the maximum dc output power (PDC-MAX) is determined by the

difference between the peak and valley voltages and currents, so a thick emitter spacer

resulted in a low PDC-MAX while including a thick collector spacer resulted in a high PDC-

MAX. As shown in Figure 3.14, RTDs with symmetric spacers with thicknesses up to

3nm had a high PDC-MAX. However, symmetric spacers RTDs with thicknesses of 8nm

had a very low PDC-MAX. As a result, asymmetrical spacer RTDs with thicknesses

ranging from 3nm to 7nm would have a moderate PDC-MAX, allowing the RTD to operate

while maintaining a low peak voltage and a moderate peak current.

Figure 3.14. The effect of varying the thickness of emitter and collector spacers on the Maximum DC

Output Power

RTDs with a thicker emitter spacer than a collector spacer (i.e. tcs=1nm, tes=10nm) had

a very low PDC-MAX, which is unsuitable for many RF applications. The NDC and PDC-

MAX could be improved using thin quantum wells. This improvement is attributed to

an increase in peak current, which will be discussed further in the following section.

3.4.2. RF Characteristics

The transport time (



) must be obtained before the RTD capacitance can be

calculated. This characteristic is required for determining whether RTD structures are

suitable for use as terahertz emitters. The transit time through the double barrier

quantum well was calculated using equation 2.12 from the previous chapter. The

transit time through the depletion region was calculated using equation 2.11 from the

previous chapter. To determine the transit time through the depletion region, the

thickness of the collector depletion region must be determined from the simulation

results, as illustrated in Figure 3.15.

Figure 3.15. Extraction of the thickness of the collector depletion region from the simulation results at

peak voltage (0.177V).

-1.5

-1

-0.5

0.5

1.5

0 0.02 0.04 0.06 0.08 0.1 0.12

Electron Energy (eV)

Thickness (μm)

collector depletion

Figure 3.16. The RTD transit time for RTDs with different thicknesses of emitter and collector spacers.

After calculating the RTD transit time and presenting it in Figure 3.16, the capacitance

of the RTD was determined and displayed in Figure 3.17. As illustrated in Figure 3.16

above, increasing the thickness of the emitter spacer seemed to have a minor impact

on the RTD transit time, whereas increasing the thickness of the collector spacer had

a significant effect. This increase was attributed to the increase in transit time through

the collector depletion region. Compared to the RTDs with thicker collector spacer

thicknesses, RTDs with collector spacer thicknesses up to 3nm would have a relatively

short transit time.

As illustrated in Figure 3.17 above, the decrease in RTD transit time have an impact

on decreasing RTD capacitance. When the emitter spacer was less than 3nm thick, and

the collector spacer was less than 5nm thick, the RTD capacitance was substantial

compared to thicker spacers. This was primarily due to the high capacitance of the

depletion region. Reduced RTD capacitance in thick emitter spacer RTDs would

support increased oscillation frequencies. The maximum operating frequency (fMAX)

was calculated using equation 2.16 from the previous chapter. Since the mesa area of

the devices was set to 1x2 μm

in this work, the series resistance of the RTD was

calculated to be 2.7 Ω using equation 2.10 from the previous chapter.

Figure 3.17. The effect of the emitter and collector spacers’ thicknesses on the RTD capacitance

As illustrated in Figure 3.18 below, changing the thickness of the emitter spacer did

not affect the maximum operation frequency, which was due to the short RTD transit

time and small RTD capacitance. On the other hand, due to the high NDC and small

RTD capacitance, very thick collector spacer RTDs would have a high maximum

operating frequency. Compared to other RTDs, RTDs with thin emitter and collector

spacers had larger NDC values, but this did not reflect into a higher maximum

operating frequency. The larger values of RTD capacitance prevented this.

Figure 3.18. The effect of the emitter and collector spacers’ thicknesses on the maximum operating

frequency

Despite the parasitic elements of the diodes that always limit high-frequency

operation, the intrinsic high-frequency limit due to both tunnelling and depletion

region delay times was given by equation 2.17 from the previous chapter. As

illustrated in Figure 3.19, increasing the thickness of the emitter spacer did not affect

the intrinsic limit frequency; however, increasing the thickness of the collector spacer

reduced the intrinsic limit frequency. This was because RTDs with a thick emitter

spacer had a short transit time, whereas RTDs with a thick collector spacer had a long

transit time. Nevertheless, RTDs with a collector spacer of 3nm had a high intrinsic

limit frequency due to their short transit time.

Figure 3.19. The intrinsic limit frequency as the emitter and collector spacers’ thicknesses vary

The maximum dc output power shown in Figure 3.14 was not practical because the

calculated actual RF power would be degraded due to the NDC being reduced and

the RTD transit time being increased. Equation 2.18 from the previous chapter has

been used to calculate the RF actual power for four RTDs: a very thick collector spacer,

a very thick emitter spacer, and symmetric spacers.

As illustrated in Figure 3.20, a thick emitter spacer had a negligible effect on the

oscillation frequency compared to a thick collector spacer. The increase in calculated

actual RF power resulting from the thick collector spacer was insignificant compared

to the decrease in calculated actual RF power as a result of the thick emitter spacer.

Figure 3.20. The actual output power as a function of the frequency for three different RTD structures

According to the previous analysis, RTDs with thick emitter spacers had a higher

operating frequency and a lower peak voltage than RTDs with thick collector spacers.

Since the depletion collector region did not expand, increasing the emitter spacer's

thickness did not affect carrier transit time. Low peak current in RTDs with thick

emitter spacers, on the other hand, resulted in low NDC and output power. RTDs with

a collector spacer of 3nm and an emitter spacer greater than 3nm demonstrated

excellent RF characteristics. As a result, the following two sections will discuss how to

modify RTDs with thick emitter spacers to increase peak current density and NDC

while maintaining a low peak voltage and high operating frequency.

1.E-06

1.E-05

1.E-04

0 200 400 600 800

Actual Output power (W)

Frequency (GHz)

tes=1nm, tcs=10nm

tes=10nm, tcs=1nm

tes=1nm, tcs=1nm

3.5. Asymmetrical spacers RTDs with varying quantum-well thickness

As previously stated, RTDs with thick emitter spacers required additional

modifications to increase the oscillation frequency while maintaining high NDC and

output power. As a result, one of the proposed modifications was to reduce the

quantum well's thickness. As mentioned in Section 2.5.2, decreasing the quantum well

thickness increases the current density, the NDC, and the maximum dc output power.

Several studies have found that decreasing the quantum well thickness increases the

oscillation frequency. Professor Asada's group reported that by reducing the quantum

well thickness of their asymmetrical spacers RTD from 4.5nm to 3.9nm and the barrier

thickness from 1.4nm to 1nm, they could increase the oscillation frequency to 1.31 THz

[19]. This increase was attributed to the carriers' transit time through the double

barriers quantum well (



) decreasing. By decreasing the quantum well thickness

from 3.9nm to 3nm, the oscillation frequency was increased to 1.42 THz with the help

of the reduced area and capacitance [106]. Further reduction in the quantum well

thickness (from 3nm to 2.5nm) resulted in an increase in the oscillation frequency to

1.92 THz [107].

All of these studies, however, used RTDs with thick collector spacers. Therefore, in

this section, RTDs with emitter spacers thicknesses ranging from 3nm to 10 nm were

investigated, with the quantum well thickness (tw) varying from 4.5nm to 2.5nm and

the emitter spacer thickness (tes) varying from 3nm to 10nm. As mentioned previously,

the collector spacer thickness (tcs) was 3nm because it demonstrated excellent RF

characteristics. Table 3.3 depicts the epi-layer structure of the investigated RTDs. The

DC and RF characteristics will be discussed in less detail than in the previous section

because the main topic of this section is the effect of varying the thickness of the

quantum well of the asymmetrical spacers RTDs.

Table 3.3. The epi-layers and material parameters of the proposed asymmetrical spacers RTDs with

varying the thicknesses of the emitter spacer and the quantum well

Layer

Material

Doping

(cm

-3

)

Thickness

(nm)

Bandgap (eV)

Ohmic layer

In0.53Ga0.47As(n++)

2E+19

0.75

Emitter

In0.53Ga0.47As(n+)

3E+18

0.75

Spacer

In0.53Ga0.47As

undoped

tes

0.75

Barrier

AlAs

undoped

1.2

3.15 (direct)

Quantum Well

In0.8Ga0.2As

undoped

0.5

Barrier

AlAs

undoped

1.2

3.15 (direct)

Spacer

In0.53Ga0.47As

undoped

0.75

Collector

In0.53Ga0.47As(n+)

3E+18

0.75

Ohmic layer

In0.53Ga0.47As(n++)

1E+19

400

0.75

Substrate

InP

3.5.1. DC characteristics

The thick emitter spacer reduced the peak voltage of the RTDs with fixed quantum

well thickness. However, the peak voltage increased when the quantum well

thickness was reduced, as shown in Figure 3.21. This rise resulted from an increase in

the first resonant energy level. In terms of current density, RTDs with thin quantum

wells had higher current densities than RTDs with thicker quantum wells, as shown

in Figure 3.22. This increase was caused primarily by an increase in the transmission

coefficient.

Figure 3.21. The peak voltage (VP) of 1X2μm

asymmetrical spacers RTDs with varying the thickness

of the emitter spacer and the quantum well

Figure 3.22. The peak current (IP) as the thickness of the emitter spacer and the quantum well vary

Figure 3.23. Effect of varying the thickness of the Emitter spacer and the quantum well on the peak-to-

valley current ratio

RTDs with thick emitter spacers had lower current densities than RTDs with thin

emitter spacers. Due to the decrease in the separation between adjacent resonant

energy levels, the leakage current components through the second resonant energy

level would decrease. Thus, the PVCR would decrease, as shown in Figure 3.23.

Because current densities are lowered, the PVCR of RTDs with thick emitter spacers

and thick quantum wells was the lowest. The NDC and maximum dc output power

increased as current densities increased, as illustrated in Figures 3.24 and 3.25. Even

with thick emitter spacers, thin quantum well RTDs could achieve a high NDC and

output power. Due to their high NDC and output power, RTDs with thin quantum

wells are excellent for terahertz emitters in high-frequency applications.

Figure 3.24. The effect of varying the thickness of the emitter spacer and quantum well on the NDC

with 1X2μm

RTD mesa area.

Figure 3.25. The effect of varying the thickness of the emitter spacer and quantum well on the

Maximum DC Output Power with 1X2μm

RTD mesa area.

3.5.2. RF Characteristics

As mentioned previously, because the series resistance was fixed in this work (as the

mesa area was fixed), the oscillation frequency depends only on the RTD capacitance

and the NDC. The capacitance of the RTD is affected by the transit time and the

capacitance of the depletion layer. As illustrated in Figure 3.26, the transit time

decreased due to the reduced transit time through the double barrier quantum well

region and the collector depletion region.

Despite the decrease in transit time, the capacitance of the RTD increased as the

quantum well thickness decreased, as illustrated in Figure 3.27. This increase resulted

from the depletion region capacitance and quantum capacitance increasing. Quantum

capacitance increased due to the high NDC.

Figure 3.26. The change in the RTD transit time as the thickness of the emitter spacer and the

quantum well change

Figure 3.27. The effect of thinning the quantum well and thickening the emitter spacer on the RTD

capacitance

The RTDs with a thin quantum well of 2.5nm and a 10nm emitter spacer may have a

small RTD capacitance and a moderately short transit time, allowing these RTDs to

operate at the highest possible operating frequency, as illustrated in Figure 3.28. While

the thin quantum RTDs with a thin emitter spacer thickness was expected to have the

highest maximum operating frequency due to their high NDC, their operating

frequency was degraded due to their high RTD capacitance values. It appears as

though using a very thick emitter spacer thickness improved their operating

frequencies for all quantum well thicknesses, as illustrated in Figure 3.28.

Figure 3.28. The effect of varying the thickness of the quantum well and the emitter spacer on the

maximum operating frequency

Figure 3.29. The effect of thinning the quantum well and thickening the emitter spacer on the intrinsic

frequency limit

Figure 3.29 above depicts the effects of varying the thickness of the emitter and

collector spacer on the intrinsic frequency limit.

Due to the excellent performance of all quantum well thicknesses when combined

with a very thick emitter spacer (i.e. 10nm), their calculated actual RF power was

calculated to demonstrate their capability to provide high RF output power at high

frequency. The very thin quantum well RTDs (i.e. tw=2.5nm) had the highest

frequency. They could potentially deliver 1mW at frequencies as high as 630 GHz, as

illustrated in Figure 3.30. The RTDs with thick quantum wells (tw=4.5nm) had the

lowest output power and operating frequency.

Figure 3.30. The actual output power as a function of the frequency for thin quantum well RTDs with

very thick emitter spacers and 1X2μm

RTD mesa area

Even though the thin quantum wells had a high NDC, a high maximum dc output

power, and a high PVCR, their peak voltage and current increased, resulting in

increased power dissipation. Additionally, the RTD transit time decreased when

using a thinner quantum well. However, the RTD capacitance increased due to an

increase in the depletion region and quantum well capacitances. These findings

affected the maximum operating frequency of RTDs with thin quantum wells and

emitter spacers. In terms of other RF characteristics, decreasing the quantum well's

thickness increased the intrinsic limit frequency and calculated actual RF power.

According to the analysis in this section, the thin quantum well RTDs had excellent

DC and RF characteristics when the emitter spacer was as thick as 10nm. However,

4.E-06

4.E-05

4.E-04

4.E-03

0 200 400 600 800 1000

Actual Output power (W)

Frequency (GHz)

tcs=3nm, tes=10nm, tw=2.5nm tcs=3nm, tes=10nm, tw=3.5nm

tcs=3nm, tes=10nm, tw=4.5nm

the peak voltage must be reduced further to make it suitable for low-power

applications. The following section will discuss another modification to the RTD

structure that will further reduce the peak voltage.

3.6. Asymmetrical spacers RTDs with deep and thin quantum-wells

While RTDs with thin quantum wells and a thick emitter spacer could have a higher

NDC and output power, their peak voltage and current are also high, resulting in

increased power dissipation. Additionally, a higher peak voltage may reduce the

efficiency of the RTD by creating a strong electric field in the collector spacer layer. As

a result, additional modifications to asymmetrical spacer RTDs should be proposed to

decrease the peak voltage and increase RTD efficiency. Kanaya et al. hypothesised that

a deep well filled with indium-rich InGaAs could reduce the peak voltage due to the

quantum well bottom's depression [108]. The layer structure and band diagram of the

asymmetrical spacers RTDs proposed in [108] are depicted in Figure 3.30.

