Doctoral Thesis in Electrical Engineering

Doctoral Thesis in Electrical Engineering

Exploiting the Terahertz Spectrum with Silicon Micromachining

Waveguide Components, Systems and Metrology

JAMES CAMPION

Stockholm, Sweden 2021

of technology

Exploiting the Terahertz Spectrum with Silicon Micromachining

Waveguide Components, Systems and Metrology

JAMES CAMPION

Doctoral Thesis in Electrical Engineering KTH Royal Institute of Technology Stockholm, Sweden 2021

Academic Dissertation which, with due permission of the KTH Royal Institute of Technology, is submitted for public defence for the Degree of Doctor of Philosophy on Monday the 29th of March 2021, Stockholm, Sweden

TRITA-EECS-AVL-2021:17 ISBN 978-91-7873-809-0

Printed by: Universitetsservice US-AB, Sweden 2021

Terahertz spannet (300 GHz - 3 THz) representerar framtiden f¨or den moderna elektroniken d¨ar det f¨or n¨arvarande finns f˚ a kostnadseffektiva l¨osningar. THz fre- kvenser ¨ar av stort intresse inom den vetenskapliga och akademiska sektorn, d¨ar de kan anv¨andas i ett flertal olika applikationer som radioastronomi, radar och tr˚ adl¨os kommunikation. Dagens THz komponenter lindras av deras h¨oga kostna- der, stora format och l˚ ag prestanda. F¨or att vi ska kunna nyttja THz frekvenser kr¨avs nya l¨osningar som m¨ojligg¨or anv¨andning av THz teknik i storskaliga applika- tioner. Teknologin m˚ aste erbjuda ypperlig(byt till f¨orstklassig, perfekt eller annat ord) mekanisk och elektrisk prestanda samt vara kompatibel med de industriella in- strumenten och dess processer. Denna avhandling presenterar utvecklandet av kisel mikrobearbetade v˚ agledarkomponenter till THz frekvenser. Kisel mikrobearbetning erbjuder en unik kombination av h¨og precision, l˚ ag f¨orlust och l˚ aga toleranser i en storskalig process.

Basen i detta arbete fokuserar p˚ a en ny kisel-p˚ a-isolator (SOI) v˚ agledarteknik som

¨ar kompatibel med dagens mikromekaniska infrastruktur. Denna teknologi anv¨ ands f¨or att implementera flera v˚ agledarfilters mellan 100-500GHz, var och en med h¨og prestanda. Vi presenterar en sammansatt plattform f¨or integreringen av integrera- de kretsar (IC) i ett helt kiselbaserat mikromekaniskt system. Till skillnad fr˚ an de tidigare l¨osningar m¨ojligg¨or denna l¨osning ett sammansatt samspel av alla signa- ler i ett och samma material. Integrering uppn˚ as genom tv˚ a unika icke galvaniska

¨overg˚ angar mellan v˚ agledare och kretsar och v˚ agledare-v˚ agledare. Halvautomatiska industriella verktyg skapar system med h¨og exakthet och anv¨ands f¨or att skapa en tr˚ adl¨os l¨ank vid D-band (110-170 GHz). Dessa resultat speglar de f¨orsta stegen i

¨overg˚ angen till denna nya teknologin i den industriella framtiden.

F¨or att denna f¨or¨andring ska vara genomf¨orbar f¨oresl˚ as en ¨overg˚ ang fr˚ an CPW-sond till rektangul¨ara v˚ agledare f¨or att m¨ojligg¨ora karakterisering p˚ a skiva vid 220 - 500 GHz. Detta tar bort behovet av att paketera varje enhet separat, en stor flaskhals i dagens industri. Noggrannheten och precisionen i mikrobearbetning, i kombination med de mekaniska egenskaper som kisel har, g¨or det mycket l¨ampligt f¨or att ska- pa v˚ agledare kalibreringsstandarder. En ny design av kalibrerings standarder som f¨orb¨attrar dagens teknik introduceras. Standardens sp˚ arbarhet ¨ar dokumenterad genom detaljerad mekanisk, elektronisk och statistisk analys av tillverkade prover.

Denna avhandling m¨ojligg¨or utvecklandet av THz komponenter och system samt

metoder f¨or att testa dessa i en etablerad teknologi som m¨ojligg¨or deras anv¨andning

i en m˚ angfald olika applikationer.

The terahertz spectrum (300 GHz - 3 THz) represents the final frontier for modern electronic and optical systems, wherein few low-cost, volume-manufacturable solu- tions exist. THz frequencies are of great scientific and commercial interest, with applications as diverse as radio astronomy, sensing and imaging and wireless com- munications. Current THz technology is restricted by its expense, form-factor and performance limitations. Future exploitation of this spectrum requires the develop- ment of new technologies which support its use in high-volume applications. Any such technology must offer excellent mechanical and electrical performance and be compatible with industrial grade tools and processes. In response to this, this the- sis presents the development of silicon micromachined waveguide components and systems for THz and sub-THz frequencies. Silicon micromachining offers a unique combination of small feature sizes and low surface roughness and manufacturing tolerances in a scalable process.

At the core of this work lies a new silicon-on-insulator (SOI) waveguide technology which minimises surface roughness to provide low insertion loss. Waveguide filters and diplexers between 100–500 GHz are implemented using this technology, each with state-of-the-art performance. A new platform for waveguide systems is devel- oped to enable fully micromachined systems to be realised. In contrast to previous solutions, this platform integrates of all DC, intermediate and radio frequency sig- nals in a single medium. Two unique non-galvanic transitions provide interfaces to active components and metallic waveguides. Semi-automated industrial tools perform system assembly with high accuracy and are used to implement complete transceivers for wireless communication at 110–170 GHz. Commercial-grade silicon germanium integrated circuits are used for all active components. This represents the first step in the adoption of this new technology in an industrial scenario.

Large-scale use of the THz spectrum necessitates a shift from discrete components to complete integrated systems, in a similar matter to that seen in digital elec- tronics and will require accurate, high-throughput characterisation and verification infrastructures. To support this, two transitions from co-planar waveguide probes to rectangular waveguide are proposed to allow for device characterisation in an on-wafer environment from 220–500 GHz. The accuracy and precision of the SOI micromachining process, coupled with the mechanical properties of silicon, make it highly suited to the creation of precision metrology standards. By harnessing these properties, a new class of micromachined waveguide calibration standards is developed, the peformance of which exceeds current solutions. Traceability of the standards is documented through detailed mechanical, electrical and statistcal analysis of fabricated samples.

This work presented in thesis enables the development of THz components and

systems, and methods to test them, in an established, high-volume technology,

enabling their use in a wide range of applications.

Tiger got to sleep, bird got to land;

Man got to tell himself he understand.

