Fundamentals of Terahertz Devices and Applications

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.

• About the Editor xviiList of Contributors xixAbout the Companion Website xxi1 Introduction to THz Technologies 1Dimitris Pavlidis2 Integrated Silicon Lens Antennas at Submillimeter-wave Frequencies 5Maria Alonso-delPino, Darwin Blanco and Nuria Llombart Juan2.1 Introduction 52.2 Elliptical Lens Antennas 72.2.1 Elliptical Lens Synthesis 82.2.2 Radiation of Elliptical Lenses 102.2.2.1 Transmission Function T(Q) 122.2.2.2 Spreading Factor S(Q) 142.2.2.3 Equivalent Current Distribution and Far-field Calculation 162.2.2.4 Lens Reflection Efficiency 172.3 Extended Semi-hemispherical Lens Antennas 192.3.1 Radiation of Extended Semi-hemispherical Lenses 202.4 Shallow Lenses Excited by Leaky Wave/Fabry–Perot Feeds 222.4.1 Analysis of the Leaky-wave Propagation Constant 242.4.2 Primary Fields Radiated by a Leaky-wave Antenna Feed on an Infinite Medium 252.4.3 Shallow-lens Geometry Optimization 272.5 Fly-eye Antenna Array 292.5.1 Silicon DRIE Micromachining Process at Submillimeter-wave Frequencies 312.5.1.1 Fabrication of Silicon Lenses Using DRIE 322.5.1.2 Surface Accuracy 332.5.2 Examples of Fabricated Antennas 35Exercises 36Exercise 1: Derivation of the Transmission Coefficients and Lens Critical Angle 36Exercise 2 37Exercise 3 38References 393 Photoconductive THz Sources Driven at 1550 nm 43Elliott R. Brown, Björn Globisch, Guillermo Carpintero, Alejandro Rivera, Daniel Segovia-Vargas and Andreas Steiger3.1 Introduction 433.1.1 Overview of THz Photoconductive Sources 433.1.2 Lasers and Fiber Optics 453.2 1550-nm THz Photoconductive Sources 473.2.1 Epitaxial Materials 473.2.1.1 Bandgap Engineering 473.2.1.2 Low-Temperature Growth 503.2.2 Device Types and Modes of Operation 523.2.3 Analysis of THz Photoconductive Sources 533.2.3.1 PC-Switch Analysis 543.2.3.2 Photomixer Analysis 563.2.4 Practical Issues 613.2.4.1 Contact Effects 623.2.4.2 Thermal Effects 633.2.4.3 Circuit Limitations 683.3 THz Metrology 713.3.1 Power Measurements 713.3.1.1 A Traceable Power Sensor 713.3.1.2 Exemplary THz Power Measurement Exercise 743.3.1.3 Other Sources of Error 773.3.2 Frequency Metrology 783.4 THz Antenna Coupling 793.4.1 Fundamental Principles 793.4.2 Planar Antennas on Dielectric Substrates 803.4.2.1 Input Impedance 813.4.2.2 ΔEIRP (Increase in the EIRP of the Transmitting Antenna) 823.4.2.3 G/T or Aeff /T 833.4.3 Estimation of Power Coupling Factor 833.4.4 Exemplary THz Planar Antennas 843.4.4.1 Resonant Antennas 843.4.4.2 Quick Survey of Self-complementary Antennas 853.5 State of the Art in 1550-nm Photoconductive Sources 873.5.1 1550-nm MSM Photoconductive Switches 873.5.1.1 Material and Device Design 873.5.1.2 THz Performance 883.5.2 1550-nm Photodiode CW (Photomixer) Sources 903.5.2.1 Material and Device Design 903.5.2.2 THz Performance 923.6 Alternative 1550-nm THz Photoconductive Sources 923.6.1 Fe-Doped InGaAs 943.6.2 ErAs Nanoparticles in GaAs: Extrinsic Photoconductivity 943.7 System Applications 973.7.1 Comparison Between Pulsed and CW THz Systems 973.7.1.1 Device Aspects 973.7.1.2 Systems Aspects 983.7.2 