As illustrated in Figure 3.31, the emitter spacer is thicker (25nm) than the collector

spacer (i.e. 2nm). The oscillation frequency of the asymmetrical spacer RTD with a

deep and thin quantum well was 1.27 THz, while the asymmetrical spacer RTD

without a deep and narrow quantum well oscillated at 0.96 THz. The oscillation

frequency increase was attributed to the short dwell time and low RTD capacitance.

This section will investigate RTDs with a 3nm collector spacer and a 10nm emitter

spacer with deep and thin quantum wells. The Indium (In) composition in the InGaAs

quantum well varied between 0.8 and 0.95, and the quantum well thickness varied

100

between 4.5nm and 2.5nm. Table 3.4 illustrates the epi-layers structure of the modified

asymmetrical spacers RTD.

Figure 3.31. The epi-layer structure and the band diagram of the asymmetrical spacers RTD with deep

and thin quantum well reported in [108].

Since some of the DC and RF characteristics, such as NDC, maximum dc output

power, and intrinsic limit frequency, were improved by using thin quantum wells,

this section will focus exclusively on the DC and RF characteristics that required

improvements, such as peak voltage and current, transit time, RTD capacitance, and

maximum operating frequency.

101

Table 3.4. The epi-layers and material parameters of the modified asymmetrical spacers RTDs with

varying the thicknesses of the emitter spacer and Indium composition (x) in the quantum well

Layer

Material

Doping

(cm

-3

)

Thickness

(nm)

Bandgap (eV)

Ohmic layer

In0.53Ga0.47As(n++)

2E+19

0.75

Emitter

In0.53Ga0.47As(n+)

3E+18

0.75

Spacer

In0.53Ga0.47As

undoped

0.75

Barrier

AlAs

undoped

1.2

3.15 (direct)

Quantum Well

InXGa1-X2As

undoped

Eg(x)

Barrier

AlAs

undoped

1.2

3.15 (direct)

Spacer

In0.53Ga0.47As

undoped

0.75

Collector

In0.53Ga0.47As(n+)

3E+18

0.75

Ohmic layer

In0.53Ga0.47As(n++)

1E+19

400

0.75

Substrate

InP

102

Figure 3.32. The effect of increasing the Indium composition in the quantum well on the peak voltage

of RTDs with various quantum well thicknesses

Figure 3.33. The peak current of asymmetrical spacers RTDs as the quantum well thickness and the

Indium composition vary

103

As shown in Figure 3.32 above, increasing the indium content in the quantum well

decreased the peak voltage point due to the material's narrow bandgap. For instance,

when the Indium composition was increased from 0.8 to 0.95, the peak voltage of

RTDs with a 2.5nm quantum well decreased from 0.83 V to 0.39 V. Additionally, RTDs

with quantum wells larger than 3.5nm had peak voltages less than 0.2 V, making them

suitable for ultra-low power consumption applications.

As with the peak voltage, the peak current has been reduced as the indium

composition has increased, as illustrated in Figure 3.33.

When the Indium composition was 0.95, only the RTDs with a 2.5nm quantum well

had a peak current greater than 10mA. In contrast, the other RTDs had much lower

peak currents. Peak current decreased rapidly for the same quantum well thickness;

for example, when the Indium composition was increased from 0.8 to 0.95, the peak

current of RTDs with a 2.5nm quantum well decreased from 37mA to 15mA. Because

the peak current decreased, it was expected that the PVCR would decrease as well.

Appendix B includes a figure illustrating the effect of increasing the Indium content

on the PVCR, as the PVCR is not the subject of this section.

As shown in Figure 3.34, the RTD transit time decreased as the Indium composition

increased, owing to the decrease in dwell time. For example, when the Indium

composition was increased from 0.8 to 0.95, the RTD transit time decreased from 283

fs to 237 fs.

104

Figure 3.34. The change in the RTD transit time as the thickness of the quantum well and the Indium

composition change

As illustrated in Figure 3.34, this decrease in the RTD transit time decreased the RTD

capacitance values. For example, when the Indium composition was increased from

0.8 to 0.95, the capacitance of RTDs with a 2.5nm quantum well decreased from 30 fF

to 19 fF. The decrease in RTD capacitance was caused by a decrease in both the RTD

transit time and the quantum capacitance. The decrease in quantum capacitance was

anticipated as the NDC decreased with increasing Indium composition. The NDC

decreased primarily as a result of low peak currents. Appendix B contains a graph

illustrating the effect of increasing the Indium content on the NDC.

105

Figure 3.35. The RTD capacitance of asymmetrical spacers RTDs as the quantum well thickness and

the Indium composition vary

As illustrated in Figure 3.35, the decrease in the RTD capacitance and the NDC

decreased the maximum operating frequency. This decrease could be avoided by

using quantum wells that are thinner and deeper. For example, RTDs with a 3.5nm

and 0.85 Indium composition had a maximum operating frequency of 591 GHz, which

was reduced to 530 GHz when the Indium composition was increased to 0.95;

however, using a thinner quantum well with a higher Indium concentration (i.e.

tw=3nm and x=0.9) increased the operating frequency to 630 GHz. Inevitably, as

transit times decreased, the intrinsic limit frequency increased. Appendix B includes

a figure demonstrating the effect of increasing the Indium content in the quantum well

on the intrinsic limit frequency.

106

Figure 3.36. The effect of varying the thickness of the quantum well and the Indium composition on

the maximum operating frequency

In terms of calculated actual RF power, increasing the Indium content reduced

calculated actual RF power. However, it increased oscillation frequency, as illustrated

in Figure 3.36. For example, when the Indium composition was increased from 0.8 to

0.85 and the oscillation frequency was increased from 774 to 791 GHz, the calculated

actual RF power of the RTDs with a 4nm quantum well decreased from 82 μW to 30

μW. As discussed previously, decreasing the quantum well thickness increased the

oscillation frequency and calculated actual RF power, as illustrated in Figure 3.36

when the quantum well thickness was reduced from 4nm to 3.5nm with a fixed

indium composition of 0.85. To increase the RF actual and oscillation frequency, the

Indium content should be increased, and the quantum well thickness should be

reduced. For instance, when the quantum well thickness was reduced from 3 to 2.5nm

107

and the Indium composition was increased from 0.9 to 0.95, the oscillation frequency

increased from 900 to 1055 GHz, and the calculated actual RF power increased from

312 to 963 μW.

Figure 3.37. The calculated actual RF power of RTDs with different quantum well thicknesses and

different Indium compositions

After discussing performance optimization for asymmetrical RTDs, this analysis

designed and examined RTD structures that exhibit excellent DC and RF

characteristics for various applications. Asymmetrical spacer RTDs with a 2.5nm

quantum well and a 0.95 Indium composition could produce 0.5 mW at a high

frequency of 690 GHz. These RTDs had a low peak voltage and a moderate peak

current while operating at frequencies greater than 1 THz. They also had a small RTD

capacitance and a significantly shorter RTD transit time. Not only high output power

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

0 200 400 600 800 1000 1200

Output power (W)

Frequency (GHz)

tw=2.5nm, x=0.95 tw=3nm, x=0.9 tw=3.5nm, x=0.85

tw=4nm, x=0.85 tw=4nm, x=0.8

108

RTDs, which are excellent candidates for use as THz emitters, but also RTDs with

relatively low peak voltages and currents while maintaining a high PVCR have been

designed, making them suitable for ultra-low power consumption applications.

3.7. Summary

This chapter began by summarising the pertinent literature on asymmetrical spacers

RTDs. Then, the SILVACO ATLAS simulation tool was discussed, which was used in

this chapter. Additionally, the two models utilised in this chapter were discussed. The

physical model was then validated using experimental data. The slight difference

between the simulated and measured data was caused by the simulation tool's

inability to simulate the measurement equipment’s parasitic effects and by the

inaccurate modelling of the formation of the 2D states in the emitter spacers. Another

explanation for the difference between the modelled and measured data could be the

self-heating of the device during processing. To demonstrate that increasing the

collector spacer thickness increases the peak voltage, thereby increasing power

dissipation, while decreasing the emitter spacer thickness decreases the peak voltage,

the thickness of the two spacers was varied between 1nm and 10nm. Although the

thick emitter spacer RTDs had low peak voltages, a large PVCR, a higher oscillation

frequency, a short RTD transit time, and a small RTD capacitance, their NDC and

output power were reduced.

Thus, to increase the NDC and output power, the quantum well thickness varied

between 4.5nm and 2.5nm. The emitter spacer thickness varied between 3nm and

109

10nm. The collector spacer thickness was maintained at 3nm. Although thin quantum

well RTDs had a high NDC, a large PVCR, a high output power, and a shorter RTD

transit time, they had a lower operating frequency, a larger RTD capacitance, and a

high peak voltage and current. The RTD structure was further modified by increasing

the amount of Indium in the quantum well. This modification decreases the peak

voltage and current and the oscillation frequency, the RTD transit time, and the RTD

capacitance. This chapter discussed RTDs suitable for high output power radio

frequency (RF) applications and RTDs suitable for low power or ultra-low power

radio frequency (RF) applications. Finally, this chapter's objective was to introduce

asymmetrical spacer RTDs and optimise their performance for various applications.

The following chapter will demonstrate the RTDs' performance in low-power

applications.

110

4. CHAPTER 4: DESIGN AND ANALYSIS OF 10 GHz RTD

BASED AMPLIFIER FOR WIRELESS COMMUNICATIONS

4.1. Introduction

In previous chapters, a thorough review of the literature and physical modelling of

resonant tunnelling diodes was conducted to establish the suitability and utility of the

tunnelling devices for microwave and THz applications. As a result, chapter four

focuses on the design and performance analysis of a narrow-band amplifier for

wireless communication systems that use resonant tunnelling diodes (RTDs). This

includes the design of passive components such as capacitors and spiral inductors and

their modelling. Additionally, this chapter summarises the pertinent literature

regarding RTDs as power amplifiers. It is critical to understand the fundamental

operation of reflection-based RTD power amplifiers before designing and analysing

such a device. The study's primary outcome is the realisation of a low-power DC

amplifier operating at 10 GHz. All design and analysis in this chapter were carried out

using the Advanced Design System (ADS) software tool.

4.2. Power amplifications using the resonant tunnelling diodes (RTDs)

Due to the RTD's unique negative differential conductance (NDC), transmission line

losses can be compensated for and used to provide gain. An RTD amplifier can be

realised in two circuit topologies: active transmission line amplifier or reflection-based

amplifier. The first attempt to use tunnel devices in conjunction with Field-Effect

111

Transistor (FET) amplification was made in 2003 [109]. The dc power output was

400μW with less than 5 dB gain. A group of researchers developed several RTD

amplifiers with high gain and excellent RF performance at frequencies around 5 GHz

[110-114]. Professor Missous and his group presented a modelling and theoretical

analysis of a high gain InGaAs/AlAs RTD reflection-based amplifier operating in the

K band in 2017 [115]. The amplifier achieved a gain of 32 dB with a very low DC power

consumption of 100 μW.

Due to the losses of the transmission lines (TLs), the RF signals propagating through

the active transmission line amplifier undergo a phase shift. As a result, we use

reflection-based amplifiers because they significantly reduce noise performance and

chip size.

The design steps for the RTD amplifier are comparable to those presented in [46, 115];

however, the main circuit was modified in this research to be consistent with the

amplifier circuit described in the literature. In addition, the operating frequency and

RTD sample are clearly different. Furthermore, this work presents the layout design

of the RTD amplifier and compares the results of the schematic simulation to the

layout design results, whereas [46, 115] only presented schematic results.

4.3. Principle operation of reflection-based RTD amplifier

In the reflection-based amplifier, the RF signal is reflected at appropriately terminated

ports to maintain a high gain at the output terminal. The RTD amplifier, as depicted

in Figure 4.1, comprises a single branch coupler and two similar RTDs. It is crucial to

112

explain the essential operation and critical factors of the branch coupler. First, the

signal is fed into the input port, and then it is split into two ports that are 90

degrees

out of phase. The signal is then reflected by the bypass capacitor CbP due to the

amplified signal (due to the NDR).

Figure 4.1. Schematic circuit of the RTD reflection-based amplifier model

The RTD port signals can then be merged in phase at the output port with a phase

difference of 270

degrees relative to the input signal at the input port. Furthermore,

because the reflected amplified signals are 180

degrees out of phase at the input port,

they cancel one another out [116]. To eliminate parasitic oscillations at low

frequencies, a bypass capacitance serves as a short circuit at undesirable frequencies

[114]. The magnitude of the reflection coefficient between the coupler and the RTDs is

used to define the amplifier's voltage gain as follows:



















(4.1)

113

Because the two RTDs are charged at the coupler termination and operated in their

NDR region, the reflection in equation (4.1) will be greater than one. To mitigate

mismatching losses, the values of these impedances must be nearly identical. The

reflection-based amplifier is used because there is no requirement for a large matching

circuit. This is primarily because the output impedance of a single coupler depends

on the component values. As a result, the components of the single coupler can be

tuned to match the RTD's impedance (ZRTD). A coupler based on lumped elements has

been developed for MMIC application [117]. Before designing the RTD amplifier

circuit, it is necessary to discuss the software tool used in this chapter, ADS. The

following section will provide a brief overview of this software tool.

4.4. Advanced Design System (ADS) software tool

Advanced Design System (ADS) is the most comprehensive and user-friendly

electronic design automation tool available for high-frequency and high-speed

products [118]. Keysight Technologies boasts the industry's broadest support, with

over one hundred foundry processes supported by ADS. Additionally, it is the

primary design tool used by all major integrated circuit suppliers. The following are

brief descriptions of the two types of analysis performed by ADS in this chapter:

a. S-parameter simulation

Using the Simulation S-Param palette's S-parameter simulation controller (S-

Parameters), you can:

114

- Obtain the scattering parameters (S-parameters) of a component, circuit, or

subnetwork and convert them to Y- or Z-parameters.

- Plot the variations in swept-frequency S-parameters with another changing variable.

- Create simulations of group delay or linear noise.

- Simulate the effects of frequency conversion on the S-parameters of a mixer-based

circuit. (This is also referred to as frequency-translating network analysis.)

Additionally, the Simulation-S Param palette contains components for general

simulation and sweep options and a variety of measurement components for

calculating pertinent measurements.

b. Harmonic balance simulation (HB)

Harmonic balance is a high-precision frequency-domain analysis technique used to

determine the steady-state solution of nonlinear circuits and systems. It is frequently

used to simulate analogue RF and microwave problems in the frequency domain.

After calculating the steady-state solution, the harmonic balance simulator can be

used to perform the following tasks:

- Calculate third-order intercept (TOI) points, total harmonic distortion (THD), and

intermodulation distortion components.

- Analyse the load-pull contours of power amplifiers.