— Kurt Vonnegut Jr, Cat’s Cradle

Contents i

List of Publications v

1 Introduction 1

1.1 Exploiting the Terahertz Spectrum: Applications and Usage Scenarios 4

1.2 Active Circuit Technologies for THz Frequencies . . . . 5

1.3 Silicon Micromachining . . . . 7

1.4 Silicon - THz’s New Steel . . . . 8

1.5 Thesis Objectives and Structure . . . . 9

2 Silicon Micromachined Waveguides 11 2.1 Background . . . . 11

2.1.1 Waveguide Theory . . . . 11

2.1.2 Terahertz Waveguide Technologies . . . . 14

2.1.3 Challenges . . . . 18

2.2 Silicon-on-Insulator Micromachined Waveguides . . . . 19

2.2.1 Achievements . . . . 22

2.2.2 Limitations . . . . 23

3 Silicon Micromachined Waveguide Filters 25 3.1 Background . . . . 25

3.1.1 Terahertz Waveguide Filters . . . . 25

3.1.2 DRIE of waveguide filters . . . . 27

3.1.3 Challenges . . . . 28

3.2 SOI Micromachined Waveguide Filters . . . . 29

3.2.1 Axial Filters . . . . 29

3.2.2 In-Plane Filters . . . . 31

3.2.3 Achievements . . . . 34

3.2.4 Limitations . . . . 34

4 Integration Techniques for Silicon Micromachined Waveguides 37 4.1 Background . . . . 37

i

4.1.1 Integrating Active Components with Waveguides . . . . 37

4.1.2 System Level Integration . . . . 39

4.1.3 Challenges . . . . 41

4.2 Integration Techniques for SOI Micromachined Waveguides . . . . . 42

4.2.1 H-plane MMIC to Waveguide Transition . . . . 42

4.2.2 Non-Galvanic Waveguide Interface for System Integration . . 44

4.2.3 Achievements . . . . 46

4.2.4 Limitations . . . . 47

5 Silicon Micromachined Waveguide Systems 49 5.1 Background . . . . 49

5.1.1 THz System Techniques . . . . 49

5.1.2 Micromachined THz Systems . . . . 50

5.1.3 Challenges . . . . 51

5.2 Silicon-on-Insulator Micromachined Systems . . . . 52

5.2.1 THz Microsystem Platform . . . . 52

5.2.2 System Design, Fabrication and Assembly . . . . 53

5.2.3 Micromachined D-band Wireless Link Transceivers . . . . 55

5.2.4 Achievements . . . . 57

5.2.5 Limitations . . . . 57

6 On-Wafer Characterisation of Micromachined Components 61 6.1 Background . . . . 61

6.1.1 Waveguide Flange Characterisation . . . . 61

6.1.2 Wafer Probing Techniques . . . . 62

6.1.3 On-wafer Characterisation of Micromachined Waveguides . . 63

6.1.4 Challenges . . . . 64

6.2 Transitions from CPW Probes to SOI Micromachined Waveguides . 64 6.2.1 Achievements . . . . 67

6.2.2 Limitations . . . . 68

7 Silicon Micromachined Components for Terahertz Metrology 69 7.1 Challenges in Terahertz Metrology . . . . 69

7.1.1 Waveguide Flange Tolerances . . . . 70

7.1.2 Calibration Standards and Techniques . . . . 72

7.1.3 Establishing Traceability . . . . 74

7.2 Silicon Micromachined Waveguide Calibration Standards . . . . 75

7.3 Alignment Techniques for Silicon Micromachined Components . . . . 77

7.4 Traceability of Silicon Micromachined Waveguide Components . . . 79

7.5 Achievements . . . . 82

7.6 Limitations . . . . 82

8 Conclusions 83

9 Outlook 85

Acknowledgments 87

Bibliography 89

This thesis is based on the following papers in peer-reviewed interna- tional journals and reviewed conference proceedings:

I. ”A Very Low Loss 220–325 GHz Silicon Micromachined Waveguide Tech- nology,”

Bernhard Beuerle, James Campion, Umer Shah and Joachim Ober- hammer, in IEEE Transactions on Terahertz Science and Technology, vol. 8, no. 2, pp. 248–250, 2018

https://doi.org/10.1109/tthz.2018.2791841

II. ”Investigation of Fabrication Accuracy and Repeatability of High-Q Silicon-Micromachined Narrowband Sub-THz Waveguide Filters,”

Oleksandr Glubokov, Xinghai Zhao, James Campion, Bernhard Beuerle, Umer Shah and Joachim Oberhammer, in IEEE Transactions on Microwave Theory and Techniques, vol. 67, no. 9, pp. 3696–3706, 2019

https://doi.org/10.1109/tmtt.2019.2926244

III. ”Micromachined Filters at 450 GHz With 1% Fractional Bandwidth and Unloaded Q Beyond 700,”

Oleksandr Glubokov, Xinghai Zhao, James Campion, Umer Shah and Joachim Oberhammer, in IEEE Transactions on Terahertz Science and Technology, vol. 9, no. 1, pp. 106–108, 2019

https://doi.org/10.1109/tthz.2018.2883075

IV. ”Silicon Micromachined D-Band Diplexer Using Releasable Filling Struc- ture Technique,”

Xinghai Zhao, Oleksandr Glubokov, James Campion, Adrian Gomez- Torrent, Aleksandr Krivovitca, Umer Shah and Joachim Oberhammer, in IEEE Transactions on Microwave Theory and Techniques, vol. 68, no.

8, pp. 3448–3460, 2020

https://doi.org/10.1109/tmtt.2020.3004585

v

V. ”Toward Industrial Exploitation of THz Frequencies: Integration of SiGe MMICs in Silicon-Micromachined Waveguide Systems,”

James Campion, Ahmed Hassona, Zhongxia Simon He, Bernhard Beuerle, Adrian Gomez-Torrent, Umer Shah, Sandro Vecchiattini, Richard Lindman, Torbjorn S. Dahl, Yinggang Li, Herbert Zirath and Joachim Oberhammer, in IEEE Transactions on Terahertz Science and Technology, vol. 9, no. 6, pp. 624–636, 2019

https://doi.org/10.1109/tthz.2019.2943572

VI. ”A 110 - 170 GHz non-Galvanic Interface for Integrating Silicon Micro- machined Chips in Metallic Waveguide Systems,”

Mikael Horberg, James Campion, Joachim Oberhammer and Ying- gang Li, in Under Review, IEEE Transactions on Microwave Theory and Techniques, 2021

VII. ”D-band SiGe transceiver modules based on silicon-micromachined inte- gration,”

Yinggang Li, Mikael H¨ orberg, Klas Eriksson, James Campion, Ahmed Hassona, Sandro Vecchiattini, Torbjorn Dahl, Richard Lindman, Mingquan Bao, Zhongxia Simon He, Franz Dielacher, Joachim Ober- hammer, Herbert Zirath and Jonas Hansyrd, in 2019 IEEE Asia-Pacific Microwave Conference APMC, 2019

https://doi.org/10.1109/apmc46564.2019.9038198

VIII. ”A CPW Probe to Rectangular Waveguide Transition for On-wafer Mi- cromachined Waveguide Characterization,”

Bernhard Beuerle, James Campion, Oleksandr Glubokov, Umer Shah and Joachim Oberhammer, in Under Review, IEEE Transactions on Mi- crowave Theory and Techniques, 2021

IX. ”On-wafer Micromachined Waveguide Characterization with CPW Probe to Rectangular Waveguide Transition up to 500 GHz,”

Bernhard Beuerle, James Campion, Oleksandr Glubokov, Umer Shah and Joachim Oberhammer, in Manuscript, 2021

X. ”Silicon Micromachined Waveguide Calibration Standards for Terahertz Metrology,”

James Campion and Joachim Oberhammer, in Submitted , IEEE Transactions on Microwave Theory and Techniques, 2021

XI. ”Repeatability of Silicon Micromachined Components Connected to Metallic Waveguide Flanges at 220 - 330 GHz,”

James Campion, Umer Shah and Joachim Oberhammer, Manuscript, 2021

XII. ”Traceability of Silicon Micromachined Waveguide Calibration Stan- dards from 330 - 500 GHz,”

James Campion and Joachim Oberhammer, Manuscript, 2021

The contribution of James Campion to each of the above publications:

• Paper I: Major part experimental work and data analysis, partial paper writing.

