Fundamentals of Terahertz Devices and Applications

An authoritative and comprehensive guide to the devices and applications of Terahertz technology

Terahertz (THz) technology relates to applications that span in frequency from a few hundred GHz to more than 1000 GHz. Fundamentals of Terahertz Devices and Applications offers a comprehensive review of the devices and applications of Terahertz technology. With contributions from a range of experts on the topic, this book contains in a single volume an inclusive review of THz devices for signal generation, detection and treatment.

Fundamentals of Terahertz Devices and Applications offers an exploration and addresses key categories and aspects of Terahertz Technology such as: sources, detectors, transmission, electronic considerations and applications, optical (photonic) considerations and applications. Worked examples?based on the contributors? extensive experience? highlight the chapter material presented. The text is designed for use by novices and professionals who want a better understanding of device operation and use, and is suitable for instructional purposes This important book:

About the Editor xvii

List of Contributors xix

About the Companion Website xxi

1 Introduction to THz Technologies 1
Dimitris Pavlidis

2 Integrated Silicon Lens Antennas at Submillimeter-wave Frequencies 5
Maria Alonso-delPino, Darwin Blanco and Nuria Llombart Juan

2.1 Introduction 5

2.2 Elliptical Lens Antennas 7

2.2.1 Elliptical Lens Synthesis 8

2.2.2 Radiation of Elliptical Lenses 10

2.2.2.1 Transmission Function T(Q) 12

2.2.2.2 Spreading Factor S(Q) 14

2.2.2.3 Equivalent Current Distribution and Far-field Calculation 16

2.2.2.4 Lens Reflection Efficiency 17

2.3 Extended Semi-hemispherical Lens Antennas 19

2.3.1 Radiation of Extended Semi-hemispherical Lenses 20

2.4 Shallow Lenses Excited by Leaky Wave/Fabry–Perot Feeds 22

2.4.1 Analysis of the Leaky-wave Propagation Constant 24

2.4.2 Primary Fields Radiated by a Leaky-wave Antenna Feed on an Infinite Medium 25

2.4.3 Shallow-lens Geometry Optimization 27

2.5 Fly-eye Antenna Array 29

2.5.1 Silicon DRIE Micromachining Process at Submillimeter-wave Frequencies 31

2.5.1.1 Fabrication of Silicon Lenses Using DRIE 32

2.5.1.2 Surface Accuracy 33

2.5.2 Examples of Fabricated Antennas 35

Exercises 36

Exercise 1: Derivation of the Transmission Coefficients and Lens Critical Angle 36

Exercise 2 37

Exercise 3 38

References 39

3 Photoconductive THz Sources Driven at 1550 nm 43
Elliott R. Brown, Björn Globisch, Guillermo Carpintero, Alejandro Rivera, Daniel Segovia-Vargas and Andreas Steiger