Wireless Communications 1003.7.3 THz Spectroscopy 1063.7.3.1 Time vs Frequency Domain Systems 1063.7.3.2 Analysis of Frequency Domain Systems: Amplitude and Phase Modulation 109Exercises (1–4) 115Exercises (5–8) THz Interaction with Matter 116Exercises (9–12) Antennas, Links, and Beams 118Exercises (13–15) Planar Antennas 120Exercises (16–19) Device Noise, System Noise, and Dynamic Range 124Exercises (20–22) Ultrafast Photoconductivity and Photodiodes 125Explanatory Notes (see superscripts in text) 127References 1284 THz Photomixers 137Emilien Peytavit, Guillaume Ducournau and Jean-François Lampin4.1 Introduction 1374.2 Photomixing Basics 1374.2.1 Photomixing Principle 1374.2.2 Historical Background 1384.3 Modeling THz Photomixers 1394.3.1 Photoconductors 1404.3.1.1 Photocurrent Generation 1404.3.1.2 Electrical Model 1424.3.1.3 Efficiency and Maximum Power 1454.3.2 Photodiode 1464.3.2.1 PIN photodiodes 1464.3.2.2 Uni-Traveling-Carrier Photodiodes 1474.3.2.3 Photocurrent Generation 1484.3.2.4 Electrical Model and Output Power 1504.3.3 Frequency Down-conversion Using Photomixers 1514.3.3.1 Electrical Model: Conversion Loss 1524.4 Standard Photomixing Devices 1534.4.1 Planar Photoconductors 1534.4.1.1 Intrinsic Limitation 1544.4.2 UTC Photodiodes 1564.4.2.1 Backside Illuminated UTC Photodiodes 1564.4.2.2 Waveguide-fed UTC Photodiodes 1564.5 Optical Cavity Based Photomixers 1584.5.1 LT-GaAs Photoconductors 1584.5.1.1 Optical Modeling 1584.5.1.2 Experimental Validation 1604.5.2 UTC Photodiodes 1674.5.2.1 Nano Grid Top Contact Electrodes 1674.5.2.2 UTC Photodiodes Using Nano-Grid Top Contact Electrodes 1674.5.2.3 Photoresponse Measurement 1684.5.2.4 THz Power Generation by Photomixing 1694.6 THz Antennas 1704.6.1 Planar Antennas 1714.6.2 Micromachined Antennas 1734.7 Characterization of Photomixing Devices 1754.7.1 On Wafer Characterization 1754.7.2 Free Space Characterization 178Exercises 180Exercise A. Photodetector Theory 180Exercise B. Photomixing Model 1801. Ultrafast Photoconductor 1802. UTC Photodiode 181Exercise C. Antennas 181References 1815 Plasmonics-enhanced Photoconductive Terahertz Devices 187Ping-Keng Lu and Mona Jarrahi5.1 Introduction 1875.2 Photoconductive Antennas 1875.2.1 Photoconductors for THz Operation 1875.2.2 Photoconductive THz Emitters 1905.2.2.1 Pulsed THz Emitters 1915.2.2.2 Continuous-wave THz Emitters 1925.2.3 Photoconductive THz Detectors 1935.2.4 Common Photoconductors and Antennas for Photoconductive THz Devices 1945.2.4.1 Choice of Photoconductor 1945.2.4.2 Choice of Antenna 1955.3 Plasmonics-enhanced Photoconductive Antennas 1965.3.1 Fundamentals of Plasmonics 1965.3.2 Plasmonics for Enhancing Performance of Photoconductive THz Devices 1975.3.2.1 Principles of Plasmonic Enhancement 1975.3.2.2 Design Considerations for Plasmonic Nanostructures 2035.3.3 State-of-the-art Plasmonics-enhanced Photoconductive THz Devices 2035.3.3.1 Photoconductive THz Devices with Plasmonic Light Concentrators 2035.3.3.2 Photoconductive THz Devices with Plasmonic Contact Electrodes 2055.3.3.3 Large Area Plasmonic Photoconductive Nanoantenna Arrays 2075.3.3.4 Plasmonic Photoconductive THz