• Paper II: Partial experimental work, minor part design and data analysis, partial paper writing.

• Paper III: Partial experimental work and paper writing.

• Paper IV: All experimental work, major part data analysis, minor part design and paper writing.

• Paper V: All design of micromachined components and data analysis, major part fabrication, experimental work and paper writing.

• Paper VI: All design and fabrication of micromachined components, partial paper writing, minor part data analysis.

• Paper VII: All design and fabrication of micromachined components, partial design of system components and paper writing.

• Paper VIII: Major part theoretical work, experimental work and data anal- ysis, partial paper writing.

• Paper IX: Partial experimental work, data analysis and paper writing.

• Paper X: All design, fabrication, experimental work and data analysis, major part paper writing.

• Paper XI: All design, experimental work and data analysis, major part paper writing.

• Paper XII: All design, fabrication, experimental work and data analysis,

major part paper writing.

The work has also been presented at the following reviewed international conferences:

13. ”Elliptical Alignment Holes Enabling Accuracte Direct Assembly of Micro- Chip to Standard Waveguide Flanges at sub-THz Frequencies,”

James Campion, Umer Shah and Joachim Oberhammer, in 2017 IEEE/MTT-S International Microwave Symposium - IMS, 2017

14. ”An Ultra Low-Loss Silicon-Micromachined Waveguide Filter for D-Band Telecommunication Applications,”

James Campion, Oleksandr Glubokov, Adrian Gomez-Torrent, Alek- sandr Krivovitca, Umer Shah, Lars Bolander, Yinggang Li and Joachim Oberhammer, in 2018 IEEE/MTT-S International Microwave Symposium - IMS, 2018

15. ”A 140 GHz Transmitter with an Integrated Chip-to-Waveguide Transition Using 130nm SiGe BiCMOS Process,”

Zhongxia Simon He, Mingquan Bao, Yinggang Li, Ahmed Hassona, James Campion, Joachim Oberhammer and Herbert Zirath in 2018 Asia-Pacific Microwave Conference (APMC), 2018

16. ”Silicon Micromachined Waveguide Calibration Shims for Terahertz Fre- quencies,”

James Campion, Umer Shah and Joachim Oberhammer, in 2019 IEEE MTT-S International Microwave Symposium (IMS), 2019

17. ”Low-Loss Silicon Micromachined Waveguides Above 100 GHz Utilising Multiple H-Plane Splits,”

Bernhard Beuerle, James Campion, Umer Shah and Joachim Oberham- mer, in 2018 48th European Microwave Conference (EuMC), 2018

18. ”Micromachined multilayer bandpass filter at 270 GHz using dual-mode circular cavities,”

Oleksandr Glubokov, Xinghai Zhao, Bernhard Beuerle, James Campion, Umer Shah and Joachim Oberhammer, in 2017 IEEE MTT-S International Microwave Symposium (IMS), 2017

The author has also contributed to the following peer-reviewed journal papers which are not included in this thesis:

19. ”Freeze-Dried Carbon Nanotube Aerogels for High-Frequency Absorber Applications,”

Ilya V. Anoshkin, James Campion, Dmitri V. Lioubtchenko and Joachim Oberhammer, in ACS Applied Materials & Interfaces, vol. 10, no. 23, pp.

19806–19811, 2018

20. ”Low-Loss, High-Linearity RF Interposers Enabled by Through Glass Vias,”

Umer Shah, James Campion and Joachim Oberhammer, in IEEE Mi-

crowave and Wireless Components Letters, vol. 28, no. 11, pp. 960–962,

2017

ARDE Aspect Ratio Dependent Etching.

BEOL Back End of Line.

BOX Buried Oxide.

CNC Computer Numerical Control.

CPW Co-Planar Waveguide.

CTE Coefficient of Thermal Expansion.

DL Device Layer.

DRIE Deep Reactive Ion Etching.

DUT Device Under Test.

FBW Fractional Bandwidth.

FTS Fourier Transform Spectroscopy.

GaAs Gallium Arsenide.

HBT Heterojunction Bipolar Transistor.

HL Handle Layer.

IC Integrated Circuit.

InP Indium Phosphide.

LRL Line Reflect Line.

MEMS Microelectromechanical Systems.

xi

mHEMT Metamorphic High Electron Mobility Transistor.

MMIC Monolithic Microwave Integrated Circuit.

MRC Misalignment Resistant Calibration.

mTRL Multiline TRL.

PCB Printed Circuit Board.

RF Radio Frequency.

RFS Releasable Filling Structure.

RIE Reactive Ion Etching.

RTD Resonant Tunnelling Diode.

SiGe Silicon Germanium.

TDS Time Domain Spectroscopy.

TRL Through Reflect Line.

VNA Vector Network Analyzer.

Introduction

The first chapter of this thesis serves as an introduction to the thesis and its con- tents. A high-level description of terahertz frequencies, technologies and their ap- plication provides context for the work presented in later chapters. The historical development of micromachining techniques, the main focus of the thesis, is charted to familiarize the reader. Specific objectives for the thesis and the structure of the remaining chapters are defined.

Terahertz frequencies (0.3–3 THz

) lie at the boundary between classical mi- crowave electronics and infrared photonics (Figure 1.1). At these frequencies, the techniques, materials and designs used in each respective field begin to reach their limits, and further scaling, be it upwards/downwards in frequency, is prohibited.

This results in a drastic reduction in output power for both electronic and pho- tonic devices, creating a band of frequencies where no high power signal sources are available [1, 2]. Historically, this region has been referred to as the THz Gap.

Terahertz frequencies offer great promise in a wide range of applications due to their unique properties, the wide swathes of available bandwidth and their inter- action with various kinds of matter [3, 4]. However, the lack of high quality THz sources, and the expense, bulk and complexity of the required componentry has largely restricted use of the THz spectrum to niche scientific and academic scenar- ios. Prior to the early 2000s, radio astronomy and molecular spectroscopy were the sole areas in which THz technology found significant use [5]. The specialised na- ture of such activities and their value to society justified the high associated cost; a lack of commercial interest in the THz spectrum provided little impetus to develop more affordable solutions. Continual advances in semiconductor design, processing

1There are several definitions of the terahertz frequency spectrum. The IEEE definition is used throughout this thesis. Frequencies below 300 GHz are referred to as sub-THz or millimeter-wave.

1

Frequency Complexit

y Applic

ation s

Systems

Comp onen ts

3 THz

λ₀(-)

3 nm 3 μm

300 μm 30 mm

3 m 300 m

f (Hz)

10¹⁶ 10¹⁴

10¹² 10¹⁰

10⁸ 10⁶

RF / Microwave / mm-Wave Terahertz IR UV

Figure 1.1: The electromagnetic spectrum and the two-dimensional THz Gap. The coloured shapes represent progress across three separate categories: components, systems and applications. Although progress is being made in realising THz com- ponents, few complete systems are available. This limits exploitation of the appli- cations of THz frequencies. RF - radio frequency, IR - infrared, UV - Ultraviolet.

The visible spectrum of light lies between the IR and UV bands.

and packaging techniques over the past two decades have pushed the operation of integrated circuits well above 300 GHz [6]. With this has come renewed interest in the THz spectrum and the promise it offers. The THz Gap can be considered as a two-dimensional phenomenon, as proposed in [7]. Rather than restricting the term to available output power, it can be extended to three general categories: compo- nents, systems and applications (Figure 1.1). Although progress is being made in the development of THz components, system development lags somewhat behind.