3.1 Introduction 43

3.1.1 Overview of THz Photoconductive Sources 43

3.1.2 Lasers and Fiber Optics 45

3.2 1550-nm THz Photoconductive Sources 47

3.2.1 Epitaxial Materials 47

3.2.1.1 Bandgap Engineering 47

3.2.1.2 Low-Temperature Growth 50

3.2.2 Device Types and Modes of Operation 52

3.2.3 Analysis of THz Photoconductive Sources 53

3.2.3.1 PC-Switch Analysis 54

3.2.3.2 Photomixer Analysis 56

3.2.4 Practical Issues 61

3.2.4.1 Contact Effects 62

3.2.4.2 Thermal Effects 63

3.2.4.3 Circuit Limitations 68

3.3 THz Metrology 71

3.3.1 Power Measurements 71

3.3.1.1 A Traceable Power Sensor 71

3.3.1.2 Exemplary THz Power Measurement Exercise 74

3.3.1.3 Other Sources of Error 77

3.3.2 Frequency Metrology 78

3.4 THz Antenna Coupling 79

3.4.1 Fundamental Principles 79

3.4.2 Planar Antennas on Dielectric Substrates 80

3.4.2.1 Input Impedance 81

3.4.2.2 ΔEIRP (Increase in the EIRP of the Transmitting Antenna) 82

3.4.2.3 G/T or A_eff /T 83

3.4.3 Estimation of Power Coupling Factor 83

3.4.4 Exemplary THz Planar Antennas 84

3.4.4.1 Resonant Antennas 84

3.4.4.2 Quick Survey of Self-complementary Antennas 85

3.5 State of the Art in 1550-nm Photoconductive Sources 87

3.5.1 1550-nm MSM Photoconductive Switches 87

3.5.1.1 Material and Device Design 87

3.5.1.2 THz Performance 88

3.5.2 1550-nm Photodiode CW (Photomixer) Sources 90

3.5.2.1 Material and Device Design 90

3.5.2.2 THz Performance 92

3.6 Alternative 1550-nm THz Photoconductive Sources 92

3.6.1 Fe-Doped InGaAs 94

3.6.2 ErAs Nanoparticles in GaAs: Extrinsic Photoconductivity 94

3.7 System Applications 97

3.7.1 Comparison Between Pulsed and CW THz Systems 97

3.7.1.1 Device Aspects 97

3.7.1.2 Systems Aspects 98

3.7.2 Wireless Communications 100

3.7.3 THz Spectroscopy 106

3.7.3.1 Time vs Frequency Domain Systems 106

3.7.3.2 Analysis of Frequency Domain Systems: Amplitude and Phase Modulation 109

Exercises (1–4) 115

Exercises (5–8) THz Interaction with Matter 116

Exercises (9–12) Antennas, Links, and Beams 118

Exercises (13–15) Planar Antennas 120

Exercises (16–19) Device Noise, System Noise, and Dynamic Range 124

Exercises (20–22) Ultrafast Photoconductivity and Photodiodes 125

Explanatory Notes (see superscripts in text) 127

References 128

4 THz Photomixers 137
Emilien Peytavit, Guillaume Ducournau and Jean-François Lampin

4.1 Introduction 137

4.2 Photomixing Basics 137

4.2.1 Photomixing Principle 137

4.2.2 Historical Background 138

4.3 Modeling THz Photomixers 139

4.3.1 Photoconductors 140

4.3.1.1 Photocurrent Generation 140

4.3.1.2 Electrical Model 142

4.3.1.3 Efficiency and Maximum Power 145

4.3.2 Photodiode 146

4.3.2.1 PIN photodiodes 146

4.3.2.2 Uni-Traveling-Carrier Photodiodes 147

4.3.2.3 Photocurrent Generation 148

4.3.2.4 Electrical Model and Output Power 150

4.3.3 Frequency Down-conversion Using Photomixers 151

4.3.3.1 Electrical Model: Conversion Loss 152

4.4 Standard Photomixing Devices 153

4.4.1 Planar Photoconductors 153

4.4.1.1 Intrinsic Limitation 154

4.4.2 UTC Photodiodes 156

4.4.2.1 Backside Illuminated UTC Photodiodes 156

4.4.2.2 Waveguide-fed UTC Photodiodes 156

4.5 Optical Cavity Based Photomixers 158

4.5.1 LT-GaAs Photoconductors 158

4.5.1.1 Optical Modeling 158

4.5.1.2 Experimental Validation 160

4.5.2 UTC Photodiodes 167