Devices with Optical Nanocavities 2105.4 Conclusion and Outlook 212Exercises 212References 2136 Terahertz Quantum Cascade Lasers 221Roberto Paiella6.1 Introduction 2216.2 Fundamentals of Intersubband Transitions 2236.3 Active Material Design 2256.4 Optical Waveguides and Cavities 2296.5 State-of-the-Art Performance and Limitations 2326.6 Novel Materials Systems 2366.6.1 III-Nitride Quantum Wells 2366.6.2 SiGe Quantum Wells 2396.7 Conclusion 242Acknowledgments 243Exercises 243References 2447 Advanced Devices Using Two-Dimensional Layer Technology 251Berardi Sensale-Rodriguez7.1 Graphene-Based THz Devices 2517.1.1 THz Properties of Graphene 2517.1.2 How to Simulate and Model Graphene? 2537.1.3 Terahertz Device Applications of Graphene 2547.1.3.1 Modulators 2547.1.3.2 Active Filters 2657.1.3.3 Phase Modulation in Graphene-Based Metamaterials 2687.2 TMD Based THz Devices 2707.3 Applications 274Exercises 279Exercise 1 Computation of the Optical Conductivity of Graphene 279Exercise 2 Terahertz Transmission Through a 2D Material Layer Placed at an Optical Interface 280Exercise 3 Transfer Matrix Approach for Multi-layer Transmission Problems 280Exercise 4 A Condition for Perfect Absorption 280Exercise 5 Terahertz Plasmon Resonances in Periodically Patterned Graphene Disk Arrays 280Exercise 6 Electron Plasma Waves in Gated Graphene 280Exercise 7 Equivalent Circuit Modeling of 2D Material-Loaded Frequency Selective Surfaces 281Exercise 8 Maximum Terahertz Absorption in 2D Material-Loaded Frequency Selective Surfaces 281References 2818 THz Plasma Field Effect Transistor Detectors 285Naznin Akter, Nezih Pala, Wojciech Knap and Michael Shur8.1 Introduction 2858.2 Field Effect Transistors (FETs) and THz Plasma Oscillations 2868.2.1 Dispersion of Plasma Waves in FETs 2878.2.2 THz Detection by an FET 2898.2.2.1 Resonant Detection 2938.2.2.2 Broadband Detection 2948.2.2.3 Enhancement by DC Drain Current 2958.3 THz Detectors Based on Silicon FETs 2968.4 Terahertz Detection by Graphene Plasmonic FETs 3018.5 Terahertz Detection in Black-Phosphorus Nano-Transistors 3068.6 Diamond Plasmonic THz Detectors 3108.7 Conclusion 312Exercises 314Exercises 1–2 314Exercises 3–10 315Exercises 11–13 316References 3169 Signal Generation by Diode Frequency Multiplication 323Alain Maestrini and Jose V. Siles9.1 Introduction 3239.2 Bridging the Microwave to Photonics Gap with Terahertz Frequency Multipliers 3249.3 A Practical Approach to the Design of Frequency Multipliers 3269.3.1 Frequency Multiplier Versus Comb Generator 3269.3.2 Frequency Multiplier Ideal Matching Network and Ideal Device Performance 3269.3.3 Symmetry at Device Level Versus Symmetry at Circuit Level 3289.3.4 Classic Balanced Frequency Doublers 3289.3.4.1 General Circuit Description 3289.3.4.2 Necessary Condition to Balance the Circuit 3299.3.5 Balanced Frequency Triplers with an Anti-Parallel Pair of Diodes 3329.3.6 Multi-Anode Frequency Triplers in a Virtual Loop Configuration 3329.3.6.1 General Circuit Description 3339.3.6.2 Necessary Condition to Balance the Circuit 3359.3.7 Multiplier Design Optimization 3379.3.7.1 General Design Methodology 3379.3.7.2 Nonlinear Modeling