- Analyse nonlinear noise.

115

The harmonic balance method assumes that the input stimulus is composed of a small

number of steady-state sinusoids. As a result, the solution is a sum of steady-state

sinusoids that includes both the input and any significant harmonics or mixing terms.

ADS electromagnetic (EM) simulation is a 2.5D model based on a 2D component

layout that can display a three-dimensional viewpoint of radio frequency current flow

in transmission lines and far-field radiation patterns. Additionally, the EM simulation

tool can account for transmission line coupling. This results in a module that is more

accurate and can be easily expanded to anticipate the performance of the circuit even

before to fabrication and actual results [118]. Indeed, the EM model includes two main

simulators: momentum RF and momentum microwave, which were used in this

study. This is because of the fact that this mode employs full-wave Green's functions,

which are frequency-dependent and account for ground plane losses in the prime

elements resulting from high-frequency operation. Following these steps, momentum

was established. Due to the fact that the simulator divides transmission lines into

small cells during the simulation process, the mesh with the highest simulation

frequency was chosen. This insures that the mesh density of cells per wavelength is

sufficient, which leads to improved simulation performance. The sole disadvantage of

a high density mesh is that the simulation process takes longer to execute. The

conductor, dielectric, and lossy layers' electrical and physical parameters, such as

dimensions, conductivity, and relative permittivity, were defined in the simulator. For

the configuration of coplanar waveguides, a finite substrate thickness was used. The

116

model is evaluated without a ground plane at the back of the structure. This eliminates

effectively the parasitics associated with grounded coplanar structures (GCPW). This

simulation used a 625 μm thick semi-insulating InP substrate with a 



of 12.5 and a

loss tangent () as low as 0.002 [119].

4.5. Modelling of Single branch coupler

A branch coupler comprises four microstrip lines, two of which have identical

impedance as the input and output ports. The other two ports' impedance is typically

expressed as 







 [120, 121]. Two critical parameters should be considered when

describing a branch coupler: the coupling factor (CF) and the directivity (Dcoupler),

which are specified in [122]:











(4.2)















(4.3)

where P1, P2, and P3 are denoted as the input power to port 1 and the output power

from ports 2 and 3, respectively.

To ensure an even power distribution between ports 3 and 4, the coupling factor (CF)

must be set to 3 dB. Couplers suitable for this application typically have a directivity

of 30-35 dB, which is critical to ensuring that the output power at port 2 is small

compared to the output power at port 3 [122]. An ADS model was created using ideal

transmission lines at a 10 GHz operating frequency to investigate the coupler

response, as illustrated in Figure 4.2.

117

Figure 4.2. The model of a single branch coupler with ideal transmission lines

Figure 4.3. The result of S-parameter simulation for single branch coupler modelled in ADS using

ideal transmission lines at 10 GHz

Because each term must produce a π/2 phase shift for the coupler to operate properly,

the electrical length was set to 90

. The simulation results indicate that the input power

-80

-60

-40

-20

5 6 7 8 9 10 11 12 13 14 15

S-Parameter Response (dB)

Frequency (GHz)

S(1,1) S(2,1)

S(3,1) S(4,1)

118

is evenly distributed between ports 3 and 4. A centre frequency of 10 GHz provides a

large 10dB bandwidth (i.e. 3.3 GHz), as illustrated in Figure 4.3. The reflection

performance at port 1 (S11 =-76.4 dB) and the received power at port 2 (S21 =-76.4 dB)

are excellent, as they are significantly less than -10 dB. In practice, such values are

difficult to achieve due to the effect of losses and parasitic, which are ignored at this

stage.

The single branch coupler was modelled using LC passive elements to model the

single branch coupler in its practical configuration, as illustrated in Figure 4.4 below.

Figure 4.4. The LC model of single branch coupler operating at 10 GHz using ADS software

These elements must be carefully adjusted to achieve a coupling factor of

approximately 3 dB and a directivity greater than 30 dB. As Figure 4.5 shows, the

coupler's performance is relatively similar to that of the first coupler with ideal

transmission lines.

119

Figure 4.5. The result of S-parameter simulation for single branch coupler modelled in ADS using LC

components at 10 GHz

The coupling factor and directivity can be determined as follows from the results of

S-parameter responses:











(4.4)













 





(4.5)

At operating frequency (i.e. 10 GHz), the coupling factor and directivity were

calculated to be 3 dB and 63.5 dB, respectively, contributing to the coupler's circuit's

excellent performance. Both S11 and S21 exhibit responses significantly less than -10 dB,

and the branch coupler exhibits a 3 dB power split. The mathematical formula for the

values of the LC elements in Figure 4.4 is:



















(4.6)

-80

-60

-40

-20

5 6 7 8 9 10 11 12 13 14 15

S-Parameter Response (dB)

Frequency (GHz)

S(1,1) S(2,1)

S(3,1) S(4,1)

120













(4.7)

























(4.8)

These equations hold only if all ports have a resistance of 50Ω. The values of the

lumped elements are shown in Table 4.1, and they are quite small.

Table 4.1. Values of LC elements in the LC single branch coupler

Component

Value

CS1

450 fF

CS2

450 fF

CP1

318 fF

CP2

318 fF

330 pH

Coupler dimensions should be scaled down as the frequency increases due to the

decrease in the values of the LC elements. The LC single coupler is preferred up to a

specific frequency because the unavoidable parasitics are much smaller than the actual

circuit elements. Beyond this frequency, another design, such as a directional coupler

based on a co-planar waveguide, would be required. Otherwise, a multilayer MMIC

121

coupler may be required as proposed for wide-band amplifiers up to 60 GHz [121].

The next step is to design the amplifier circuit, including the single coupler and the

RTD, and evaluate the RTD amplifier's ability to provide the required gain and

functionality.

4.6. Simulation of RTD amplifier

This section discusses modelling a 10 GHz reflection-based amplifier using

InGaAs/AlAs NDR RTDs. The RTD sample XMBE#300, whose epi-layers structure

shows in Table 3.1, with a mesa area of 4x4 μm

, was chosen due to its low current

density (i.e. 1.17 mA/µm

). The large mesa area device was used to ensure that large

devices can also achieve a high gain at the output port while consuming little DC

power. This section discusses the extraction of the RTD resistance and capacitance.

Additionally, the passive components in the RTD amplifier circuit are modelled. The

final part will compare the results of the RTD amplifier's schematic and layout design.

4.6.1. Extraction of the RRTD and CRTD

Due to the absence of a representation block for the RTD in the ADS software tool, the

equivalent circuit for the RTD, as illustrated in Figure 4.6, should be used for circuit

analysis.

122

Figure 4.6. The equivalent circuit of the intrinsic RTD

Due to the difficulty of extracting equivalent circuit components from large area

device measurements in the NDR region, as stated in [46], the measured I-V

characteristics are fitted with a 3

degree polynomial function to obtain the RRTD

illustrated in Figure 4.7 below. The excellent agreement between the measured and

fitted data is illustrated in Figure 4.7. The modelled RRTD is calculated using the

relationship 



, as illustrated in Figure 4.7. To calculate the RTD

capacitance, the pre-peak and pre-valley measured points are used to calculate the

CRTD in the NDR region, as illustrated in Figure 4.8. When the bias voltage is 0.35 V,

the extracted RRTD is -100Ω, and the extracted CRTD is 100 fF. The calculated series

resistance is 0.5Ω.

123

Figure 4.7. Measured and fitted forward I-V characteristics as well as extracted junction resistance of

the RTD XMBE#300 with a 16μm

mesa size

Figure 4.8. Extraction of the RTD capacitance from the measured S-parameters

-100

-80

-60

-40

-20

100

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Junction Resistance (

Ω)

Current (mA)

Voltage (V)

Measured data

Fitted data (Polynomial function)

100

120

140

160

180

0.1 0.15 0.2 0.25 0.3 0.35 0.4

Capacitance (fF)

Voltage (V)

124

The intrinsic device's actual S11 value lies outside the normalized Smith chart's unit

circle (|S11 > 1|), or it is greater than 0dB on the x-y graph, indicating that the reflected

power is greater than the incident power, as illustrated in Figure 4.9.

Figure 4.9. Left and right sides: measured S11 for intrinsic device sample #300 with a mesa area of

4×4μm2 biased in the NDR region plotted in smith chart and x-y graph, respectively.

This is because the RTD has a negative resistance, indicating that it can generate power

at the measured frequencies.

Because the input impedance of the RTD sample XMBE#300 (RRTD=-100Ω) is different

from the standard 50Ω, the LC components of the single coupler had to be carefully

optimised. For effective operation of the RTD amplifier circuit, the single branch

coupler's inductance should be between 510 and 610pH, and its capacitance should be

between 80 and 261fF.

To characterise the performance of the typical lumped-element hybrid coupler, which

consists of four spiral inductors and four MIM capacitors, a resistance of 100Ω and a

125

capacitance of 100fF were used in place of the RTDs on ports 3 and 4. S-parameters for

the designed coupler are depicted in Figure 4.10.

Figure 4.10. The result of S-parameter simulation for single branch coupler modelled in ADS using LC

components with a resistance of 100Ω and a capacitance of 100fF at 10 GHz

At the design frequency of 10 GHz, the coupler had return losses (S11) and isolations

(S21) of -44dB and -14.75dB. Transmission (S41) and coupling (S31) were simulated at -

4.53dB and -2.2dB, respectively.

4.6.2. Schematic circuit of the RTD amplifier

Before modelling the RTD amplifiers' passive components, a schematic circuit similar

to that shown in Figure 4.1 was designed using a single coupler and the RTD's

equivalent circuit. This procedure was performed to ensure that the RTD amplifier

could operate at 10 GHz. The RTD amplifier's schematic circuit is shown in Figure

4.11, and the LC components used in this circuit are listed in Table 4.2. Figure 4.12

-50

-40

-30

-20

-10

5 6 7 8 9 10 11 12 13 14 15

S-Parameter Response (dB)

Frequency (GHz)

S(1,1) S(2,1)

S(3,1) S(4,1)

126

illustrates the gain and S11 values obtained from the schematic circuit. At a frequency

of 10 GHz, the gain was 14.6dB, and S11 was -16.2dB. A 1.32 GHz 3dB bandwidth was

obtained. Between 9.9 GHz and 10.1 GHz, the amplifier's S11 was less than -10dB.

Figure 4.11. The schematic circuit of the reflection-based amplifier built-in ADS shows two RTDs with

an LC branch coupler

Table 4.2.Values of LC elements in the schematic RTD amplifier circuit

Component

Value

243 fF

CP1

80 fF

CP2

261 fF

510 pH

610 pH

Cbp

5 pF

127

Figure 4.12. The gain and return loss of the RTD amplifier schematic circuit using RTD sample

XMBE#300 with a mesa area of 4X4 μm

over the X-band

4.6.3. Modelling of circuit passive components

Passive components can be used in electronic circuits for various functions, including

biasing, DC blocking, and matching circuits. These components are responsible for

determining the output power, bandwidth cut-off frequency, and other critical

characteristics of the electronic circuit system. They are critical in the Microwave

Monolithic Integrated Circuit (MMIC) technology, allowing passive components and

RTD devices to coexist on the same substrate. Furthermore, the fabrication process

heavily influences the performance of passive components. To avoid significant

inconsistencies between the fabricated and designed circuits, a precise physical design

of these components that considers all parasitic elements should be obtained. The

passive components, which are metal-insulator-metal (MIM) capacitors and spiral

-20

-10

8 9 10 11 12

S-Parameter Response (dB)

Frequency (GHz)

S(1,1)

Gain

128

inductors, are modelled and simulated in ADS in this work. They are then used to

construct the layout of an RTD amplifier. The steps for designing MIM capacitors and

spiral inductors are similar to those described in [46, 57]; however, in this work, the

passive components are only designed and compared to the equivalent circuit results.

The work described in [46, 57] designed and fabricated passive components, and then

compared the measurements to the design results.

- Metal-Insulator-Metal (MIM) capacitors

The capacitance of passive components is defined as their ability to store charge,

which determines their impedance to radio frequency signals. The capacitors can be

charged and discharged to pass RF signals. Interdigital capacitors and metal-

insulator-metal (MIM) capacitors are the two types of capacitors used in MMIC

circuits. The interdigital capacitors rely on the fringing capacitance, which is limited

to one pF [120]. On the other hand, MIM capacitors have a structure that consists of a

dielectric layer sandwiched between two relatively large metal plates, as shown in

Figure 4.13.

Many materials, such as silicon nitride (Si3N4) or silicon dioxide, can be used as

dielectric layers (SiO2). Because the thickness and insulation of the dielectric material

can affect the breakdown voltage and high-frequency operation of MIM capacitors,

Silicon Nitride is preferred over Silicon dioxide. Silicon Nitride has a relative dielectric

constant between 7 and 7.5, whereas Silicon dioxide has a dielectric constant of 4.5.

Furthermore, the loss in the MIM capacitor is typically heavily weighted in the

129

dielectric loss tangent of the dielectric material [120]. Silicon Nitride has a loss tangent

of around 0.0003, which is very small compared to other dielectric materials. A lower

loss tangent means lower losses in MIM capacitors, which reduces parasitic losses in

the circuit [120].

Figure 4.13. The schematic of the MIM capacitor: (a) a top view and (b) a cross-section view

Many MIM capacitor models have been studied and demonstrated [123, 124]. As

shown in Figure 4.14, L. Wang et al. reported an equivalent circuit model of the MIM

capacitor [125], which is used in this work. C12 is the main parameter of the equivalent

circuit, and it is calculated using the physical dimensions of the parallel plates of the

capacitor, as well as the type of dielectric material and its thickness, as follows:



















(4.9)

130

where W and L are the length and width of the dielectric material, t is the thickness of

the dielectric material, and 0 and r are the dielectric constant of the free space and the

dielectric material.

Figure 4.14. The equivalent circuit model of the MIM capacitor [125].

Silicon Nitride (Si3N4) with a thickness of 200 nm is used as the dielectric material in

this work. The metal thickness is 1 μm, and the thickness of the InP substrate is 625

μm. The width and length of MIM capacitors used in this work are listed in Table

4.3. The width of the capacitor was larger than the length of the capacitor to reduce

the parasitic resistance and inductance [126].

The capacitance of the dielectric material causes conductance loss, G, which can be

expressed as follows:

 











(4.10)

where tand is the loss tangent of the used insulating material.

131

Table 4.3. The width and length of the MIM capacitors used in this work

Capacitor

Value

Width

Length

243 fF

29 μm

24 μm

CP1

80 fF

15 μm

14 μm

CP2

261 fF

31 μm

26 μm

The parasitic inductances and capacitances L11,22 and C11,22 are the top and bottom

plate inductances and capacitances, respectively. The transmission line equations are

used to calculate the series inductances and parallel capacitances as follows [125]:



















(4.11)





















(4.12)

where c is the speed of the light, 



is the effective dielectric constant, L is the

capacitor’s length, and Z0 is the characteristic impedance, equal to 50.