4.5.2.1 Nano Grid Top Contact Electrodes 167

4.5.2.2 UTC Photodiodes Using Nano-Grid Top Contact Electrodes 167

4.5.2.3 Photoresponse Measurement 168

4.5.2.4 THz Power Generation by Photomixing 169

4.6 THz Antennas 170

4.6.1 Planar Antennas 171

4.6.2 Micromachined Antennas 173

4.7 Characterization of Photomixing Devices 175

4.7.1 On Wafer Characterization 175

4.7.2 Free Space Characterization 178

Exercises 180

Exercise A. Photodetector Theory 180

Exercise B. Photomixing Model 180

1. Ultrafast Photoconductor 180

2. UTC Photodiode 181

Exercise C. Antennas 181

References 181

5 Plasmonics-enhanced Photoconductive Terahertz Devices 187
Ping-Keng Lu and Mona Jarrahi

5.1 Introduction 187

5.2 Photoconductive Antennas 187

5.2.1 Photoconductors for THz Operation 187

5.2.2 Photoconductive THz Emitters 190

5.2.2.1 Pulsed THz Emitters 191

5.2.2.2 Continuous-wave THz Emitters 192

5.2.3 Photoconductive THz Detectors 193

5.2.4 Common Photoconductors and Antennas for Photoconductive THz Devices 194

5.2.4.1 Choice of Photoconductor 194

5.2.4.2 Choice of Antenna 195

5.3 Plasmonics-enhanced Photoconductive Antennas 196

5.3.1 Fundamentals of Plasmonics 196

5.3.2 Plasmonics for Enhancing Performance of Photoconductive THz Devices 197

5.3.2.1 Principles of Plasmonic Enhancement 197

5.3.2.2 Design Considerations for Plasmonic Nanostructures 203

5.3.3 State-of-the-art Plasmonics-enhanced Photoconductive THz Devices 203

5.3.3.1 Photoconductive THz Devices with Plasmonic Light Concentrators 203

5.3.3.2 Photoconductive THz Devices with Plasmonic Contact Electrodes 205

5.3.3.3 Large Area Plasmonic Photoconductive Nanoantenna Arrays 207

5.3.3.4 Plasmonic Photoconductive THz Devices with Optical Nanocavities 210

5.4 Conclusion and Outlook 212

Exercises 212

References 213

6 Terahertz Quantum Cascade Lasers 221
Roberto Paiella

6.1 Introduction 221

6.2 Fundamentals of Intersubband Transitions 223

6.3 Active Material Design 225

6.4 Optical Waveguides and Cavities 229

6.5 State-of-the-Art Performance and Limitations 232

6.6 Novel Materials Systems 236

6.6.1 III-Nitride Quantum Wells 236

6.6.2 SiGe Quantum Wells 239

6.7 Conclusion 242

Acknowledgments 243

Exercises 243

References 244

7 Advanced Devices Using Two-Dimensional Layer Technology 251
Berardi Sensale-Rodriguez

7.1 Graphene-Based THz Devices 251

7.1.1 THz Properties of Graphene 251

7.1.2 How to Simulate and Model Graphene? 253

7.1.3 Terahertz Device Applications of Graphene 254

7.1.3.1 Modulators 254

7.1.3.2 Active Filters 265

7.1.3.3 Phase Modulation in Graphene-Based Metamaterials 268

7.2 TMD Based THz Devices 270

7.3 Applications 274

Exercises 279

Exercise 1 Computation of the Optical Conductivity of Graphene 279

Exercise 2 Terahertz Transmission Through a 2D Material Layer Placed at an Optical Interface 280

Exercise 3 Transfer Matrix Approach for Multi-layer Transmission Problems 280

Exercise 4 A Condition for Perfect Absorption 280

Exercise 5 Terahertz Plasmon Resonances in Periodically Patterned Graphene Disk Arrays 280

Exercise 6 Electron Plasma Waves in Gated Graphene 280

Exercise 7 Equivalent Circuit Modeling of 2D Material-Loaded Frequency Selective Surfaces 281

Exercise 8 Maximum Terahertz Absorption in 2D Material-Loaded Frequency Selective Surfaces 281