of the Schottky Diode Barrier 3479.3.7.3 3D Modeling of the Extrinsic Structure of the Diodes 3489.3.7.4 Modeling and Optimization of the Diode Cell 3499.3.7.5 Input and Output Matching Circuits 3519.4 Technology of THz Diode Frequency Multipliers 3519.4.1 From Whisker-Contacted Diodes to Planar Discrete Diodes 3519.4.2 Semi-Monolithic Frequency Multipliers at THz Frequencies 3529.4.3 THz Local Oscillators for the Heterodyne Instrument of Herschel Space Observatory 3549.4.4 First 2.7 THz Multiplier Chain with More Than 10 μW of Power at Room Temperature 3569.4.5 High Power 1.6 THz Frequency Multiplied Source for Future 4.75 THz Local Oscillator 3589.5 Power-Combining at Sub-Millimeter Wavelength 3619.5.1 In-Phase Power Combining 3629.5.1.1 First In-Phase Power-Combined Submillimeter-Wave Frequency Multiplier 3629.5.1.2 In-Phase Power Combining at 900 GHz 3649.5.1.3 In-Phase Power-Combined Balanced Doublers 3649.5.2 In-Channel Power Combining 3659.5.3 Advanced on-Chip Power Combining 3679.5.3.1 High Power 490–560 GHz Frequency Tripler 3699.5.3.2 Dual-Output 550 GHz Frequency Tripler 3699.5.3.3 High-Power Quad-channel 165–195 GHz Frequency Doubler 3709.6 Conclusions and Perspectives 372Exercises 373Exercise 1 373Exercises 2–5 374Explanatory Notes (see superscripts in text) 374References 37510 GaN Multipliers 383Chong Jin and Dimitris Pavlidis10.1 Introduction 38310.1.1 Frequency Multipliers 38310.1.2 Properties of Nitride Materials 38410.1.3 Motivation and Challenges 38510.2 Theoretical Considerations of GaN Schottky Diode Design 38610.2.1 Analysis by Analytical Equations 38610.2.1.1 Nonlinearity and Harmonic Generation 38610.2.1.2 Nonlinearity of Ideal Schottky Diode 38810.2.1.3 Series Resistance 39110.2.2 Analysis by Numeric Simulation 39410.2.2.1 Introduction of Semiconductor Device Numerical Simulation 39410.2.2.2 Parameters for GaN-Based Device Simulation 39510.2.2.3 Simulation Results 39810.2.3 Conclusions on Theoretical Considerations of GaN Schottky Diode Design 40710.3 Fabrication Process of GaN Schottky Diodes 40710.3.1 Fabrication Process 40710.3.2 Etching 40910.3.3 Metallization 41010.3.3.1 Ohmic Contacts on GaN 41010.3.3.2 Schottky Contacts on GaN 41010.3.4 Bridge Interconnects 41310.3.4.1 Dielectric Bridge 41310.3.4.2 Optical Air-bridge 41310.3.4.3 E-beam Air-bridge 41410.3.5 Conclusion on Fabrication Process of GaN Schottky Diodes 41410.4 Small-signal High-frequency Characterization of GaN Schottky Diodes 41410.4.1 Current-voltage Characteristics 41410.4.2 Small-signal Characterization and Equivalent Circuit Modeling 41510.4.2.1 Step 1. Parasitic Elements 41710.4.2.2 Step 2. Junction Capacitance 41910.4.2.3 Step 3. Optimization 41910.4.2.4 Summary 42010.4.3 Results 42210.4.4 Conclusion 42310.5 Large-signal On-wafer Characterization 42310.5.1 Characterization Approach 42310.5.2 Large Signal Measurements of GaN Schottky Diodes 42410.5.2.1 LSNA With 50 Ω Load 42410.5.2.2 Time Domain Waveforms 42510.5.2.3 Instant C–V Under Large-signal Driven Conditions 42610.5.2.4 Power Handling Characteristics 42710.5.3 LSNA With Harmonic Load-pull 42710.5.4 Conclusion 42810.6 GaN Diode Implementation for