Because MIM capacitors are typically square, their series resistances R11,22 are trivial.

The parasitic inductances can be reduced further by increasing the width dimension

[126]. This is especially important in high-speed operation, where parasitics degrade

circuit performance.

Figure 4.15 depicts the MIM capacitor layout design and the S-parameters response of

each capacitor. As depicted in Figure 4.15, the S-parameter responses of the layout

132

design and equivalent circuit model are in excellent accordance at the simulated

frequencies. The parasitic inductances and capacitances of each capacitor are listed in

Table 4.4. Due to Si3N4's comparatively low tangent loss, the conductance loss was

relatively small.

Figure 4.15.EM simulation (red lines) and Equivalent circuit (blue dots) S-parameters response of

80fF, 243fF, and 261fF MIM capacitors in the frequency range of 0.1-40GHz plotted on a Smith chart

along with the layout of the MIM capacitors depicted in ADS-schematic

133

Table 4.4. The parasitics inductances and capacitance of the MIM capacitors used in this work

Capacitor

C12

L11,22

C11,22

243 fF

31 pH

24 fF

CP1

80 fF

24 pH

25 fF

CP2

261 fF

35 pH

24 fF

- Spiral inductors

In high-frequency integrated circuits, specifically CMOS and other technologies, the

use of on-chip inductors has increased [127]. In ultra-high-speed digital

communication transceivers with data rates exceeding 100 Gb/s, spiral inductors are

exceptionally useful. They were studied in the mm-wave regime [128]. Due to the fact

that the performance of a spiral inductor tends to decrease during high-frequency

operation, achieving a minimum quality factor greater than 10 remains difficult [127,

129]. Typically, planar inductors are created by laying out a single metal track with an

overlapping transmission line for interconnection. Square spirals, which are depicted

in Figure 4.16, are the most prevalent inductors used in integrated circuits.

The total inductance is calculated by adding the self and mutual inductances, as well

as the number of turns (nL) and physical dimensions of the inductor, such as the outer

diameter (DL), inner diameter (dL), track width (WL), track separation (SL), and overall

length of the track (PL) [130]. The spiral's inductance can be calculated using the

formula [131]:

134































(4.13)



















(4.14)

where 



is the free space permeability, and 



and 



are 2.34 and 2.75 for square

planar inductors [131]. The main component in the equivalent circuit shown in Figure

4.16 is the inductance, LS, and other parasitics due to fringing and track length effects

can be calculated using a π model extraction procedure [129]:























(4.15)



















(4.16)





















(4.17)





















(4.18)

CS and Csub1,2 are caused by the inter-turn crossover and the metal-to-ground plane

interaction, respectively.

Spiral inductors with track widths of 6μm and track separations of 4μm were

modelled with the ADS momentum tool and compared to the equivalent circuit. As

shown in Figure 4.17 below, the equivalent circuit model and modelled results for 510

and 610 pH inductors are well-matched.

135

Table 4.5 displays the values of the equivalent circuit's components for the spiral

inductors L1 and L2 used in this work. S11 shows inductive behaviour, and the S21

response does not intersect with the chart's centre line, indicating that the self-

resonant frequency (SRF) is clearly greater than 40 GHz

Figure 4.16. Spiral inductor cross-section and equivalent circuit model including both primary and

parasitic components

Table 4.5. The Equivalent circuit’s components of the spiral inductors used in this work

Inductor

Csub1,2

510 pH

6 pH

0.6 Ω

31 fF

610 pH

7 pH

0.6 Ω

33 fF

136

Figure 4.17.EM simulation (red lines) and Equivalent circuit (blue dots) S-parameters response of

510pH and 610pH spiral inductors in the frequency range of 0.1-40GHz plotted on a Smith chart

along with the layout of the spiral inductor depicted in ADS-schematic

137

4.6.4. Layout design of RTD amplifier

After verifying the RTD amplifier's operation with a schematic circuit and modelling

the passive components of the RTD amplifier, the layout of these passive components

was used to build the RTD amplifier's layout, followed by a comparison of the

schematic and layout results. The layout of the RTD, which includes the passive

components, is depicted in Figure 4.18.

Figure 4.18. The layout of the 10 GHz reflection-based RTD amplifier

The gain and S11 values obtained from the layout design of the RTD amplifier circuit

are shown in Figure 4.19. The layout's length and width are 600 μm and 540 μm,

respectively.

138

Figure 4.19. The gain and return loss of the RTD amplifier layout using RTD sample XMBE#300 with

a mesa area of 4x4 μm

over the X-band

The gain was 13.5dB, and S11 was -11.7dB at a frequency of 10 GHz. A 3dB bandwidth

of 1.48 GHz was achieved. The amplifier's S11 was less than -10dB between 10 GHz

and 10.46 GHz frequencies. Both RTDs were biased in the NDR region, at 0.35V, using

a bias current of approximately 9.17 mA, resulting in low dc power consumption of

3.2 mW. The critical FOM (figure of merit) for low power RF applications was 4.22

dB/mW, representing the gain in dB over the dc power consumed (in mW) by the

integrated circuit. The current work is compared in Table 4.6 to other X band

amplifiers.

The difference between Figure 4.19 and Figure 4.12 is due to the CPW structure being

incorporated into the layout design. However, the layout design results indicated that

-20

-10

8 9 10 11 12

S-Parameter Response (dB)

Frequency (GHz)

S(1,1) Gain

139

the RTD amplifier performed well compared to other amplifiers operating in the X-

band frequency range.

Table 4.6. Comparison of RTD based amplifier and other device technologies

Ref

This work

[132]

[133]

[134]

[135]

[136]

Technology

4x4 μm

RTDs

65nm

CMOS

28 nm

CMOS

40 nm

CMOS

55 nm

CMOS

0.25 μm GaN

transistors

Freq. (GHz)

12.2

10.56

11.7

6.5-12

8-12

Gain (dB)

13.5

19.5

15.3

20.7

BW (GHz)

1.48

2.9

4.3

5.5

PDC (mW)

3.2

5.9

750

FOM (dB/mW)

4.22

3.3

1.02

1.1

0.28

0.04

Chip size area

(mm

)

0.324

0.8

2.25

0.162

0.98

4.68

4.7. Summary

The fundamental operation of reflection-based amplifiers has been discussed, as well

as a review of state of the art in the application of RTDs in amplification. The

performance of a 10 GHz reflection-based amplifier was modelled and analysed by

utilising the NDR capability of the InGaAs/AlAs RTD. This circuit used an active

device with a 16 μm

mesa area RTD. The components of the equivalent circuit were

extracted in order to simulate the equivalent circuit in place of the RTD. Prior to

140

designing the layout of the RTD amplifier, the schematic circuit and modelling of the

circuit's passive components were completed. Due to the constructive combination of

in-phase electromagnetic waves at the output port of the amplifier, a gain of 13.5 dB

was obtained at 10 GHz while keeping a low DC power consumption of 3.2 mW. This

relates to a figure of merit of 4.22 dB/mW, which is the highest reported at X-band to

date, validating the amplifier's outstanding performance.

141

5. CHAPTER 5: DEVELOPMENT OF RTD OSCILLATORS FOR

HIGH-FREQUENCY APPLICATIONS

5.1. Introduction

Earlier chapters conducted a thorough review of the literature and high frequency

equivalent circuit modelling of resonant tunnelling diodes to determine their

suitability and utility for microwave and THz applications. Chapter four discussed

reflection-based amplifiers with RTDs as active loads. The purpose of this chapter is

to demonstrate how to model a high-frequency oscillator using an integrated RTD

biased in the NDR region. To meet the oscillation requirements, a properly operating

stabilising circuit must be used. The RTD oscillator's output power limitations are

investigated. This includes the design and modelling of passive components such as

capacitors and coplanar waveguides. All design and analysis in this chapter were

carried out using the Advanced Design System (ADS) software tool.

The design steps for the 100 GHz RTD oscillator are similar to those presented in [46,

57]; however, in this work, a device with smaller mesa area and high negative

differential conductance (NDC) is used in order to increase the output power without

the need of increasing the mesa area. In addition, the circuit's passive components are

designed and evaluated based on their performance at 100.2 GHz as compared to 101

GHz for [46] and 109 GHz for [57].

142

5.2. Conditions for the Design of RTDs Oscillators

As illustrated in Figure 5.1, an RTD oscillator is composed of three major components:

the RTD device, the resonator, and the stabilising circuit. An RTD can be used in the

circuit if its net negative differential resistance is greater than zero. Resonators serve

as inductors, Los, and are frequently implemented with antennas and transmission

lines such as microstrip lines, CPS, and CPWs. CPWs were chosen for this project due

to their ease of fabrication, as they do not require via holes, as do conventional

transmission lines. Stabilizing circuits, or decoupling circuits, are typically

constructed by connecting the resistor Rsh and the capacitor Ccp in parallel. The

oscillator circuit depicted in Figure 5.1 uses a voltage bias, Vbias, to place the diode in

the negative differential resistance region. Rb and Lb denote the parasitics generated

by the DC biasing cable.

Figure 5.1. A single RTD oscillator topology with stabilizing circuit components: decoupling capacitor

and shunt resistor

143

The inductance of the CPW and the intrinsic capacitance of the RTD both contribute

to high-frequency oscillation by resonating at a frequency determined by their

corresponding values. To conduct a theoretical analysis of the circuit's operation and

for simplicity's sake, the effect of parasitic elements was omitted. To maintain the

oscillation, the imaginary component of the admittance is set to zero from the

oscillator circuit as follows:





















 (5.1)

Thus, the oscillation frequency can be expressed as follows:





















(5.2)

Due to additional parasitics not accounted for by the formula, the actual frequency of

oscillation will differ slightly from the value specified by equation (5.2). Consequently,

the selection of an inductor value is not random, as this critical factor is dependent on

the length of the CPW conductor being tuned. The maximum operating frequency and

RF power of the RTDs are critical parameters in the design of the circuit; the former is

specified by: 





































  , which can be rearranged to form the

following:

































 



























(5.3)

144





, as derived from equation (5.3), can provide useful information about the extent

to which the upper oscillation frequency is influenced by the device capacitance, series

resistance, current difference, and voltage span. To maximise fmax even further, the

trade-off between mesa area and series resistance must be efficiently stable. The

thickness of the spacer can be increased, resulting in a reduction in CRTD without

reducing the mesa area. This can also help improve the PVCR by reducing the number

of ionised impurity scattering events. However, thick collector spacers increase the

transit time of carriers in the collector depletion region and decrease the peak current

density due to the suppression of the current flow [57]. As a result, RTDs with thick

emitter spacers are an excellent choice for high-frequency operation without

increasing the transit time of the carriers [104]. The optimization of an RTD structure

with thick emitter spacers was discussed in detail in Chapter 3 and will not be

repeated here.

5.3. Oscillator Circuit's DC Stability

Apart from the RTD's self-capacitance and the resonator's inductance, additional

requirements must be satisfied in order to maintain the oscillation. This is simply

because of a plateau-like current oscillation in the device's NDR region, which results

in a radio frequency distribution between low and designed frequencies [18]. This

work addressed this issue through the use of a stabilising circuit RC combination. The

shunt resistor, RSH, is used to eliminate low-frequency parasitic bias oscillations (2-

145

3GHz). The real part of the admittance is given by the intrinsic equivalent circuit of an

RTD integrated with a resonator:



























































(5.4)

To maintain the oscillation at the desired frequency, Real(Yin) must be negative,

indicating that the circuit is unstable. However, the real part of the admittance is

positive at low frequencies, which contributes to parasitic oscillation suppression, and

the circuit is stable (no oscillation), which results in





  



. This

condition 







must be satisfied in order to do so. It is critical to note that RSH

must be small enough to meet the bias stability condition and decrease the oscillator's

DC power consumption (i.e., this allows an increase in the DC to RF conversion

efficiency), but large enough to enhance the circuit's extracted RF power [137].

However, because the shunt resistor uses power, a decoupling capacitor is added to

act as a short circuit at a high frequency, preventing the resistor from dissipating RF

power. The following formula can be used to determine the value of the decoupling

capacitor:















 (5.5)

5.4. Modelling of 100 GHz RTD oscillator

As one of the primary aims of this thesis is to realise a high-frequency oscillator using

resonant tunnelling diodes as an active device, it is essential to model such an

integrated circuit prior to its fabrication, including all the DC characteristics necessary

146

for a high-performance RTD oscillator. The device was grown using Solid Source

Molecular Beam Epitaxy (SSMBE) on a semi-insulating InP substrate, and its epitaxial

structure is shown in Table (5.1).

Table 5.1.The epi-layers and material parameters of the XMBE#300 sample

Layer

Material

Doping

(cm

-3

)

Thickness

(nm)

Bandgap (eV)

Ohmic layer

In0.53Ga0.47As(n++)

2E+19

0.75

Emitter

In0.53Ga0.47As(n+)

3E+18

0.75

Spacer

In0.53Ga0.47As

undoped

0.75

Barrier

AlAs

undoped

1.2

3.15 (direct)

Quantum Well

In0.8Ga0.2As

undoped

4.5

0.5

Barrier

AlAs

undoped

1.2

3.15 (direct)

Spacer

In0.53Ga0.47As

undoped

0.75

Collector

In0.53Ga0.47As(n+)

3E+18

0.75

Ohmic layer

In0.53Ga0.47As(n++)

1E+19

400

0.75

Substrate

InP

147

The I-V characteristic of a diode with a 4 μm

mesa is illustrated in Figure 5.2. The

diode's DC characteristics at room temperature are shown in Table (5.2). This device

has a relatively large GRTD of 57.8 mS and a high peak current density of 3.3 mA/μm

in the reverse bias direction, as well as a high PVCR of 4.6 in the reverse bias direction,

implying a higher output power. These characteristics can easily be enhanced further

by reducing the well and barrier thicknesses. After de-embedding the parasitic bond

capacitance and inductance, the diode's self-capacitance was determined [215]. The

device's equivalent circuit was then validated by fitting a model to the measured

scattering data. To this end, it was determined that the estimated intrinsic capacitance

in the middle of the NDR is 9 fF/μm

. As a result, the device's critical parameter, fmax,

has been determined to be 800 GHz using the equivalent circuit's extracted values.