References 281

8 THz Plasma Field Effect Transistor Detectors 285
Naznin Akter, Nezih Pala, Wojciech Knap and Michael Shur

8.1 Introduction 285

8.2 Field Effect Transistors (FETs) and THz Plasma Oscillations 286

8.2.1 Dispersion of Plasma Waves in FETs 287

8.2.2 THz Detection by an FET 289

8.2.2.1 Resonant Detection 293

8.2.2.2 Broadband Detection 294

8.2.2.3 Enhancement by DC Drain Current 295

8.3 THz Detectors Based on Silicon FETs 296

8.4 Terahertz Detection by Graphene Plasmonic FETs 301

8.5 Terahertz Detection in Black-Phosphorus Nano-Transistors 306

8.6 Diamond Plasmonic THz Detectors 310

8.7 Conclusion 312

Exercises 314

Exercises 1–2 314

Exercises 3–10 315

Exercises 11–13 316

References 316

9 Signal Generation by Diode Frequency Multiplication 323
Alain Maestrini and Jose V. Siles

9.1 Introduction 323

9.2 Bridging the Microwave to Photonics Gap with Terahertz Frequency Multipliers 324

9.3 A Practical Approach to the Design of Frequency Multipliers 326

9.3.1 Frequency Multiplier Versus Comb Generator 326

9.3.2 Frequency Multiplier Ideal Matching Network and Ideal Device Performance 326

9.3.3 Symmetry at Device Level Versus Symmetry at Circuit Level 328

9.3.4 Classic Balanced Frequency Doublers 328

9.3.4.1 General Circuit Description 328

9.3.4.2 Necessary Condition to Balance the Circuit 329

9.3.5 Balanced Frequency Triplers with an Anti-Parallel Pair of Diodes 332

9.3.6 Multi-Anode Frequency Triplers in a Virtual Loop Configuration 332

9.3.6.1 General Circuit Description 333

9.3.6.2 Necessary Condition to Balance the Circuit 335

9.3.7 Multiplier Design Optimization 337

9.3.7.1 General Design Methodology 337

9.3.7.2 Nonlinear Modeling of the Schottky Diode Barrier 347

9.3.7.3 3D Modeling of the Extrinsic Structure of the Diodes 348

9.3.7.4 Modeling and Optimization of the Diode Cell 349

9.3.7.5 Input and Output Matching Circuits 351

9.4 Technology of THz Diode Frequency Multipliers 351

9.4.1 From Whisker-Contacted Diodes to Planar Discrete Diodes 351

9.4.2 Semi-Monolithic Frequency Multipliers at THz Frequencies 352

9.4.3 THz Local Oscillators for the Heterodyne Instrument of Herschel Space Observatory 354

9.4.4 First 2.7 THz Multiplier Chain with More Than 10 μW of Power at Room Temperature 356

9.4.5 High Power 1.6 THz Frequency Multiplied Source for Future 4.75 THz Local Oscillator 358

9.5 Power-Combining at Sub-Millimeter Wavelength 361

9.5.1 In-Phase Power Combining 362

9.5.1.1 First In-Phase Power-Combined Submillimeter-Wave Frequency Multiplier 362

9.5.1.2 In-Phase Power Combining at 900 GHz 364

9.5.1.3 In-Phase Power-Combined Balanced Doublers 364

9.5.2 In-Channel Power Combining 365

9.5.3 Advanced on-Chip Power Combining 367

9.5.3.1 High Power 490–560 GHz Frequency Tripler 369

9.5.3.2 Dual-Output 550 GHz Frequency Tripler 369

9.5.3.3 High-Power Quad-channel 165–195 GHz Frequency Doubler 370

9.6 Conclusions and Perspectives 372

Exercises 373

Exercise 1 373

Exercises 2–5 374

Explanatory Notes (see superscripts in text) 374

References 375

10 GaN Multipliers 383
Chong Jin and Dimitris Pavlidis

10.1 Introduction 383

10.1.1 Frequency Multipliers 383

10.1.2 Properties of Nitride Materials 384

10.1.3 Motivation and Challenges 385

10.2 Theoretical Considerations of GaN Schottky Diode Design 386

10.2.1 Analysis by Analytical Equations 386

10.2.1.1 Nonlinearity and Harmonic Generation 386

10.2.1.2 Nonlinearity of Ideal Schottky Diode 388

10.2.1.3 Series Resistance 391

10.2.2 Analysis by Numeric Simulation 394

10.2.2.1 Introduction of Semiconductor Device Numerical Simulation 394

10.2.2.2 Parameters for GaN-Based Device Simulation 395

10.2.2.3 Simulation Results 398

10.2.3 Conclusions on Theoretical Considerations of GaN Schottky Diode Design 407

10.3 Fabrication Process of GaN Schottky Diodes 407

10.3.1 Fabrication Process 407

10.3.2 Etching 409

10.3.3 Metallization 410

10.3.3.1 Ohmic Contacts on GaN 410

10.3.3.2 Schottky Contacts on GaN 410

10.3.4 Bridge Interconnects 413

10.3.4.1 Dielectric Bridge 413

10.3.4.2 Optical Air-bridge 413

10.3.4.3 E-beam Air-bridge 414

10.3.5 Conclusion on Fabrication Process of GaN Schottky Diodes 414

10.4 Small-signal High-frequency Characterization of GaN Schottky Diodes 414

10.4.1 Current-voltage Characteristics 414

10.4.2 Small-signal Characterization and Equivalent Circuit Modeling 415

10.4.2.1 Step 1. Parasitic Elements 417

10.4.2.2 Step 2. Junction Capacitance 419

10.4.2.3 Step 3. Optimization 419