Only when both needs are fulfilled and THz technology is widely available will the potential applications of THz technology be able to be realised.

THz components are largely dominated by a single technology: the hollow rect-

angular waveguide. While partially for historical reasons, the benefits offered by

rectangular waveguides and the accumulated knowledge in their design and use

ensure continued prevalence. Metallic hollow waveguides provide a sealed electro-

(a) (b)

Figure 1.2: (a) A 1.2 THz Schottky diode based receiver front-end for planetary science, with waveguide blocks fabricated by CNC milling [9]. (b) Cube satellite radiometer front-end for ice cloud monitoring at 874 GHz [10].

magnetic enclosure and a low loss tranmission medium, unlike that found in planar integrated circuit (IC) transmission lines [8]. Their design is conceptually simple, allowing them to be realised using industrial tools such as computer numerical con- trol (CNC) milling. They suffer, however, from some inherent weaknesses. Their large mass and volume prevents compact integration and results in THz systems be- ing prohibitively bulky (Figure 1.2). The feature size and level of precision required in THz waveguides is beyond the capabilities of conventional CNC tools, making them both challenging and highly expensive to produce, while the serial nature of such processes limits production volumes. The maximum complexity of metallic waveguide components is also hampered by the capabilities of CNC milling. These limitations drive a search for alternative technologies with which to realise THz components and systems.

This thesis proposes a solution to all of the above in the form of silicon micro-

machined waveguides - hollow waveguides etched in silicon wafers; highly precise,

volume-manufacturable and potentially low cost. New kinds of silicon microma-

chined waveguides are proposed and realised to build complete components and

systems for use at sub-THz and THz frequencies. In doing so, this thesis seeks

to enable the widespread exploitation of the THz spectrum and push THz tech-

nology into the commercial and industrial sectors, enabling new applications. To

understand the impact of achieving this goal, it is instructive to first consider the

conceivable applications of the THz spectrum and their implications on THz tech-

nology.

0 50 100 150 200 250 300 350 400 450 0.1

1 10 100

Frequency (GHz)

Attenuation(dB/km)

N x 250MHz channels

Frequency bands

100mm/h 50mm/h 20mm/h 5mm/h 0mm/h 90

22 29 8

7 15 29 49 30

100 110 120 130 140

68GHz Spectrum not yet allocated W band D band

150 160 170 180GHz

Figure 1.3: Atmospheric attenuation (dB/km) of signals ranging from 0–450 GHz.

Each curve represents the attenuation for a given rainfall rate. Frequency bands targeted in next generation wireless networks (6G) are also indicated. Adapted from [11].

1.1 Exploiting the Terahertz Spectrum: Applications and Usage Scenarios

Historically, THz frequencies have been limited to a select few applications, where their uniqueness cannot be ignored. One such application is radio astronomy. Many small to medium sized molecules have rotational or vibrational modes within the THz spectrum, permitting us to detect and study them [12]. This allows us to de- termine the composition of the universe around us and understand how it came to be. Even if this were the only application of THz frequencies we would still pursue improvements in THz technology, such is the value it contributes both scientifi- cally and economically [13]. Thankfully, this is not the case. THz spectroscopy techniques also find use in contexts as diverse as material characterisation [14], detection of toxic compounds [15] and examination of DNA molecules [16]. Imag- ing and sensing systems also rely on the interaction of THz radiation with matter.

Such systems can be used in security contexts to detect explosives and weaponry [17, 18], with the possibility to scan targets at a distance [19]. More sedate, but no less important, is the utilisation of such techniques in in vivo examinations of the human body [20] or inspection of the food and water we eat and drink [21]. These represent a melding of microwave electronic and optical techniques - the required signal sources are often designed using microwave techniques, while detection and system design lies closer to the field of optics.

Quite aside from the above applications lies the field of wireless communications,

which is heavily reliant on microwave engineering techniques and Radio Frequency (RF) circuitry. The continued increase in demand for wireless data shows no signs of abating, with the global average consumption per subscriber month expected to reach 34 GB by 2026 [22]. The recent roll-out of 5G networks will not be sufficient to meet this demand [23]. This quandary is one of the key factors driving the devel- opment of the next generation of mobile networks - 6G - where the sub mm-wave and terahertz spectrum will play a central role [24] Despite the relative infancy of 5G infrastructure, attention has now turned to 6G, which represents the next horizon in wireless systems. The development of 6G infrastructure presents new opportunities and challenges which must be addressed in a holistic manner [25, 26].

One of the biggest opportunities is in the area of wireless backhaul, used to transfer data to and from individual cells in a wireless network. The wide swathes of band- width available at THz frequencies are without compare, although it comes with an increase in atmospheric attenuation. The D-band of frequencies (110–170 GHz) offers reasonably low atmospheric attenuation and is thus the target of the next generation of backhaul architecture [11] (Figure 1.3). Above the D-band, a total of 160 GHz of spectrum has been allocated for use in wireless communications systems between 250–450 GHz. A data rate of up to 1 petabit/second (1 million Gbps) can be achieved in a 100 GHz channel [27]; the promise of the THz spectrum to meet our need for more data is thus undoubtable

.

1.2 Active Circuit Technologies for THz Frequencies

Wireless systems, regardless of their operational frequency, require two fundamen- tal components: a source of radiation, and a way of receiving and detecting it. If information is not to be lost, the power level of the source must be sufficiently high to overcome the noise generated in the receiver and any attenuation incurred be- tween them. Our use of the THz spectrum has long been restricted by the dearth of such components. Examination of the saturated output power of electronic solid state sources (Figure 1.4) reveals a sharp roll-off in available power above 100 GHz. This picture is starting to change, however, and significant progress has been made over the past 3 decades that may make high power, room temperature THz sources readily available. Solid-state THz sources can be divided into two distinct categories: two-terminal (such as Schottky, Gunn, resonant-tunnelling and Esaki diodes) and three-terminal (bipolar, heterojunction bipolar, and high elec- tron mobility transistor) devices. Within each sub-category of device exists a range of various implementations, utilising different materials, processing techniques and designs. Two-terminal devices were the first to achieve high power levels at THz fre- quencies and are well suited to radio astronomy and spectroscopy applications, with

2Although this figure is almost incomprehensibly large, it represents but 5% of the computa- tional power of the human brain [27].

-30 -20 -10 0 10 20 30 40 50 60 70

0.1 1 10 100 1000

Psat(dBm)

Frequency (GHz) CMOS

SiGe GaN GaAs LDMOS InP Trend_CMOS Trend_SiGe Trend_GaN Trend_GaAs Trend_LDMOS Trend_InP Oscillators Multipliers

Figure 1.4: Saturated output power of various transistor amplifier, multiplier and oscillator based sources up to 3 THz. Data from [33].

the Schottky diode offering the best performance due to their high responsivity and low noise temperature [2, 9, 28]. Schottky diode mixers have been demonstrated at frequencies as high as 3.2 THz [29]. New approaches to power combining have led to substantial improvements in the output power of Schottky diode frequency mul- tipliers, with 1.64 mW reported at 1.64 THz [30]. Recent breakthroughs in resonant tunnelling diode (RTD) technology has pushed their operation above 1.92 THz [31];

progress had, for many years, stagnated at 712 GHz [32].