Table 5.2.The DC characteristics of the RTD sample XMBE#300 with a mesa area of 4 μm

at room

temperature

(mA)

|ΔI| (mA)

|ΔV| (V)

PVCR

| (mS)

max

(μW)

Forward

6.13

3.4

0.26

3.8

19.6

166

Reverse

13.2

10.4

0.27

4.6

57.8

527

148

Figure 5.2. I-V characteristic of the InGaAs/AlAs RTD device sample XMBE#300 with a mesa area of 4

μm

A CPW resonator was used to connect the oscillator's passive and active components

and to determine the circuit's oscillation frequency. The dimensions of the CPWs are

calculated in this work using the "LineCalc" tool embedded in Agilent Technologies'

Keysight-ADS. To obtain the physical dimensions of the resonator, several parameters

must be defined, including 



, the thickness and loss tangent of the substrate, as well

as the conductor's skin depth. To match the standard equipment configuration, the

CPW's characteristic impedance was set to 50Ω. Additionally, the electrical length, ,

should be less than 90°, ensuring that the shorted coplanar structure has an inductive

reactance. The initial step in designing RTD oscillators is to determine the oscillation

frequency, which is given in equation (5.2). The wavelength of the resulting RF signal

can then be given as follows:

-15

-10

-5

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

Current (mA)

Voltage (V)

149















(5.6)

where  is the speed of light and 



is the average of the relative dielectric constant

between the substrate and air.

The input impedance of the short end CPW is theoretically determined using the well-

known transmission line impedance relationship [138]:





























(5.7)

Inevitably, the oscillator's inductance is not entirely determined by the CPW's physical

length. This is because the current flows through the conductor film at the ends of the

slots, resulting in the storage of magnetic energy behind the termination [139]. Thus,

an inductive reactance is located beyond the slots, denoted by 



, and the

effective length extension, 



, can be calculated as follows [23]:











(5.8)

w denotes the signal line width, and s denotes the gap distance between the signal line

and the CPW's ground plane.

The inductance of this extension length is expressed by the following formula:



















(5.9)

Each wavelength of radio frequency signals has a 2π phase variation; thus, the phase

velocity is defined as  [140]. The total physical length of the shorted CPW is

150

as follows from equations (5.7), (5.8), and (5.9), taking into account the effect of





[18]:



























































(5.10)

Using ADS tools, the resonator length at the oscillation frequency was calculated, and

a result comparable to the equation was obtained (5.10). Importantly, the primary

behaviour of shorted transmission line stubs with narrow centre conductor width at

high frequencies is inductive [120].

Figure 5.3.The Measured I-V characteristics of the RTD XMBE#300 with 4 m

device size in

comparison with a 6

order polynomial fitting equation modelled in Keysight-ADS.

Since ADS does not include a built-in model for tunnelling devices, the RTD was built

using an SDD2P (Symbolically Defined Devices Two Ports) block and a 6th order

polynomial equation. The realised module used the reverse bias direction of the

-14

-12

-10

-8

-6

-4

-2

-1 -0.8 -0.6 -0.4 -0.2 0

Current (mA)

Voltage (V)

Measured data

Fitted data

(Polynomial function)

151

measured I-V characteristic, as shown in Figure 5.3, because DC performance is better

in the reverse bias direction than in the forward bias direction. In the NDR region of

the experimental data, the biasing equipment setup causes a current oscillation that

looks like a plateau.

The intrinsic equivalent circuit of the RTD in the module was constructed, as shown

in Figure 5.4, by connecting a dynamic current source in parallel with the CRTD. This

means that such a configuration is implemented under the assumption that the

measured I-V characteristic of the device includes both the series and junction

resistances (i.e.  



). In this work, a shunt resistor, RSH, and a decoupling

capacitor, CCP, are used to implement a stabilising circuit that reduces parasitic

oscillation and avoids RSH from dissipating RF power at the operating frequency.

Consideration was given to the non-ideal nature of the passive components in order

to prevent significant design errors and ensure that simulation results are

representative of actual practical data. The equivalent circuit models for RSH used in

this study are those presented by S. Renu et al. [141], which include a series inductance

called LS because of the length of the NiCr. Due to the









value of 57.8 mS, the

shunt resistor RSH should not exceed 17Ω. A 16Ω shunt resistor was used in this work.

Also, the equivalent circuit reported by L. Wang et al. [125], represents the MIM

capacitance. This circuit includes the prime lumped component and the inductances

of the top and bottom metals (L11 and L22). It also considers the impact of the substrate's

loss tangent, which is defined as 







, where  is the angular frequency

152

and  is the insulating material's loss tangent. The dimensions of the decoupling

capacitance have been optimised to compensate for the components' non-ideal

behaviour, such as the added inductance and resistance of metals. The following

section will discuss and analyse in detail the extraction of the equivalent circuit

parameters' model for passive elements.

The parasitics of the dc bias setup, Rbias and Lbias, were estimated to be 1Ω and 1nH,

respectively, as shown in Figure 5.4. The RTD sample #300 is biased in the NDR

region, and a load resistor with a 50Ω value is employed to match the measuring

equipment's input impedance with a dc block capacitance (Cdc). The circuit was

simulated using the transient simulation tool at a 100 GHz operating frequency using

the following component values: RSH=16Ω, CCP=19 pF. Given that the entire circuit will

be monolithically integrated on an InP substrate with a 



of 12.5, a CPW inductor

with a value of LOS=70 pH was calculated to correspond to a 1.15mm wavelength

signal at a frequency of 100GHz. With this in mind, the electrical length of the

transmission line was determined to be 22.7°, implying that the resonator's physical

length is 74 μm.

153

Figure 5.4.The schematic of the RTD oscillator circuit in ADS software using RTD sample XMBE#300

with 4 μm

A 2D electromagnetic model integrated into ADS-momentum was employed to

simulate the CPW resonator, allowing for the coupling effect of adjacent transmission

lines and ground plane losses to be implemented into the simulation. Figure 5.5

depicts the output voltage signal across the load resistor RL at time intervals of 5 ns

and 100 ps. The peak to peak voltage of the sinusoidal wave is 184 mV. The RF output

power was then extracted using a Fast Fourier Transform (FFT), as shown in Figure

5.6. The resulting power at the fundamental frequency of 100.2 GHz is 83 μW (-10.8

dBm). The spectrum also reveals that the first harmonic takes place at 200.4 GHz with

a very low power of 0.09 μW.

154

Figure 5.5. The output voltage signal across the load resistor for the simulation of 100GHz RTD

oscillator a) over 5 ns time span b) over 100 ps time span

-120

-80

-40

120

950 951 952 953 954 955

Output Voltage (mV)

Time (ns)

-120

-80

-40

120

950 950.02 950.04 950.06 950.08 950.1

Output Voltage (mV)

Time (ns)

155

Figure 5.6. The output power spectrum across the load of the RTD oscillator modelled in ADS using

RTD XMBE#300 with 4 m

device size

As expected, the simulated oscillation frequency differs slightly from the calculated

one, primarily because of the parasitic components associated with the circuit model.

Theoretically, the maximum output power is achievable when the condition (









) is met for a single RTD oscillator, where 



is the load's conductance. Because

the negative conductance of the RTD reduces with frequency, the condition must be

met at the required operating frequency. The circuit's DC-to-AC efficiency is one of

the most crucial characteristics of RTD oscillators, and it remains a source of

contention. When power is dissipated in the shunt resistance, this critical factor was

determined to be 2.3%.

-120

-80

-40

0 50 100 150 200 250 300

RF Power (dBm)

Frequency (GHz)

156

5.5. Modelling of passive components for the 100 GHz RTD oscillator

- Modelling of MMIC MIM Capacitor

The previous chapter demonstrated the modelling of MIM capacitors. The MIM

capacitor Ccp was modelled in this section to determine if it was acting as a short

circuit at the designed frequency. Because the CCP had a value of 19 pF, the capacitor's

width and length were 280 μm and 210 μm, respectively. The substrate was 625 μm

thick, while the metals were 1 μm thick. Silicon Nitride (Si3N4) was used as the

dielectric material and had a thickness of 200 nm. The capacitor's width should be

greater than its length in order to minimise parasitic resistance and inductance [126].

As a result of the reduced impedance of the shunt capacitor at the resonance

frequency, the oscillator's output power increases. For frequencies above 84 GHz, the

proposed MIM capacitor acted as a short circuit. The capacitor acts as a short circuit,

as illustrated in Figure 5.7, and the frequency range is indicated (up to 120 GHz). The

input reflection coefficient, S11, increases slowly while the power gain, S21, decreases

as the frequency increases due to the parasitic inductance's impedance increasing.

Nevertheless, the MIM capacitor's overall performance is excellent, and the input

reflection coefficient is nearly zero (i.e. -14.7 dB).

157

Figure 5.7. The results of the S-parameters simulation for the 19 pF MIM capacitor

- Modelling of MMIC Nickel Chromium (NiCr) Resistor

MMIC designs utilise resistors in a variety of ways, including feedback, biasing,

matching, and termination. There are two commonly used techniques for realising a

resistor in MMIC circuits. The first method is to incorporate an active semiconductor

layer beneath the MMIC surface or to incorporate impurities into the active

158

semiconductor layer, resulting in the formation of a resistive region. However, this

approach has a drawback, which is the active semiconductor layer's high-temperature

coefficient of resistance (TCR) (3000 ppm/

C). As a result, the resistor's behaviour

changes significantly during high-temperature processing [142].

The alternative method is to use a thin film of a resistive metal alloy, such as Tantalum

(TaN) or Nickel Chromium (NiCr). The resistivity of NiCr is temperature insensitive

[120]. Thus, the NiCr material was proposed as the thin-film resistor in this work.

Resistors made of semiconductor materials have sheet resistance, Rsheet, which is ideal

for resistors with a high value due to its value (i.e. a few hundred ohms per square).

Typically, the sheet resistance of thin-film materials is less than that of the active layer.

The resistance of thin-film sheet is typically between 20Ω/□ and 50Ω/□, which makes

it ideal for producing low-value resistors. To meet the requirements of the RTD

oscillator circuits, the small value resistor must be more accurate.

The resistive material used in the thin-film resistor should have high resistivity, a high

current capability, and a low coefficient of resistance at low temperatures. NiCr

resistors have several advantages: they are simple to fabricate, their geometrical size

can be varied to control the sheet resistance, and their TCR is as low as 77 ppm/

making them stable over a wide temperature range [143]. Figure 5.8 illustrates the

geometry of the thin-film resistor.

159

Figure 5.8. The thin-film NiCr resistor's geometry [57].

The sheet resistance of NiCr, Rsheet, in this work is 50Ω/□ through controlling the film

thickness. The resistance of the 3-dimensional conductor can be expressed as follows:

















(5.11)













(5.12)

where ρ, l, and t are the resistivity, the length, and the thickness of the resistor,

respectively, and the width and the cross-sectional area of the resistive material are

denoted as w and A.

The NiCr resistor is used in the RTD oscillator circuit to suppress low-frequency

parasitic oscillations caused by the DC setup. As illustrated in Figure 5.9, an

equivalent circuit for the NiCr resistance has been proposed [141].

The primary resistance, Re, can be computed using equation (5.12), and the series

inductance, Ls, can be expressed as follows [141]:

160



































   (5.13)

The parallel capacitors, Csub1 and Csub2, are implemented due to capacitance between

the ground plane and the metal; they are neglected in the analysis because there is no

ground plane in the structure of the device.

The parameters LR1, LR2, and LR3 are controlled through the simulation in order to

achieve a correlation between the simulated and measured results. The value of the Re

should be less than the negative differential resistance of the RTD, which is equal to

1/GRTD, in order to suppress the low-frequency bias and increase the RF output power

[137].

Figure 5.9. The equivalent circuit of NiCr resistor [141].

Given that the negative differential conductance of XMBE#300 (GRTD) is 57.8mS, the

NiCr resistance value in this work is 16Ω, which indicates that the resistance has a

width of 19 μm and a length of 12 μm when the thin film is 100 nm thick. The length

161

of the thin film must be less than its width in order to minimise the value of series

parasitic inductance. Thus, as illustrated in Figure 5.10, the NiCr resistor's input

reflection and power gain were constant with frequency.

Figure 5.10. The S-parameters results for 16  NiCr resistor

The parasitic inductance in this circuit was negligible due to the thin-width film's

being greater than its length. Because the value of the NiCr resistor is proportional to

162

the negative differential conductance, the negative differential conductance should be

sufficiently large to prevent the RF output power from being dissipated in the circuit.

5.6. Summary

Modelling double barriers electromagnetically RTD measurements on InGaAs/AlAs

sample XMBE#300 were made using 4 μm

mesa device with a peak current density

of 3.3 mA/μm

that was integrated with a coplanar waveguide resonator. Through the

use of the diode's negative differential resistance feature, a 100 GHz oscillator with an

output power of 83 μW was realised. Advanced design system software was used to

model the circuits. We considered all parasitic elements associated with the passive

components to ensure the circuit's practical performance. In addition, an investigation

into the effect of stabilising resistance on extracted power revealed that extracted

power increases as stabilising resistor value increases. Each parasitic component was

modelled in order to determine its performance at 100 GHz.

163

6. CHAPTER 6: CONCLUSION AND FUTURE WORKS

6.1. Conclusion

The resonant tunnelling diode, which functions on the principle of quantum

mechanical tunnelling, is the fastest solid-state semiconductor device that can be used

as a compact THz source and operates at room temperature. The RTD oscillator has

achieved a fundamental frequency of 2THz by utilising highly strained Indium rich

quantum wells. At room temperature, the RTD operates at a low voltage, which

reduces the integrated circuit's power consumption and the devices dissipation.

Negative differential resistance and low bias requirements make this device unique

for applications involving mm and sub-mm wavelengths. High yield DBQW-RTD

reproducibility and manufacturability are now possible due to the advancement of

MBE techniques that produce highly uniform and smooth monolayer films. RTDs

with 1 μm

mesa are easily fabricated with inexpensive i-line lithography technology.

These devices' performance capabilities surpass those of deep submicron feature

CMOS and HEMT based solid-state devices due to their ability to operate at

frequencies higher than 1 THz while maintaining an excellent current density.

This thesis investigated the performance and capabilities of optimized mm-wave

electronic devices based on tunnel diodes. This was accomplished by creating an

accurate physical model of a state-of-the-art Resonant Tunnelling Diode (RTD) grown

via molecular beam epitaxy on an InP platform. The diode's DC and RF properties

have been accurately reproduced using the physical models developed. After

164

validating the RTD's physical model, the model was used to investigate ways to

reduce the peak voltage to reduce power dissipation. This study detailed the RTD

modelling operation using the SILVACO ATLAS tool for physical modelling and

Keysight's Advanced Design System (ADS) software for implementing these RTDs in

their applications.