10.4.2.4 Summary 420

10.4.3 Results 422

10.4.4 Conclusion 423

10.5 Large-signal On-wafer Characterization 423

10.5.1 Characterization Approach 423

10.5.2 Large Signal Measurements of GaN Schottky Diodes 424

10.5.2.1 LSNA With 50 Ω Load 424

10.5.2.2 Time Domain Waveforms 425

10.5.2.3 Instant C–V Under Large-signal Driven Conditions 426

10.5.2.4 Power Handling Characteristics 427

10.5.3 LSNA With Harmonic Load-pull 427

10.5.4 Conclusion 428

10.6 GaN Diode Implementation for Signal Generation 428

10.6.1 Large-signal Modeling of GaN Schottky Diodes 428

10.6.2 Frequency Doubler 430

10.7 Multiplier Considerations for Optimum Performance 434

Exercises 440

References 442

11 THz Resonant Tunneling Devices 447
Masahiro Asada and Safumi Suzuki

11.1 Introduction 447

11.2 Principle of RTD Oscillators 449

11.2.1 Basic Operation of RTD 449

11.2.2 Principle of Oscillation 451

11.2.3 Effect of Electron Delay Time 452

11.2.3.1 Degradation of NDC at High Frequency 452

11.2.3.2 Generation of Reactance at High Frequency 453

11.3 Structure and Oscillation Characteristics of Fabricated RTD Oscillators 454

11.3.1 Actual Structure of RTD Oscillators 454

11.3.2 High-frequency Oscillation 456

11.3.3 High-output Power Oscillation 460

11.4 Control of Oscillation Spectrum and Frequency 463

11.4.1 Oscillation Spectrum and Phase-Locked Loop 463

11.4.2 Frequency-tunable Oscillators 465

11.5 Targeted Applications 467

11.5.1 High-speed Wireless Communications 467

11.5.2 Spectroscopy 469

11.5.3 Other Applications and Expected Future Development 470

Exercises 471

Exercise 1–6 471

Exercise 7–8 472

References 472

12 Wireless Communications in the THz Range 479
Guillaume Ducournau and Tadao Nagatsuma

12.1 Introduction 479

12.2 Evolution of Telecoms Toward THz 479

12.2.1 Brief Historic 479

12.2.2 Data Rate Evolution 480

12.2.3 THz Waves: Propagation, Advantages, and Disadvantages 480

12.2.4 Frequency Bands 482

12.2.5 Potential Scenarios 483

12.2.6 Comparison Between FSO and THz 484

12.3 THz Technologies: Transmitters, Receivers, and Basic Architecture 485

12.3.1 THz Sources 485

12.3.2 THz Receivers 486

12.3.3 Basic Architecture of the Transmission System 486

12.4 Devices/Function Examples for T-Ray CMOS 488

12.4.1 Photomixing Techniques for THz CMOS 488

12.4.2 THz Modulated Signals Enabled by Photomixing 489

12.4.3 Other Techniques for the Generation of Modulated THz Signals 492

12.4.4 Integration, Interconnections, and Antennas 492

12.4.4.1 Integration 492

12.4.4.2 Antennas 493

12.5 THz Links 493

12.5.1 Modulations and Key Indicators of a THz Communication Link 493

12.5.2 State-of-the-Art of THz Links 494

12.5.2.1 First Systems 494

12.5.2.2 Photonics-Based Demos 495

12.5.2.3 Electronic-Based Demos 496

12.5.2.4 Beyond 100 GHz High Power Amplification 497

12.5.2.5 Table of Reported Systems 498

12.6 Toward Normalization of 100G Links in the THz Range 498

12.7 Conclusion 502

12.8 Acronyms 502

Exercise: Link Budget of a THz Link 503

References 504

13 THz Applications: Devices to Space System 511
Imran Mehdi

13.1 Introduction 511

13.1.1 Why Is THz Technology Important for Space Science? 512

13.1.2 Fundamentals of THz Spectroscopy 516

13.1.3 THz Technology for Space Exploration 517

13.2 THz Heterodyne Receivers 518

13.2.1 Local Oscillators 521

13.2.1.1 Frequency Multiplied Chains 523

13.2.2 Mixers 524

13.2.2.1 Room Temperature Schottky Diode Mixers 524

13.2.2.2 SIS Mixer Technology 526

13.2.2.3 Hot Electron Bolometric (HEB) Mixers 527

13.2.2.4 State-of-the-Art Receiver Sensitivities 529

13.3 THz Space Applications 530

13.3.1 Planetary Science: The Case for Miniaturization 530

13.3.2 Astrophysics: The Case for THz Array Receivers 533

13.3.3 Earth Science: The Case for Active THz Systems 535

13.4 Summary and Future Trends 538

Acknowledgment 539

Exercises 539

Exercise 1–3 539

Exercise 4 540

References 540

Index 547

Dimitris Pavlidis is a Research Professor at Florida International University. He has been Professor of Electrical Engineering and Computer Science at the University of Michigan (UofM) from 1986 to 2004 and a Founding Member of UofM's first of its kind NASA THz Center in 1988. He served as Program Director in Electronics, Photonics and Magnetic Devices (EPMD) at the National Science Foundation. He received the decoration of "Palmes Academiques" in the order of Chevalier by the French Ministry of Education and Distinguished Educator Award of the IEEE/MTT-S and is an IEEE Life Fellow.