Transistor based sources have also undergone rapid evolution, raising their op- erating frequency, efficiency and available power to new heights. While their noise performance cannot rival that of Schottky diodes, transistor based sources allow for the creation of multi-functional MMICs (monolithic microwave integrated circuits) on a single substrate. Early progress was made using III-V devices such as gallium arsenide (GaAs) metamorphic high electron mobility transistors (mHEMTs) [34].

However, it took the development of indium phosphide (InP) HEMT technologies

to allow transistors to achieve a maximum frequency of oscillation (f

) above

1.5 THz [35]. InP heterostructures have also been used to create heterojunction

bipolar transistors (HBTs), the f

of which can exceed 1 THz [36]. Silicon based

THz transistors have grown from the digital electronics industry to act as viable al-

ternatives to InP and GaAs devices. The f

of CMOS transistors peaks at around

300 GHz, far below III-V devices [7]. However, by combining large-arrays of transis-

tors, useful power levels can be achieved over 1 THz [37]. Silicon Germanium (SiGe)

HBTs and BiCMOS (bicombinatory CMOS) offer higher f

(720 GHz, [38]), with

future scaling and processing improvements expected to bring their operation above

2 THz [39]. Spatial combining techniques can be used to boost achievable output power levels, in a similar manner as to with CMOS [40]. The high level of inte- gration of silicon technologies makes them highly appealing for commercial THz applications [41].

Vacuum electronics can provide high power, stable sources of THz radiation. How- ever, as they are not adopted in this thesis, their performance is not discussed here.

The interested reader is referred to [42] for a complete review of such technologies.

1.3 Silicon Micromachining

Microelectromechanical Systems (MEMS), combine electrical and mechanical com- ponents in a single device which is fabricated using microfabrication batch pro- cessing techniques [43]. The advent of MEMS in the 1970s and 80s led to rapid industrial development and the creation of countless new techniques and devices, including highly miniaturised pressure, temperature and chemical sensors [44]. To- day, MEMS is a mature technology; advanced infrastructure and processes permit high-volume production of MEMS components, which are found in a wide range of consumer and industrial products. MEMS techniques were later adapted to RF frequencies, creating the field known as RF MEMS [45]. RF MEMS designs enable reconfigurable components to be realised and offer certain distinct advantages over solid state alternatives, including high linearity, high resonator quality factor and increased power handling capabilities [46]. RF MEMS technology has been success- fully harnessed to create reconfigurable waveguide components at THz frequencies [47, 48].

One of the core techniques utilised in MEMS is micromachining, which grew out of the IC sector, where it is used to pattern electronic components in silicon. MEMS exploits the mechanical, rather than electrical, properties of silicon [49]

. Two distinct approaches to micromachining exist - surface and bulk micromachining.

Whereas surface micromachining involves the processing of thin films deposited on a silicon wafer, bulk micromachining refers to processes wherein the substrate itself is patterned and shaped [50]. Etching processes are our primary tool for shaping silicon and can be performed both istropically and anisotropically using either wet or dry etching. Although widely used throughout the MEMS field, wet etching pro- cesses are limited in terms of their anisotropy and hence achievable aspect ratio.

The same is true of dry etching processes such as reactive ion etching (RIE), where the substrate is bombarded with ions from a plasma, creating anisotropic features [51]. Deep reactive ion etching (DRIE) techniques enable much higher aspect ratios to be achieved. Here, passivation is applied to the sidewalls of an etched area to

3Micromachining and MEMS are not specifically restricted to silicon, although it is the preva- lent material in use today. The discussion here is limited to silicon for brevity. Micromachining of other materials is discussed in Chapter 2.

control the degree of anisotropy. Passivation and etching can be performed simul- taneously, as in cryogenic DRIE [52], or in alternate steps using time-multiplexing.

The latter technique was developed at Robert Bosch GmbH in the mid 1990s [53–

56] and is commonly referred to as the Bosch process.

DRIE is the most widespread method of silicon micromachining thanks to its ability to realise high aspect ratios in a stable, repeatable process. DRIE, and the Bosch process in particular, has several associated hindrances. The time-multiplexed na- ture of the Bosch process creates “scallops” on the sidewalls of an etch which can affect device performance. Aspect ratio dependent etching (ARDE) causes the sid- wall profile of an etch to vary depending on its aspect ratio; devices incorporating different feature sizes, etch depths and aspect ratios can have multiple sidewall pro- files as a result of ARDE. In general, ARDE causes the sidewalls of a DRIE trench to slope - the direction and angle of the slope is process dependent. Tuning of the Bosch process can help to alleviate some of the above defects [57], but they are impossible to eliminate entirely. A full review of high aspect ratio etching and its related challenges can be found in [51].

Micromachining is a highly promising solution for the creation of THz waveguide components and systems as it combines the precision of photolithographic tech- niques with the ability to manufacture at high-volumes using MEMS infrastructure.

The mechanical properties of silicon also make it a well-suited replacement for tradi- tional metallic components. Much pioneering work in this area has been performed at NASA’s Jet Propulsion Laboratory, where silicon micromachined waveguides, antennas and packages for use up to 1.9 THz have been implemented [8, 58].

1.4 Silicon - THz’s New Steel

In 1974, M. Lepselter of Bell Laboratories gave a talk entitled ”Silicon Technology - the New Steel” wherein he argued that the emergence of silicon integrated cir- cuits would usher in a new industrial revolution, in the same way that steel did a century beforehand [59]. His prediction would prove to be true - silicon integrated circuits and MEMS components lie at the heart of the digital electronics which have revolutionised modern society. In light of the applications described previ- ously, it appears that silicon is well poised to have a similar impact on the THz spectrum. Many of the application scenarios envisaged for this spectrum depend on the availability of low cost, high performance components that can be manufactured and deployed in high-volumes. Of the active circuit technologies outlined above, only those based on silicon fulfill these criteria [7, 60]. Their potential integration density and the ability to implement THz and digital electronics is unmatched.

Despite this, waveguides will remain the transmission line medium of choice. It

is therefore imperative that a waveguide technology which fits the above criteria

be realised. Silicon micromachined waveguides are the most promising candidates

to achieve this goal, as will be shown throughout this thesis. Through combining

silicon with silicon (passive with active), further improvements in integration, RF performance and compactness can be realised and complete systems can be built.

In essence, this represents the central concept of this thesis - by availing of silicon micromachining’s batch processing nature and precision, we can enable use of the THz spectrum in large-scale, industrial scenarios, where current THz technologies are simply too expensive and bulky.

1.5 Thesis Objectives and Structure

The primary aim of this thesis is to demonstrate the potential of silicon micro- machining techniques to enable low-cost, volume-manufacturable THz circuits and systems to be realised. In doing so, the thesis strives to highlight the benefits of such techniques and their advantages over the current state-of-the-art. Industrial compatibility, automated processing and fabrication tolerances are specific points of focus, as these factors are critical to our goals. In addition, the same techniques are applied to the field of THz metrology, where silicon micromachining enables new solutions to several obstacles faced in the characterisation of THz components. The thesis consists of 9 chapters, each focusing on a specific topic related to the above objectives. Each chapter begins with a short introduction to provide context to the work presented in each of the related papers, which are then briefly summarized.

For each topic, the major challenges, achievements and limitations are defined to aid understanding and highlight the main contributions of each paper.