This work aims to conduct detailed modelling of asymmetrical spacer RTDs with a

2μm

mesa area to determine approaches for lowering the peak voltage while

maintaining reasonable DC and RF characteristics. The thickness of both spacers was

varied to determine their effect on the RTDs' DC and RF characteristics. It was realised

that RTDs with a thick collector spacer have a higher peak voltage and current. In

contrast, RTDs with a thick emitter spacer have a lower peak voltage and current. By

thickening the collector spacer, the RTD transit time was increased, resulting in a

decrease in the RTDs' intrinsic limit frequency.

On the other hand, the RTDs with thick emitter spacers had short RTD transit times,

low RTD capacitance, and a high intrinsic limit frequency. Additionally, by increasing

the thickness of the emitter spacer, the PVCR has been increased. While the thick

emitter spacer RTDs had low peak voltages, a high PVCR, a higher oscillation

frequency, a short RTD transit time, and a small RTD capacitance, their NDC and

output power were decreased. As a result, modifications to the asymmetrical spacers

RTDs structure were made to increase the NDC and dc maximum output power. The

first modification decreased the thickness of the quantum well by varying the

165

thickness of the emitter spacer while maintaining the thickness of the collector spacer.

This modification increased the NDC, dc maximum output power, and intrinsic limit

frequency; however, it increased the peak voltage and current. As a result, reducing

the quantum well thickness was not the optimal way to increase the NDC and output

power while maintaining low peak voltage. Although thin quantum well RTDs had a

high NDC, a large PVCR, a high output power, and a shorter RTD transit time, they

operated at a lower frequency, had a larger RTD capacitance, and produced a high

peak voltage and current. The RTD structure was further modified by increasing the

amount of Indium in the quantum well. Not only the peak voltage and current are

decreased, but also the oscillation frequency, the RTD transit time, and the RTD

capacitance. This work demonstrated RTDs suitable for high output power radio

frequency (RF) applications and RTDs suitable for low power or ultra-low power

radio frequency (RF) applications.

Utilising InGaAs/AlAs RTD sample #300 with a 16 μm

mesa size, this project

modelled and theoretically analysed an X-band reflection-based amplifier. The

analysis included the extraction of the components of the RTD equivalent circuit as

well as the modelling of the passive components. The model was constructed using a

lumped element branch-line coupler and two active RTD loads. A gain of 13.5 dB at

10 GHz was achieved while only 3.2 mW of DC power was consumed by

constructively combining the amplified in-phase electromagnetic waves at the output

166

port. This gives a figure of merit of 4.22 dB/mW, the highest reported to date at X-

band, confirming the amplifier's high performance.

Additionally, by integrating with a coplanar waveguide resonator, an electromagnetic

model of a 4 μm

InGaAs/AlAs RTD sample #300 with a JP of 3.3mA/μm

was

performed. The model incorporates a 100 GHz oscillator with an output power of 83

μW. Additionally, the spectrum indicates that the first harmonic occurs at ~200 GHz

with a very low power of 0.09 μW. The RTD oscillator's passive components,

including NiCr resistors, parallel plate capacitors, and CPW transmission lines, were

all modelled.

6.2. Future works

Since several RTD devices have been physically modelled and characterised with

regards to their DC and RF parameters, which is critical before the time-consuming

growth and fabrication processes. The following step to this work is to fabricate the

RTDs that demonstrated superior performance in terms of low dc consumption and

compare their measurements' results to those obtained from the model. These RTDs

can then be used in integrated circuit amplifier circuits to reduce dc power

consumption further and boost gain. Because large mesa area RTDs performed well

in RTD amplifier circuits, small mesa area RTDs should perform better due to their

low dc power consumption.

Additionally, designing reflection-based amplifiers with these RTDs at frequencies

greater than 20 GHz would benefit their use in mm-wave 5G wireless communication

167

systems. Indeed, the primary objective is to demonstrate a quantum device based on

a narrow band amplifier that is low in cost, consumes less than 1 mW of power, and

is based on a narrow band amplifier. At this stage, the lumped-element branch line

coupler operating at frequencies between 5 and 100GHz can be accurately modelled

using the commercial software Keysight-ADS momentum and 3D simulator EMPro.

Thinner substrates of 100 μm or less will be required to minimise losses associated

with low noise figure properties and further mitigate parasitics' effects. After

optimising the required modelling results, the amplifier can be constructed using low

dc power consumption RTDs. The circuit's FOM will then be measured and compared

to state of the art.

Additionally, an intriguing and potentially useful integrated circuit is a low-power

full-duplex bidirectional amplifier. These circuits are beneficial in RFID tags and other

wireless transceiver systems. They typically consist of two identical one-port

amplifiers with a single branch coupler.

The RTD amplifier presented here could be a good candidate for 5G/6G wireless

systems that require amplifiers with low dc power consumption and high output

power. Furthermore, these systems necessitate faster semiconductor technologies

than CMOS. As a result, the RTD oscillators developed in this thesis could help 5G/6G

technologies overcome the speed limitations associated with CMOS and GaN

technologies.