Chapters 2 - 5 are structured consecutively, with each subsequent chapter build- ing on the last. Chapter 2 contains a brief introduction to waveguide theory and a review of THz waveguide technologies. Three different silicon micromachined waveguide technologies (Paper I, X) are presented and their performance bench- marked. In Chapter 3, two of these three are used to implement low loss waveguide filters in a variety of designs and configurations (Paper II, III, IV). The implemen- tation of complete micromachined THz systems is discussed in both Chapter 4 and Chapter 5, wherein two unique integration methods (Paper V, VI) and their use in a D-band wireless transceiver (Paper VII) is presented.

Chapters 6 and 7 are specifically focused on the challenges associated with ex- perimental characterisation of micromachined components and in THz waveguide metrology, respectively. Two novel transitions are presented in Chapter 6 to allow for silicon micromachined waveguides to be characterised using standard wafer prob- ing techniques (Paper VIII, IX). Chapter 7 outlines the contributions of Paper X, XI and XII to the field of THz metrology and the potential of silicon micromachin- ing techniques to overcome major challenges in the field.

High-level conclusions are drawn in Chapter 8 and a future outlook for the work

presented in the thesis, and THz circuits and systems in general, is outlined in

Chapter 9.

Silicon Micromachined Waveguides

This chapter introduces the silicon-on-insulator micromachined waveguide technol- ogy which is utilised in components and systems presented in later chapters. A brief overview of waveguide theory introduces the relevant concepts and parameters, while a review of existing terahertz waveguide technologies establishes the state of the art.

2.1 Background

2.1.1 Waveguide Theory

An arbitrary rectangular waveguide of cross-sectional dimension a×b, a > b, permit- tivity ǫ and permeability µ (Figure 2.1(a)) supports TE

modes whose magnetic field along z (H

) satisfy

H

(x, y, z) = A

cos mπx

a cos nπy

b e

(2.1)

where m and n are the mode indices (integer valued) in x and y, A

an arbitrary amplitude constant and γ the complex propagation coefficient of the waveguide

[61]. In turn, γ is defined as

γ = α + jβ (2.2)

1This thesis focuses on hollow rectangular waveguides, operating at frequencies where only the dominant TE¹⁰ mode propagates. The discussion here is thus limited to such waveguides.

This material is provided as a primer for concepts introduced in later chapters.

11

a

ε, μ b

(a)

E-plane

(b) TE₁₀mode

E

H-plane

(c) H x

z y

x y z

Figure 2.1: (a) Arbitrary rectangular waveguide of cross-sectional dimension a × b.

(b) E-plane and E-field of the TE

waveguide mode. (c) H-plane and H-field of the same.

where α and β are the waveguide’s attenuation and propagation constant, respec- tively. The propagation constant β,

β = q

k

− k

=

s

k

−  mπ a



−  nπ b



; k = ω √ µǫ (2.3)

is positive only when k > k

, the cut-off wave number. As such, propagation occurs in the waveguide only for frequencies f greater than the cutoff frequency f

,

f

= 1 2π√µǫ

s

 mπ a



+  nπ

b



. (2.4)

The wave impedance Z

and guided wavelength λ

of a TE mode are

Z

= kη

β ; η ≈ 377Ω; λ

= 2π

β . (2.5)

In a hollow rectangular waveguide operating in TE

mode, β, and hence f

, Z

and λ

are thus determined by the width of the waveguide (a). This is extremely relevant at THz frequencies, where changes in a due to the result of fabrication tolerances can significantly alter β. The attenuation constant of a rectangular waveguide,

α = α

+ α

, (2.6)

comprises both dielectric (α

) and conductive (α

) terms. Use of a hollow waveguide

eliminates any dielectric losses, reducing α to conductive loss only. The conductive

loss per unit length (in dB/mm) in a rectangular waveguide is given by

α

= α

(1+K

) (2.7)

α

= 4.58 × 10

f σ

2

+ 1 b

q

1 −

!

(2.8)

K

= 2 π arctan

 1.4  R

δ



(2.9)

where α

it the total conductive loss, α

the loss due to conductivity σ

and K

the surface roughness factor. R

is the mean surface roughness of the waveguide’s metallisation and δ the skin depth. Thus, for a fixed a and b, the loss α

is de- termined by σ

and R

alone

. Provided that sufficiently thick metal is applied to the walls of the waveguide, R

is the only fabrication process dependent parameter that impacts α

. Achieving low loss in hollow waveguides is therefore a matter of minimising surface roughness.

The choice of metal coating is a trade-off between cost, process compatibility, in- tended application and performance. While they offer very high conductivity, met- als such as silver and copper are prone to oxidisation and tarnish over time. Gold is the most common metal coating in high-end THz waveguide components and sys- tems as it offers high conductivity and broad process compatibility and is chemically inert. Few methods exist for manufacturing hollow waveguides as a single piece with sufficient precision for THz applications. THz waveguides are therefore often re- alised as two separate parts which are later mechanically fastened together, creating a split-block waveguide. Splitting can be performed along either the waveguide’s E- or H-plane (Figure 2.1(b), (c)). An E-plane split is preferred in many waveguide technologies as it is tolerant to the presence of small gaps along this plane - no surface current lines are broken if the gap is electrically small and the waveguide functions as if properly connected. This also simplifies the insertion of active com- ponents inside a waveguide, as discussed in Chapter 4. Improper connection of an H-plane split waveguide results in significant leakage occurring; achieving proper connection is very challenging at THz frequencies. However, the use of an H-plane split offers several advantages related to the fabrication of micromachined waveg- uides, as will be discussed shortly.

The relation between f

, Z

, λ

and a requires that the dimensions of rectangular waveguides be well defined. Recommended dimensions for THz waveguides were proposed in [69] and have since been largely adopted (Table 2.1), although some variation between waveguide manufacturers occurs [70]. The waveguide bands def- initions listed in Table 2.1 are used throughout all other sections of this thesis.

2Many models for conductive loss exist [62–65]. Accurate determination of α in rectangular waveguides is an active field of research [66–68]. The formulation here is chosen to aid qualitative understanding.

Table 2.1: THz Waveguide Bands and Dimensions

Waveguide Dimensions Frequency WM-864 864 µm×432 µm 220–330 GHz WM-570 570 µm×285 µm 330–500 GHz WM-380 380 µm×190 µm 500–750 GHz WM-250 250 µm×125 µm 750–1100 GHz WM-164 164 µm×82 µm 1.1–1.7 THz WM-106 106 µm×53 µm 1.7–2.6 THz WM-71 71 µm×35.5 µm 2.6–4 THz

2.1.2 Terahertz Waveguide Technologies

Hollow rectangular waveguides are the transmission line medium of choice at THz frequencies, thanks to their low insertion loss, shielded electromagnetic environment and compatibility with modular system architectures. The prevailing method for fabricating such waveguides is CNC milling, wherein a metal substrate is milled to form the body of the waveguide. This fabrication method has several limitations, as will shortly be discussed. As a result, numerous alternatives have been proposed, each promising improvement over CNC milling in one or more aspects. Table 2.2 summarizes the insertion loss per unit length of a range of state-of-the-art THz waveguide technologies. These waveguides are grouped by their method of fabrica- tion to allow comparison. A brief review of these methods will now be performed.

The main performance metric of interest here is the achievable insertion loss. The performance of waveguide technologies and materials are further discussed in Chap- ter 3 and Chapter 5 in the context of component design and system integration and packaging, respectively.