168

169

APPENDICES

A. DC SIMULATION SCRIPTS FOR RESONANT TUNNELING DIODES (RTDs)

i. NEGF CODE

#==============================================================#

# TITILE: RTD, 2X1 12-45-12, AlAs-InGaAs-AlAs XMBE#300 # NEGF code

#==============================================================#

go atlas

#---------------------------------------------------------#

# Section 1: Device Specification & Default Value #

#---------------------------------------------------------#

## EpiLayer Thickness ##

set t_contact=0

set t_ohmic1=0.045

set t_emitter=0.045

set t_spacer1=0.005

set t_barrier1=0.0012

set t_well=0.0045

set t_barrier2=0.0012

set t_spacer2=0.005

set t_collector=0.025

set t_ohmic2=0.4

## Doping Concentrations ##

set d_ohmic1=2e19

set d_emitter =3e18

set d_collector =3e18

set d_ohmic2=1e19

## Device Size, Mesa Area ##

set d_mesa=2

170

#---------------------------------------------------------#

# Section 2: Structure Specification #

#---------------------------------------------------------#

## Device Thickness ##

set I=$t_contact

set A=$I+$t_ohmic1

set B=$A+$t_emitter

set C=$B+$t_spacer1

set D=$C+$t_barrier1

set E=$D+$t_well

set F=$E+$t_barrier2

set G=$F+$t_spacer2

set H=$G+$t_collector

set J=$H+$t_ohmic2

####--------------------Device Mesh--------------------####

mesh diag.flip width=1

## x.mesh ##

x.mesh location=0 s=0.1

x.mesh location=$d_mesa s=0.1

## y.mesh ##

y.mesh loc=0 s=0.05

y.mesh loc=$I s=0.001

y.mesh loc=$A s=0.001

y.mesh loc=$B s=0.0005

y.mesh loc=$C s=0.00001

y.mesh loc=$D s=0.00005

y.mesh loc=$E s=0.00001

y.mesh loc=$F s=0.0005

y.mesh loc=$G s=0.001

y.mesh loc=$H s=0.001

y.mesh loc=$J s=0.001

171

####-------------------Device Region-------------------####

region num=1 name=contact1 material=Gold y.min=0 y.max=$I

equil.negf

region num=2 name=ohmic1 material=InGaAs x.comp=0.47

y.min=$I y.max=$A equil.negf

region num=3 name=emitter material=InGaAs x.comp=0.47 y.min=$A

y.max=$B equil.negf

region num=4 name=spacer1 material=InGaAs x.comp=0.47 y.min=$B

y.max=$C equil.negf

region num=5 name=barrier1 material=AlAs y.min=$C y.max=$D

calc.strain

region num=6 name=well material=InGaAs x.comp=0.2 y.min=$D

y.max=$E calc.strain

region num=7 name=barrier2 material=AlAs y.min=$E y.max=$F

calc.strain

region num=8 name=spacer2 material=InGaAs x.comp=0.47 y.min=$F

y.max=$G equil.negf

region num=9 name=collector material=InGaAs x.comp=0.47

y.min=$G y.max=$H equil.negf

region num=10 name=ohmic2 material=InGaAs x.comp=0.47 y.min=$H

y.max=$J equil.negf

####---------------------Electrode---------------------####

elec num=1 name=anode material=Gold top

elec num=2 name=cathode material=Gold bottom

####----------------------Doping-----------------------####

doping reg=2 uniform n.type conc=$d_ohmic1

doping reg=3 uniform n.type conc=$d_collector

doping reg=9 uniform n.type conc=$d_emitter

doping reg=10 uniform n.type conc=$d_ohmic2

#---------------------------------------------------------#

# Section 3: Material Model Specification #

#---------------------------------------------------------#

172

####----------------------Material---------------------####

#==================

#AlAs

#==================

material reg=5 name=barrier1 permittivity=10 eg300=3.15

affinity=2.91 me.tunnel=0.09 mc=0.15

material reg=7 name=barrier2 permittivity=10 eg300=3.15

affinity=2.91 me.tunnel=0.09 mc=0.15

#==================

#InGaAs x.comp=0.2

#==================

material reg=6 name=well permittivity=14.6 eg300=0.51

affinity=4.729 mc=0.034

#===================

#InGaAs x.comp=0.47

#===================

material reg=2 name=ohmic1 permittivity=13.9 eg300=0.75

affinity=4.6 mc=0.044

material reg=3 name= emitter permittivity=13.9 eg300=0.75

affinity=4.6 mc=0.044

material reg=4 name= spacer1 permittivity=13.9 eg300=0.75

affinity=4.6 mc=0.044

material reg=8 name= spacer2 permittivity=13.9 eg300=0.75

affinity=4.6 mc=0.044

material reg=9 name= collector permittivity=13.9 eg300=0.75

affinity=4.6 mc=0.044

material reg=10 name= ohmic2 permittivity=13.9

eg300=0.75 affinity=4.6 mc=0.044

#---------------------------------------------------------#

# Section 4: Numerical Method Section #

#---------------------------------------------------------#

173

####----------------------output------------------------####

output con.band val.band eigen=9 charge e.mobility

h.mobility e.velocity h.velocity BAND.PARAM ERRORS

QFN PHOTOGEN QSS RECOMB TRAPS TRAPS.FT

####----------------------Traps------------------------####

inttrap acceptor midgap density=7e15 degen.fac=10 sign=1e-13

sigp=1e-13

####----------------------Model------------------------####

models n.negf_pl1d p.negf_pl1d NPRED.NEGF=30 QCRIT.NEGF=0.002

esize.negf=10001 eig.ymin=$B eig.ymax=$G

models FERMIDIRAC SRH CONMOB QTUNN.BBT

QTUNN.EL DEVDEG.B AutoBBt prints

method carr=0 trap newton gummel

####----------------------Impact-----------------------####

impact selb

#----------------------------------------------------------#

# Section 5: Output Specification #

#----------------------------------------------------------#

log outf=RTD300.log

solve init

save outf=RTD300init.str negf.log negf.eig

solve v2=0 name=cathode vstep=0.005 vfinal=1

save outf=RTD300_v1.str negf.log negf.eig

log off

tonyplot RTD300init.str

tonyplot RTD300_v1.str

tonyplot RTD300.log

174

quit

ii. SIS CODE

#==============================================================#

# TITILE: RTD, 2X1 12-45-12, AlAs-InGaAs-AlAs XMBE#300 # SIS code

#==============================================================#

go atlas

#---------------------------------------------------------#

# Section 1: Device Specification & Default Value #

#---------------------------------------------------------#

## EpiLayer Thickness ##

set t_contact=0

set t_ohmic1=0.045

set t_emitter=0.045

set t_spacer1=0.005

set t_barrier1=0.0012

set t_well=0.0045

set t_barrier2=0.0012

set t_spacer2=0.005

set t_collector=0.025

set t_ohmic2=0.4

## Doping Concentrations ##

set d_ohmic1=2e19

set d_emitter =3e18

set d_collector =3e18

set d_ohmic2=1e19

## Device Size, Mesa Area ##

set d_mesa=2

#---------------------------------------------------------#

175

# Section 2: Structure Specification #

#---------------------------------------------------------#

## Device Thickness ##

set I=$t_contact

set A=$I+$t_ohmic1

set B=$A+$t_emitter

set C=$B+$t_spacer1

set D=$C+$t_barrier1

set E=$D+$t_well

set F=$E+$t_barrier2

set G=$F+$t_spacer2

set H=$G+$t_collector

set J=$H+$t_ohmic2

####--------------------Device Mesh--------------------####

mesh diag.flip width=1

## x.mesh ##

x.mesh location=0 s=0.1

x.mesh location=$d_mesa s=0.1

## y.mesh ##

y.mesh loc=0 s=0.05

y.mesh loc=$I s=0.001

y.mesh loc=$A s=0.001

y.mesh loc=$B s=0.0005

y.mesh loc=$C s=0.00001

y.mesh loc=$D s=0.00005

y.mesh loc=$E s=0.00001

y.mesh loc=$F s=0.0005

y.mesh loc=$G s=0.001

y.mesh loc=$H s=0.001

y.mesh loc=$J s=0.001

####-------------------Device Region-------------------####

176

region num=1 name=contact1 material=Gold y.min=0 y.max=$I

equil.negf

region num=2 name=ohmic1 material=InGaAs x.comp=0.47

y.min=$I y.max=$A equil.negf

region num=3 name=emitter material=InGaAs x.comp=0.47 y.min=$A

y.max=$B equil.negf

region num=4 name=spacer1 material=InGaAs x.comp=0.47 y.min=$B

y.max=$C equil.negf

region num=5 name=barrier1 material=AlAs y.min=$C y.max=$D

calc.strain qtregion=1

region num=6 name=well material=InGaAs x.comp=0.2 y.min=$D

y.max=$E calc.strain qtregion=2

region num=7 name=barrier2 material=AlAs y.min=$E y.max=$F

calc.strain qtregion=3

region num=8 name=spacer2 material=InGaAs x.comp=0.47 y.min=$F

y.max=$G equil.negf

region num=9 name=collector material=InGaAs x.comp=0.47

y.min=$G y.max=$H equil.negf

region num=10 name=ohmic2 material=InGaAs x.comp=0.47 y.min=$H

y.max=$J equil.negf

####---------------------Electrode---------------------####

elec num=1 name=anode material=Gold top

elec num=2 name=cathode material=Gold bottom

####----------------------Doping-----------------------####

doping reg=2 uniform n.type conc=$d_ohmic1

doping reg=3 uniform n.type conc=$d_collector

doping reg=9 uniform n.type conc=$d_emitter

doping reg=10 uniform n.type conc=$d_ohmic2

####----------------------Interface-----------------------####

interface s.c region=1

interface s.s region=2

interface s.s region=3

interface s.i region=4

177

interface s.i region=5

interface s.i region=6

interface s.i region=7

interface s.s region=8

interface s.s region=9

interface s.c region=10

interface tunnel region=5 dy.tunnel=0.001

interface tunnel region=6 dy.tunnel=0.001

interface tunnel region=7 dy.tunnel=0.001

#---------------------------------------------------------#

# Section 3: Material Model Specification #

#---------------------------------------------------------#

####----------------------Material---------------------####

#==================

#AlAs

#==================

material reg=5 name=barrier1 permittivity=10 eg300=3.15

affinity=2.91 me.tunnel=0.268 mc=0.268

material reg=7 name=barrier2 permittivity=10 eg300=3.15

affinity=2.91 me.tunnel=0.268 mc=0.268

#==================

#InGaAs x.comp=0.2

#==================

material reg=6 name=well permittivity=14.6 eg300=0.51

affinity=4.729 mc=0.034

#===================

#InGaAs x.comp=0.47

#===================

material reg=2 name=ohmic1 permittivity=13.9 eg300=0.75

affinity=4.6 mc=0.044

178

material reg=3 name= emitter permittivity=13.9 eg300=0.75

affinity=4.6 mc=0.044

material reg=4 name= spacer1 permittivity=13.9 eg300=0.75

affinity=4.6 mc=0.044

material reg=8 name= spacer2 permittivity=13.9 eg300=0.75

affinity=4.6 mc=0.044

material reg=9 name= collector permittivity=13.9 eg300=0.75

affinity=4.6 mc=0.044

material reg=10 name= ohmic2 permittivity=13.9

eg300=0.75 affinity=4.6 mc=0.044

#---------------------------------------------------------#

# Section 4: Numerical Method Section #

#---------------------------------------------------------#

####----------------------output------------------------####

output con.band val.band eigen=7 charge e.mobility

h.mobility e.velocity h.velocity BAND.PARAM ERRORS

QFN DEVDEG PHOTOGEN QSS QTUNN.BBT QTUNN.EL

RECOMB TRAPS TRAPS.FT U.BBT

####----------------------Model------------------------####

models sis.el sis.ho sis.nlderivs QTREGION=1 FERMIDIRAC

CONMOB SRH Analytic DEVDEG.B AutoBBT prints

models sis.el sis.ho sis.nlderivs QTREGION=2 FERMIDIRAC

CONMOB SRH Analytic DEVDEG.B AutoBBT prints

models sis.el sis.ho sis.nlderivs QTREGION=3 FERMIDIRAC

CONMOB SRH Analytic DEVDEG.B AutoBBT prints

method climit=1e-4 itlimit=100 maxtraps=20

179

#----------------------------------------------------------#

# Section 5: Output Specification #

#----------------------------------------------------------#

log outf=RTD_sis.log

solve init

save outf=RTD_sis_init.str

solve v2=0 name=cathode vstep=0.005 vfinal=1

save outf=RTD_sis_v1.str

log off

tonyplot RTD_sis_init.str

tonyplot RTD_sis_v1.str

tonyplot RTD_sis.log

quit

180

B. SUPPLEMENTARY FIGURES FOR SECTION 3.6

Effect of varying the quantum well thickness and the Indium composition on the PVCR

The NDC of asymmetrical spacers RTDs as the quantum well thickness and the Indium composition

vary

181

The change in the intrinsic limit frequency as the thickness of the quantum well and the Indium

composition change

182

REFERENCES

1. Partin, D.L., Lead Salt Quantum Well Diode-Lasers. Superlattices and

Microstructures, 1985. 1(2): p. 131-135.

2. Lyakh, A., et al., 3 W continuous-wave room temperature single-facet emission from

quantum cascade lasers based on nonresonant extraction design approach. Applied

Physics Letters, 2009. 95(14).

3. Kim, S.M., et al., Biomedical terahertz imaging with a quantum cascade laser.

Applied Physics Letters, 2006. 88(15).

4. Liang, G.Z., T. Liu, and Q.J. Wang, Recent Developments of Terahertz Quantum

Cascade Lasers. Ieee Journal of Selected Topics in Quantum Electronics, 2017.

23(4).

5. Jung, S.Y., et al., Broadly tunable monolithic room-temperature terahertz quantum

cascade laser sources. Nature Communications, 2014. 5.

6. Hu, Q., et al., Terahertz Quantum Cascade Lasers and Real-Time T-Ray Imaging.

Future Trends in Microelectronics: Up the Nano Creek, 2007: p. 347-358.

7. Wang, X.M., et al., High-power terahertz quantum cascade lasers with similar to

0.23 W in continuous wave mode. Aip Advances, 2016. 6(7).

8. Li, L.H., et al., Terahertz quantum cascade lasers with > 1 W output powers.

Electronics Letters, 2014. 50(4): p. 309-310.

9. Williams, B.S., et al., High-power terahertz quantum-cascade lasers. Electronics

Letters, 2006. 42(2): p. 89-91.

10. Fathololoumi, S., et al., Terahertz quantum cascade lasers operating up to similar to

200 K with optimized oscillator strength and improved injection tunneling. Optics

Express, 2012. 20(4): p. 3866-3876.

11. Wade, A., et al., Magnetic-field-assisted terahertz quantum cascade laser operating

up to 225 K. Nature Photonics, 2009. 3(1): p. 41-45.

12. Alekseev, E. and D. Pavlidis, GaN Gunn diodes for THz signal generation. 2000

Ieee Mtt-S International Microwave Symposium Digest, Vols 1-3, 2000: p.

1905-1908.

13. Panda, A.K., et al., Studies on the Characteristics of GaN-based Gunn Diode for

THz Signal Generation. Apmc: 2009 Asia Pacific Microwave Conference, Vols

1-5, 2009: p. 1565-+.

14. Amir, F., M. Missous, and M. University of, Advanced physical modelling of step

graded Gunn diode for high power terahertz sources. 2011.

15. Khalid, A., et al., In0.53Ga0.47As Planar Gunn Diodes Operating at a

Fundamental Frequency of 164 GHz. Ieee Electron Device Letters, 2013. 34(1): p.

39-41.

16. Song, H.-J., H.-J. Song, and T. Nagatsuma, Handbook of terahertz technologies :

devices and applications. 2015.

17. Izumi, R., S. Suzuki, and M. Asada. 1.98 THz resonant-tunneling-diode oscillator

with reduced conduction loss by thick antenna electrode. in 2017 42nd International

183

Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz). 2017.

IEEE.

18. Wang, J. and G. University of, Monolithic microwave/millimetrewave integrated

circuit resonant tunnelling diode sources with around a milliwatt output power.

2014.

19. Kanaya, H., et al., Fundamental Oscillation up to 1.31 THz in Resonant Tunneling

Diodes with Thin Well and Barriers. Applied Physics Express, 2012. 5(12).

20. Asada, M. and S. Suzuki, Compact THz Oscillators with Resonant Tunneling

Diodes and Application to High-Capacity Wireless Communications. 2013 21st

International Conference on Applied Electromagnetics and Communications

(Icecom 2013), 2013.

21. Shiraishi, M., et al., High Output Power (similar to 400 mu W) Oscillators at

around 550GHz Using Resonant Tunneling Diodes with Graded Emitter and Thin

Barriers. Applied Physics Express, 2011. 4(6).

22. Wang, L., Reliable design of tunnel diode and resonant tunnelling diode based

microwave sources. 2011, University of Glasgow. p. xxxv, 222 p.

23. Suzuki, S. and M. Asada, Coherent power combination in highly integrated

resonant tunneling diode oscillators with slot antennas. Japanese Journal of

Applied Physics Part 2-Letters & Express Letters, 2007. 46(45-49): p. L1108-

L1110.

24. Asada, M. and S. Suzuki, Theoretical analysis of coupled oscillator array using

resonant tunneling diodes in subterahertz and terahertz range. Journal of Applied

Physics, 2008. 103(12).

25. Stephan, K.D., et al., 5 Mw Parallel-Connected Resonant-Tunneling Diode

Oscillator. Electronics Letters, 1992. 28(15): p. 1411-1412.

26. Cantu, H.I. and W.S. Truscott, Injection-locking and power combining with double

barrier resonant tunnelling diodes. Electronics Letters, 2001. 37(20): p. 1264-1265.

27. Suzuki, S., et al., High-Power Operation of Terahertz Oscillators With Resonant

Tunneling Diodes Using Impedance-Matched Antennas and Array Configuration.

Ieee Journal of Selected Topics in Quantum Electronics, 2013. 19(1).

28. Kasagi, K., S. Suzuki, and M. Asada, Large-scale array of resonant-tunneling-

diode terahertz oscillators for high output power at 1 THz. 2019. 125(15): p. 151601.

29. Hinata, K., et al., Sub-Terahertz Resonant Tunneling Diode Oscillators with High

Output Power (similar to 200 mu W) Using Offset-Fed Slot Antenna and High

Current Density. Applied Physics Express, 2010. 3(1).

30. Kobayashi, K., et al., Analysis of a high-power resonant-tunneling-diode terahertz

oscillator integrated with a rectangular cavity resonator. 2020. 59(5): p. 050907.

31. Izumi, R., et al., Resonant-tunneling-diode terahertz oscillator with a cylindrical

cavity for high-frequency oscillation. 2019. 9(8): p. 085020.

32. Malhotra, I., K.R. Jha, and G. Singh, Terahertz antenna technology for imaging

applications: a technical review. International Journal of Microwave and

Wireless Technologies, 2018. 10(3): p. 271-290.

184

33. Murphy, K.S., et al., Millimetre wave aviation security scanner. 36th Annual 2002

International Carnahan Conference on Security Technology, Proceedings,

2002: p. 162-166.

34. Arnone, D., C. Ciesla, and M. Pepper, Terahertz imaging comes into view.

Physics World, 2000. 13(4): p. 35-40.

35. Liu, J., et al., Identification of high explosive RDX using terahertz imaging and

spectral fingerprints, in Journal of Physics: Conference Series 2016.

36. Skvortsov, L.A., Standoff Detection of Hidden Explosives and Cold and Fire Arms

by Terahertz Time-Domain Spectroscopy and Active Spectral Imaging (Review).

Journal of Applied Spectroscopy, 2014. 81(5): p. 725-749.

37. Yu, C., et al., The potential of terahertz imaging for cancer diagnosis: A review of

investigations to date. Quant Imaging Med Surg, 2012. 2(1): p. 33-45.

38. Giordani, M., M. Mezzavilla, and M. Zorzi, Initial Access in 5G mmWave

Cellular Networks. Ieee Communications Magazine, 2016. 54(11): p. 40-47.

39. Lie, D.Y.C., et al., A Review of 5G Power Amplifier Design at cm-Wave and mm-

Wave Frequencies. Wireless Communications & Mobile Computing, 2018.

40. Cheng, C.C., et al., Silicon Process Impact on 5G NR mmWave Front End Design

and Performance. 2019 International Symposium on Vlsi Design, Automation

and Test (Vlsi-Dat), 2019.

41. Oshima, N., et al., Wireless Data Transmission of 30 Gbps at a 500-GHz Range

Using Resonant-Tunneling-Diode Terahertz Oscillator. 2016 Ieee Mtt-S

International Microwave Symposium (Ims), 2016.

42. Guo, Y., et al., Power allocation for massive MIMO: impact of power amplifier

efficiency. 2016. 59(2): p. 1-9.

43. Li, L., et al., mmWave communications for 5G: implementation challenges and

advances. 2018. 61(2): p. 021301.

44. Lee, M.A., B. Easter, and H.A. Bell, Tunnel diodes. Modern electrical studies.

1967.

45. Sze, S.M. and K.K. Ng, Physics of semiconductor devices. 2007.

46. Muttlak, S., Advanced InP/InGaAs electronic/optoelectronic integrated circuits for

high speed MMIC applications. 2020.

47. Yamamoto, H.J.A.P.A., Resonant tunneling condition and transmission coefficient

in a symmetrical one-dimensional rectangular double-barrier system. 1987. 42: p.

245-248.

48. Sze, S.M., et al., High-speed semiconductor devices. A Wiley-Interscience

publication. 1990.

49. Esaki, L., New Phenomenon in Narrow Germanium p − n Junctions. Phys. Rev.,

1958. 109(2): p. 603-604.

50. Esaki, L., Properties of heavily-doped germanium and narrow pn junctions, in Solid-

State Physics Proc. International Conf. 1960: Brussels. p. 514-523.

51. Carroll, J.M., Tunnel-diode and semiconductor circuits. 1963.

52. Allford, C.P., et al., Thermally activated resonant tunnelling in GaAs/AlGaAs triple

barrier heterostructures. Semiconductor Science and Technology, 2015. 30(10).

185

53. Chang, L.L., L. Esaki, and R. Tsu, Resonant Tunneling in Semiconductor Double

Barriers. Applied Physics Letters, 1974. 24(12): p. 593-595.

54. Mizuta, H., T. Tanoue, and P. Cambridge University, The physics and

applications of resonant tunnelling diodes. Cambridge studies in semiconductor

physics and microelectronic engineering. 1995.

55. Brown, E.R., et al., Oscillations up to 712 Ghz in Inas/Alsb Resonant-Tunneling

Diodes. Applied Physics Letters, 1991. 58(20): p. 2291-2293.

56. Ismail, K., B.S. Meyerson, and P.J. Wang, Electron Resonant Tunneling in Si/Sige

Double Barrier Diodes. Applied Physics Letters, 1991. 59(8): p. 973-975.

57. Md Zawawi, M.A.b., Advanced In0.8Ga0.2As/AlAs resonant tunneling diodes for

applications in integrated mm-waves MMIC oscillators. 2015.

58. Shewchuk, T.J., et al., Resonant Tunneling Oscillations in a Gaas-Alxga1-Xas

Heterostructure at Room-Temperature. Applied Physics Letters, 1985. 46(5): p.

508-510.

59. Tsuchiya, M., H. Sakaki, and J. Yoshino, Room-Temperature Observation of

Differential Negative-Resistance in an Alas/Gaas/Alas Resonant Tunneling Diode.

Japanese Journal of Applied Physics Part 2-Letters, 1985. 24(6): p. L466-L468.

60. Tsuchiya, M. and H. Sakaki, Dependence of Resonant Tunneling Current on Well

Widths in Alas/Gaas/Alas Double Barrier Diode Structures. Applied Physics

Letters, 1986. 49(2): p. 88-90.

61. Wolak, E., et al., The Design of Gaas/Alas Resonant Tunneling Diodes with Peak

Current Densities over 2x105 a Cm-2. Journal of Applied Physics, 1991. 69(5): p.

3345-3350.

62. Inata, T., et al., Excellent Negative Differential Resistance of Inalas-Ingaas Resonant

Tunneling Barrier Structures Grown by Mbe. Japanese Journal of Applied

Physics Part 2-Letters, 1986. 25(12): p. L983-L985.

63. Inata, T., et al., A Pseudomorphic In0.53ga0.47as Alas Resonant Tunneling Barrier

with a Peak-to-Valley Current Ratio of 14 at Room-Temperature. Japanese Journal

of Applied Physics Part 2-Letters & Express Letters, 1987. 26(8): p. L1332-

L1334.

64. Matsuzaki, H., et al., High peak current density and low peak voltage strained

In0.9-0.8Ga0.1-0.2As/AlAs RTD grown by metal organic chemical vapor deposition.

Compound Semiconductors 2001, 2002(170): p. 63-67.

65. Adachi, S., E. Institution Of, and I. Technology, Properties of aluminium gallium

arsenide. 2006.

66. Adachi, S., W. John, and Sons, Physical properties of III-V semiconductor

compounds : InP, InAs, GaAs, GaP, InGaAs, and InGaAsP. 1992.

67. Bhattacharya, P., Properties of lattice-matched and strained indium gallium arsenide

[electronic resource]. EMIS data reviews 8. 1993.

68. Muttlak, S.G., et al., InGaAs/AlAs Resonant Tunneling Diodes for THz

Applications: An Experimental Investigation. Ieee Journal of the Electron Devices

Society, 2018. 6(1): p. 254-262.

186

69. Asada, M., S. Suzuki, and N. Kishimoto, Resonant Tunneling diodes for sub-

terahertz and terahertz oscillators. Japanese Journal of Applied Physics, 2008.

47(6): p. 4375-4384.

70. Reeves, G.K. and H.B. Harrison, Obtaining the Specific Contact Resistance from

Transmission-Line Model Measurements. Electron Device Letters, 1982. 3(5): p.

111-113.

71. Kanaya, H., et al., Structure dependence of oscillation characteristics of resonant-

tunneling-diode terahertz oscillators associated with intrinsic and extrinsic delay

times. Japanese Journal of Applied Physics, 2015. 54(9).

72. Bresse, J. and S.J.S.-S.E. Blayac, Epitaxial layer sheet resistance outside and under

ohmic contacts measurements using electrostatic force microscopy. 2001. 45(7): p.

1071-1076.

73. Liu, Q., et al., Unified AC model for the resonant tunneling diode. 2004. 51(5): p.

653-657.

74. Hu, Y.H.Y. and S.S.S.J.J.j.o.a.p. Stapleton, Capacitance of a resonant tunneling

diode. 1992. 31(1R): p. 23.

75. Lake, R. and J.J.I.T.o.E.D. Yang, A physics based model for the RTD quantum

capacitance. 2003. 50(3): p. 785-789.

76. Trofimenkoff, F. and O.J.P.o.t.I. Nakahara, Collector depletion region transit time.

1964. 52(1): p. 86-87.

77. Orihashi, N., et al., Experimental and theoretical characteristics of sub-terahertz and

terahertz oscillations of resonant tunneling diodes integrated with slot antennas.

2005. 44(11R): p. 7809.

78. Figueiredo, J.M.L., Optoelectronic properties of resonant tunnelling diodes. 2000.

79. Brown, E., High-speed resonant-tunneling diodes, in VLSI Electronics

Microstructure Science. 1994, Elsevier. p. 305-350.

80. Kim, C. and A.J.I.T.o.C.T. Brandli, High-frequency high-power operation of tunnel

diodes. 1961. 8(4): p. 416-425.

81. Sollner, T.C.L.G., et al., Quantum Well Oscillators. Applied Physics Letters,

1984. 45(12): p. 1319-1321.

82. Reddy, M., et al., Monolithic Schottky-collector resonant tunnel diode oscillator

arrays to 650 GHz. Ieee Electron Device Letters, 1997. 18(5): p. 218-221.

83. Orihashi, N., S. Suzuki, and M. Asada, One THz harmonic oscillation of resonant

tunneling diodes. Applied Physics Letters, 2005. 87(23).

84. Suzuki, S., et al., Fundamental Oscillation of up to 831 GHz in GaInAs/AlAs

Resonant Tunneling Diode. Applied Physics Express, 2009. 2(5).

85. Suzuki, S., et al., Fundamental oscillation of resonant tunneling diodes above 1 THz

at room temperature. Applied Physics Letters, 2010. 97(24).

86. Feiginov, M., et al., Resonant-tunnelling-diode oscillators operating at frequencies

above 1.1 THz. Applied Physics Letters, 2011. 99(23).

87. Koyama, Y., R. Sekiguchi, and T. Ouchi, Oscillations up to 1.40 THz from

Resonant-Tunneling-Diode-Based Oscillators with Integrated Patch Antennas.

Applied Physics Express, 2013. 6(6).

187

88. Kishimoto, N., et al., Frequency increase of resonant tunneling diode oscillators in

sub-THz and THz range using thick spacer layers. 2008. 1(4): p. 042003.

89. Kanaya, H., et al., Fundamental oscillation up to 1.42 THz in resonant tunneling

diodes by optimized collector spacer thickness. 2014. 35(5): p. 425-431.

90. Maekawa, T., et al., Frequency increase in terahertz oscillation of resonant

tunnelling diode up to 1.55 THz by reduced slot-antenna length. Electronics

Letters, 2014. 50(17): p. 1214-1215.

91. Asada, M., S.J.J.o.I. Suzuki, Millimeter,, and T. Waves, Room-temperature

oscillation of resonant tunneling diodes close to 2 THz and their functions for various

applications. 2016. 37(12): p. 1185-1198.

92. Remnev, M., I.Y. Kateev, and V.J.S. Elesin, Effect of spacer layers on current-

voltage characteristics of resonant-tunneling diode. 2010. 44(8): p. 1034-1039.

93. Shi, X., et al., Enhancing power density of strained In0. 8Ga0. 2As/AlAs resonant

tunneling diode for terahertz radiation by optimizing emitter spacer layer thickness.

2017. 112: p. 435-441.

94. Inc, S.I.J.S., Atlas User’s Manual. 2016. p. p 89.

95. Syme, R.T., et al. Novel GaAs/AlAs tunnel structures as microwave detectors. in

Quantum Well and Superlattice Physics IV. 1992. International Society for Optics

and Photonics.

96. Vurgaftman, I., J.á. Meyer, and L.á.J.J.o.a.p. Ram-Mohan, Band parameters for

III–V compound semiconductors and their alloys. 2001. 89(11): p. 5815-5875.

97. Song, H.-J., T.J.I.t.o.t.s. Nagatsuma, and technology, Present and future of

terahertz communications. 2011. 1(1): p. 256-263.

98. Mizuta, H. and T. Tanoue, The physics and applications of resonant tunnelling

diodes. 1995.

99. Jonsson, B. and S.T.J.I.j.o.q.e. Eng, Solving the Schrodinger equation in arbitrary

quantum-well potential profiles using the transfer matrix method. 1990. 26(11): p.

2025-2035.

100. Shams, M.I.B., et al., An accurate interband tunneling model for InAs/GaSb

heterostructure devices. 2013. 10(5): p. 740-743.

101. Kucharski, M., et al. A 109–137 GHz power amplifier in SiGe BiCMOS with 16.5

dBm output power and 12.8% PAE. in 2017 47th European Microwave Conference

(EuMC). 2017. IEEE.

102. Lee, Y.-C., T.-Y. Chen, and J.Y.-C. Liu. An adaptively biased stacked power

amplifier without output matching network in 90-nm CMOS. in 2017 IEEE MTT-S

International Microwave Symposium (IMS). 2017. IEEE.

103. Lin, J.-L., et al. A K-band transformer based power amplifier with 24.4-dBm output

power and 28% PAE in 90-nm CMOS technology. in 2017 IEEE MTT-S

International Microwave Symposium (IMS). 2017. IEEE.

104. Alqurashi, A. and M. Missous. Physical Modeling of Asymmetric Spacers

Resonant Tunneling Diodes (RTDs). in 2021 IEEE Latin America Electron Devices

Conference (LAEDC). 2021. IEEE.

188

105. Genoe, J., et al., Capacitances in double-barrier tunneling structures. 1991. 38(9): p.

2006-2012.

106. Ouchi, T., et al., Terahertz imaging system for medical applications and related high

efficiency terahertz devices. 2014. 35(1): p. 118-130.

107. Maekawa, T., et al., Oscillation up to 1.92 THz in resonant tunneling diode by

reduced conduction loss. Applied Physics Express, 2016. 9(2).

108. Kanaya, H., S. Suzuki, and M.J.I.E.E. Asada, Terahertz oscillation of resonant

tunneling diodes with deep and thin quantum wells. 2013. 10(18): p. 20130501-

20130501.

109. Cidronali, A., et al., MMIC applications of heterostructure interband tunnel

devices. 2003. 51(4): p. 1351-1367.

110. Lee, J., et al. 5 GHz low-power RTD-based amplifier MMIC with a high figure-of-

merit of 24.5 dB/mW. in 2013 International Conference on Indium Phosphide and

Related Materials (IPRM). 2013. IEEE.

111. Lee, J., et al. Negative-differential-conductance RTD amplifier MMIC with record

foms of gain-to-dc power ratio and noise figure. in 26th International Conference on

Indium Phosphide and Related Materials (IPRM). 2014. IEEE.

112. Lee, J., K.J.I.M. Yang, and W.C. Letters, RF power analysis on 5.8 GHz low-power

amplifier using resonant tunneling diodes. 2016. 27(1): p. 61-63.

113. Lee, J. and K.J.E.L. Yang, Temperature-dependent characteristics of InP-RTD-based

microwave amplifier IC. 2017. 53(15): p. 1058-1060.

114. Lee, J., et al., Reflection-type RTD low-power amplifier with deep sub-mW DC

power consumption. 2014. 24(8): p. 551-553.

115. Muttlak, S., et al. Modeling of high gain and μW level power consumption resonant

tunneling diode based amplifiers. in 2017 10th UK-Europe-China Workshop on

Millimetre Waves and Terahertz Technologies (UCMMT). 2017. IEEE.

116. Doychinov, V., Quantum Barrier Devices for Sub-Millimetre Wave Detection.

2015, University of Leeds.

117. Vogel, R.W.J.I.T.o.M.T. and Techniques, Analysis and design of lumped-and

lumped-distributed-element directional couplers for MIC and MMIC applications.

1992. 40(2): p. 253-262.

118. Automation, E.D., Software, Advanced Design System (ADS), Version 2017. 2017,

The Keysight Technologies, Inc., Santa Rosa, CA, USA.

119. Vinayak, S., et al., Ni–Cr thin film resistor fabrication for GaAs monolithic

microwave integrated circuits. 2006. 514(1-2): p. 52-57.

120. Marsh, S., Practical MMIC design. 2006.

121. Robertson, I.D., S. Lucyszyn, and E. Institution of Electrical, RFIC and MMIC

design and technology. IEE circuits, devices and systems series 13. 2001.

122. Liao, S.Y., Microwave devices and circuits. Prentice-Hall International editions.

1990.

123. Mellberg, A. and J. Stenarson, An evaluation of three simple scalable MIM

capacitor models. Ieee Transactions on Microwave Theory and Techniques,

2006. 54(1): p. 169-172.

189

124. Lombard, P., et al., MIM capacitors model determination and analysis of parameter

influence. ISIE 2005: Proceedings of the IEEE International Symposium on

Industrial Electronics 2005, Vols 1- 4, 2005: p. 1129-1132.

125. Wang, L., R.M. Xu, and B. Yan, MIM capacitor simple scalable model

determination for MMIC application on GAAS. Progress in Electromagnetics

Research-Pier, 2006. 66: p. 173-178.

126. Arshad, S. and M. University of, Low-Power Wideband InP-Based Low Noise

Amplifiers for the Square Kilometre Array Radio Telescope. 2009.

127. Haobijam, G. and R.P. Palathinkal, Design and analysis of spiral inductors. 2014:

Springer.

128. Dickson, T.O., et al., 30-100-GHz inductors and transformers for millimeter-wave

(Bi) CMOS integrated circuits. 2005. 53(1): p. 123-133.

129. Aryan, N.P., Design and Modeling of Inductors, Capacitors and Coplanar

Waveguides at Tens of GHz Frequencies. 2014: Springer.

130. Shepherd, P.R.J.I.t.o.m.t. and techniques, Analysis of Square-Spiral Inductors for

Use in MMIC's (Short Paper). 1986. 34(4): p. 467-472.

131. Mohan, S.S., et al., Simple accurate expressions for planar spiral inductances. 1999.

34(10): p. 1419-1424.

132. Zhang, J., D. Zhao, and X. You. A CMOS LNA with Transformer-Based

Integrated Notch Filter for Ku-Band Satellite Communications. in 2021 IEEE MTT-

S International Microwave Symposium (IMS). 2021. IEEE.

133. Zhu, W., et al., A 10.56-GHz broadband transceiver with integrated T/R switching

via matching network reuse and 0.3–2.1-GHz baseband in 28-nm CMOS technology.

2019. 67(7): p. 2599-2617.

134. Peng, N. and D. Zhao. A Ku-band low-noise amplifier in 40-nm CMOS. in 2019

IEEE International Conference on Integrated Circuits, Technologies and Applications

(ICTA). 2019. IEEE.

135. Gao, H., et al., A 6.5–12-GHz balanced variable-gain low-noise amplifier with

frequency-selective gain equalization technique. 2020. 69(1): p. 732-744.

136. Kim, D., et al., An X-band switchless bidirectional GaN MMIC amplifier for phased

array systems. 2014. 24(12): p. 878-880.

137. Hinata, K., et al., High Power THz Oscillators with Offset-fed Slot Antenna and

High Current Density Resonant Tunneling Diodes. 2009 34th International

Conference on Infrared, Millimeter, and Terahertz Waves, Vols 1 and 2, 2009:

p. 264-265.

138. Simons, R.N., Coplanar waveguide circuits, components, and systems. 2004: John

Wiley & Sons.

139. Beilenhoff, K., et al., Open and short circuits in coplanar MMIC's. 1993. 41(9): p.

1534-1537.

140. Da Silva, E., High frequency and microwave engineering. 2001: Newnes.

141. Sharma, R., et al., RF parameter extraction of MMIC nichrome resistors.

Microwave and Optical Technology Letters, 2003. 39(5): p. 409-412.

190

142. Vinayak, S., et al., Ni-Cr thin film resistor fabrication for GaAs monolithic

microwave integrated circuits. Thin Solid Films, 2006. 514(1-2): p. 52-57.

143. Driad, R., et al., Investigation of NiCr Thin Film Resistors for InP-Based Monolithic

Microwave Integrated Circuits (MMICs). Journal of the Electrochemical Society,

2011. 158(5): p. H561-H564.