CNC Milling

CNC milling is the mainstay of current THz technology. Metallic CNC milled waveguide components form a large part of all THz systems in use today across both industrial and academic sectors. The widespread nature of this technology is partly due to its historical prevalence but also to the availability of the required tools and infrastructure and lack of compelling alternatives. The performance of CNC milled waveguide components is well established; insertion losses as low as 0.014–0.018 dB/mm between 210–280 GHz were reported in [74]. Tolerances of

±2.5 µm can be achieved by pushing modern CNC tools to their limits [75]. CNC

milling is not without its restrictions, however. Achieving the low surface roughness

(a) (b)

(c) (d)

Figure 2.2: (a, b) CNC milled waveguide components for use at (a) 260 GHz [71]

and (b) 140 GHz [72]. (c, d) 3D printed waveguides for 325–500 GHz, manufactured using two different technologies [73].

and precise tolerances required in THz applications is very challenging. All tooling and process routines must be specially adapted to ensure acceptable performance.

The process is entirely serial in nature, prohibiting the large-scale manufacture of waveguide components. As a result, high-end CNC milled waveguides are expen- sive. Potential miniaturisation of CNC milled components is limited by the process itself - each part must remain sufficiently large to allow for it to be milled. These characteristics make CNC milling unsuited to the high-volume applications outlined in Chapter 1, although it will continue to play a role in other areas.

The performance of CNC milling machines is currently sufficient for realising com-

ponents up to 1 THz. Above this, tolerances better than 1 µm are necessary. Ad-

vancements in the field of vacuum electronics have created a need for hollow waveg-

uides with extremely low loss for use in travelling-wave-tube amplifiers [76] above

200 GHz. This has spurred the development of a prototype nano-CNC machine

which can achieve tolerances of the order of 1 µm and surface roughness below

200 nm [77], [78]. Special diamond based tooling can be used to perform a final

finishing pass on the milled faces and reduce R

to below 40 nm [79]. While they can undoubtedly offer excellent performance, such tools are likely to remain the preserve of specialised applications due to their prohibitive cost and manufacturing processes.

3D Printing

3D printed waveguides are becoming increasingly prevalent due to their low weight, reduced cost and compatibility with complex geometries [80–83]. Metal coated 3D printed waveguides can achieve very low loss (0.018–0.02 dB/mm) between 220–

330 GHz [84]. However, application of such technologies above 1 THz is limited by the achievable feature size and surface roughness [85],which causes a sharp rise in insertion loss [86]. These parameters are strongly dependent on the 3D printing technology, material and print configuration [73] (Figure 2.2(c), 2.2(d)). New tech- niques such as two-photon polymerisation may push the performance of 3D printed waveguides beyond its current limits [87].

Electroforming

Electroforming refers to a general process category wherein electrodeposition is used to deposit metal on surface of an object such as a mould. Waveguides are formed using the latter as the inner volume must be hollow. Several techniques suitable for forming THz waveguides have been developed over the past two decades. LIGA (Lithographie, Galvanformung, Abformung) is a well-established technique that can be used to create moulds with tolerances of 1 µm [76] and surface roughness between 150–200 nm [79]. The approach in [76] utilised a synchotron to perform X-ray lithography, limiting it to specialised applications. UV-LIGA (Figure 2.3(a)) removes this need and enables the creation of waveguide moulds in thick resists such as SU-8 or KMPR [88]. Waveguide components using these processes have been demonstrated in [88–95], among others. Many of these use silicon micromachining to create the required mould.

Thick resist micromachining

The need to dissolve the mould, and the accuracy required to produce it, makes the above electroforming techniques time consuming and complex. By utilising the same materials as electroforming in a different manner, micromachining of thick resists can be used to implement precision hollow waveguide components without the need for subsequent mould removal. The substrate material then forms the body of the waveguide and is later coated with a conductive material. Patterning can be performed with standard photolithographic tools and micromachining techniques.

SU-8 [96] is the most widely adopted material in this category as it can be patterned

(a) (b)

Figure 2.3: Waveguides fabricated using (a) UV-LIGA [95] and (b) DRIE with post-etching oxidation [101].

with high aspect ratios and offers very low surface roughness [97]. As such, the reported performance of passive SU-8 waveguide components is very good [83, 98–

100]. The smooth surfaces of such waveguides results in insertion loss as low as 0.03–0.05 dB/mm [98]. The main restrictions in the use of SU-8 waveguides are related to its mechanical properties (c.f. Chapter 5). The difficulty associated with evenly depositing thick layers of such resists should also be noted.

Silicon Micromachining

The potential of silicon micromachining to fulfill the criteria outlined previously was

outlined in Chapter 1. Due to the planar nature of their source material, silicon

micromachined waveguides must be manufactured in a split topology. In contrast

to metallic waveguides, silicon micromachined waveguides can be split along their

H-plane, as the smooth, flat topography of prime silicon wafers enables them to be

bonded together in various ways [102]. Any joint between two such wafers is then

connected at an atomic scale and no RF leakage occurs. An E-plane split waveg-

uide can be realised by etching two a/2 deep trenches in a silicon wafer, which

are then bonded together (Figure 2.4(a), (e)). If an H-plane split waveguide is

desired, a trench of width a with depth b is etched and then attached to a separate

silicon wafer (Figure 2.4(b), (f)). These approaches suffer from several inherent

drawbacks. The E-plane split waveguide requires an etch depth twice that of an

H-plane split one, leading to ARDE limitations. All four walls of an E-plane waveg-

uide are formed by rough etched surfaces, while three of four walls in an H-plane

split configuration are rough. Deep etching in silicon can create a rounded surface

at the bottom of the trench, changing the waveguide’s cross section [51]. Precise

control of the etch depth is also required. The development of grass on the bottom of the etched trench places limits on the depth and surface roughness of such an etch [103].

Early silicon micromachined waveguides [104–107] made use of such designs, which were later improved further. E-plane and H-plane split waveguides with losses as low as 0.08–0.12 dB/mm and 0.06–0.12 dB/mm at 500–750 GHz are reported in [108]. Through etching of the complete silicon wafer is also possible [109], but re- sults in a waveguide with four rough walls, in a similar manner to an E-plane split.

Following etching of the waveguide a subsequent oxidation and wet etch step can be used to smooth out etching defects (Figure 2.3(b)). A reduction in R

by a factor of 5 from this process was reported in [101], resulting in an insertion loss of 0.05–0.007 dB/mm between 500–750 GHz. However, this required an additional 17 hours of thermal oxidation to be performed, adding significant cost. This process is considered to be at odds with the high-volume applications targeted in this thesis.

The above review is far from exhaustive. Several techniques were omitted for brevity. Additional historical detail on the development of micromachining tech- niques for the creation of hollow waveguides can be found in [110] and [111].

2.1.3 Challenges

Successfully implementing a high-performance THz waveguide technology around which to build complete systems encompasses many hurdles:

• Surface roughness: Assuming the waveguide is covered with sufficient metal, its insertion loss is determined by the surface roughness alone. Low insertion loss is one of the primary advantages of hollow waveguides; minimis- ing surface roughness is vital.

• Process complexity: The fabrication process should comprise as few steps as possible. Each step should be possible to perform with standardised tools and routines.

• Feature size control: Any geometrical dependency on the process parame- ters should be removed where possible. Geometry should instead be defined only by photolithograpy (or other patterning method) and the thickness of the various layers.

• Process scalability: The technology must be able to be realised in large

volumes at relatively low cost while maintaining the above qualities. Serial

Table 2.2: Terahertz Waveguide Technologies

Reference Technology Split Freq. (GHz) IL (dB/mm)

[109] CNC E 325–360 0.20–0.25

[112] CNC E 220–330 0.03–0.06

[74] CNC E 210–280 0.014–0.018

[113] FR4 - 220–330 0.18–0.511

[114] LTCC - 300 1.36

[84] 3D printed - 220–330 0.018–0.02

[86] 3D printed - 500–750 0.13–0.28

[86] 3D printed - 750–1100 1.0–1.9

[98] SU-8 E 220–325 0.03–0.05

[115] DRIE H 500–700 0.10–0.20

[109] DRIE - 325–360 0.125–0.15

[116] DRIE H 325–440 0.35–0.4

[117] DRIE double H 325–500 0.125–0.225

[108] DRIE E 500–750 0.08–0.12

[108] DRIE H 500–750 0.06–0.12

[101] DRIE, w oxidation E 500–750 0.05–0.07

[118] DRIE, w oxidation E 750–1100 0.2–0.25

[119] DRIE H 750–1100 0.38–0.42

[120] DRIE triple H 110–170 0.008–0.016

Paper I DRIE double H 220–325 0.02–0.07

Paper X DRIE - 325–500 0.05–0.15

fabrication processes should be avoided.

• Compatibility with IC processes: Complete systems require the combi- nation of active components with passive waveguides. The waveguide tech- nology should be compatible with standard IC fabrication processes to allow for potential heterogeneous integration or co-fabrication of the two distinct media.

2.2 Silicon-on-Insulator Micromachined Waveguides

In response to the above challenges, this thesis presents a new waveguide technology

based on micromachined silicon-on-insulator (SOI) wafers. This technology forms

the backbone of the components and systems presented in the remaining chapters of this thesis. The design, fabrication and performance of waveguides implemented in this technology is reported in detailed in Paper I, IV and X and are summarized here.

DL HL BOX

Silicon on Insulator (SOI)

Double H-plane Split (Paper I)

Triple H-plane Split (Paper IV)

Axial Through Etch (Paper X)

DRIE DRIE

a a (a * b)

b b/2

b/2

Silicon

E-plane Split Single H-plane Split

DRIE

a a/2

a b

b

b DRIE

Si SiO₂ Au

(a)

(e)

(c)

(g) (h)

(b)

(f)

(d)

(i)

Figure 2.4: Comparison of various silicon micromachined waveguide topologies based on silicon and silicon on insulator wafers. (a,e) Single E-plane split, (b, f) single H-plane split, (c, g) double H-plane split (Paper I), (h) triple H-plane split ([120], Paper IV) and (d, i) axial through etch (Paper X).

A silicon-on-insulator wafer comprises three separate physical layers (Figure 2.4) - two silicon layers, the device and handle layer (DL and HL, respectively), sep- arated by a thin buried silicon oxide (SiO

) layer, referred to as the BOX layer.

In essence, an SOI wafer is two separate silicon wafers which are bonded together at the BOX layer

. Both wafers must initially be sufficiently thick to support the wafer-wafer bonding process. The two layers can later be thinned by chemical or me- chanical processing to create SOI wafers with specific DL and HL thicknesses. Each layer can be processed separately, allowing complex geometries to be realised. SOI wafers have been extensively used in the development of micromachined co-planar waveguide (CPW) probes for on-wafer device characterisation at THz frequencies [122–126] and radio astronomy components [127]. In all of these, only the SOI’s DL forms part of the final device; the HL is removed during processing. Reck et al. demonstrated an E-plane split waveguide using SOI wafers at 750–1100 GHz,

3Historically, insulating materials other than silicon dioxide have also been used [121], but SiO2is the most common insulator in modern SOI wafers.

where the DL is used to form one half of the waveguide [118]. Previous work at KTH led to the development of waveguide integrated MEMS components, where the DL again acted as the functional layer [47, 48].

By contrast, the waveguide technology developed here adopts the HL as the main functional layer. A waveguide is created by etching a trench of width a and depth b in the HL of the SOI wafer (Figure 2.4(c)). The BOX layer acts as an etch stop, preventing etching of the DL. The height of the waveguide is therefore defined by the HL thickness and its tolerance, removing the need for precise depth control. The BOX layer is later removed, exposing the bottom surface of the DL. To complete the waveguide, the wafer is metallised and a separate silicon wafer (also metallised) is bonded to it. The resulting waveguide has H-plane splits along both its top and bottom walls and is denoted as a double H-plane split (Figure 2.4(g)).

As only two of its surfaces are etched during DRIE, the overall surface roughness is greatly reduced. The waveguides presented in Paper I have a reduced height of 275 µm. Although this increases their insertion loss (c.f. Eq. 2.7), reducing the etch depth ensures that the aspect ratio is kept within a suitable range and limits the sidewall roughness, which is intrinsically linked to etch depth. If a full height waveguide is desired, a pair of H-plane etched waveguides can be joined at their centre to create a triple H-plane split (Figure 2.4(h)). This approach further reduces α

while also maintaining a low R

and extends the applicability of the SOI waveguide technology to frequencies as low as 110 GHz [120]. This increases the industrial relevance of the technique, as it removes one of the limitations of tra- ditional silicon micromachined waveguides (which cannot be etched to full depth at such frequencies). Aside from H-plane topologies, the SOI technology is also compatible with axial through wafer etch implementations, as used in [47, 48] and Paper X. Here, the waveguide aperture is etched through one or more layers of the SOI (Figure 2.4(d), (i)). The resulting waveguide is then perpendicular to the plane of the wafer; its length is defined by the thickness of the chosen layers. Through etched waveguides suffer from the fact that all four of their sides are etched and are thus rough.

The measured insertion loss per unit length of all three kinds of waveguide is

plotted in Figure 2.5(a). Effective conductivity (σ

) values for each were extracted

by fitting the theoretical insertion loss to each result. Of the three, the triple H-

plane split had the highest σ

, closely followed by the double H-plane split (1.5

and 1.4 × 10

S/m, respectively.) These values are of the order of those reported

in [118], without the use of any surface roughness reduction methods. The benefit

of such techniques is accentuated by the relatively low σ

of the through etched

waveguide. Benchmarking of the insertion loss of each waveguide further emphasises

the promise of the SOI technologies proposed here (Table 2.2).

100 150 200 250 300 350 400 450 500 Frequency (GHz)

−0.20

−0.15

−0.10

−0.05 0.00 0.05

|S21|(dB/mm)

Triple H Split Double H Split Through Etch

σef f= 1.5 × 10⁷

σef f= 1.4 × 10⁷

σef f= 0.6 × 10⁷

(a)

HL

DL 1651 μm

400 μm

(b)

HL DL

864 μm 275 μm

(c)

DL

570 μm 285 μm

(d)

Figure 2.5: (a) Measured insertion loss per unit length of the waveguide tech- nologies presented in [120] (110–170 GHz), Paper I (220–330 GHz) and Paper X (325–500 GHz). The theoretical insertion loss for of each waveguide with bulk gold conductivity (σ = 4.1 × 10

S/m) and fitted effective conductivity σ

is also shown. (b, c, d) SEM images of each waveguide.

2.2.1 Achievements

• Low insertion loss: By eliminating roughness on two of the waveguide sur- faces, the double and triple H-plane split topologies achieve very low insertion loss and compare favourably with the state-of-the-art.

• Process simplicity: Fabrication of such waveguides requires a total of two

masks and silicon etches. No additional oxidation steps or other surface rough-

ness treatments were used.