Signal Generation 42810.6.1 Large-signal Modeling of GaN Schottky Diodes 42810.6.2 Frequency Doubler 43010.7 Multiplier Considerations for Optimum Performance 434Exercises 440References 44211 THz Resonant Tunneling Devices 447Masahiro Asada and Safumi Suzuki11.1 Introduction 44711.2 Principle of RTD Oscillators 44911.2.1 Basic Operation of RTD 44911.2.2 Principle of Oscillation 45111.2.3 Effect of Electron Delay Time 45211.2.3.1 Degradation of NDC at High Frequency 45211.2.3.2 Generation of Reactance at High Frequency 45311.3 Structure and Oscillation Characteristics of Fabricated RTD Oscillators 45411.3.1 Actual Structure of RTD Oscillators 45411.3.2 High-frequency Oscillation 45611.3.3 High-output Power Oscillation 46011.4 Control of Oscillation Spectrum and Frequency 46311.4.1 Oscillation Spectrum and Phase-Locked Loop 46311.4.2 Frequency-tunable Oscillators 46511.5 Targeted Applications 46711.5.1 High-speed Wireless Communications 46711.5.2 Spectroscopy 46911.5.3 Other Applications and Expected Future Development 470Exercises 471Exercise 1–6 471Exercise 7–8 472References 47212 Wireless Communications in the THz Range 479Guillaume Ducournau and Tadao Nagatsuma12.1 Introduction 47912.2 Evolution of Telecoms Toward THz 47912.2.1 Brief Historic 47912.2.2 Data Rate Evolution 48012.2.3 THz Waves: Propagation, Advantages, and Disadvantages 48012.2.4 Frequency Bands 48212.2.5 Potential Scenarios 48312.2.6 Comparison Between FSO and THz 48412.3 THz Technologies: Transmitters, Receivers, and Basic Architecture 48512.3.1 THz Sources 48512.3.2 THz Receivers 48612.3.3 Basic Architecture of the Transmission System 48612.4 Devices/Function Examples for T-Ray CMOS 48812.4.1 Photomixing Techniques for THz CMOS 48812.4.2 THz Modulated Signals Enabled by Photomixing 48912.4.3 Other Techniques for the Generation of Modulated THz Signals 49212.4.4 Integration, Interconnections, and Antennas 49212.4.4.1 Integration 49212.4.4.2 Antennas 49312.5 THz Links 49312.5.1 Modulations and Key Indicators of a THz Communication Link 49312.5.2 State-of-the-Art of THz Links 49412.5.2.1 First Systems 49412.5.2.2 Photonics-Based Demos 49512.5.2.3 Electronic-Based Demos 49612.5.2.4 Beyond 100 GHz High Power Amplification 49712.5.2.5 Table of Reported Systems 49812.6 Toward Normalization of 100G Links in the THz Range 49812.7 Conclusion 50212.8 Acronyms 502Exercise: Link Budget of a THz Link 503References 50413 THz Applications: Devices to Space System 511Imran Mehdi13.1 Introduction 51113.1.1 Why Is THz Technology Important for Space Science? 51213.1.2 Fundamentals of THz Spectroscopy 51613.1.3 THz Technology for Space Exploration 51713.2 THz Heterodyne Receivers 51813.2.1 Local Oscillators 52113.2.1.1 Frequency Multiplied Chains 52313.2.2 Mixers 52413.2.2.1 Room Temperature Schottky Diode Mixers 52413.2.2.2 SIS Mixer Technology 52613.2.2.3 Hot Electron Bolometric (HEB) Mixers 52713.2.2.4 State-of-the-Art Receiver Sensitivities 52913.3 THz Space Applications 53013.3.1 Planetary Science: The Case for Miniaturization 53013.3.2 Astrophysics: The Case for THz Array Receivers 53313.3.3 Earth Science: The Case for Active THz Systems 53513.4 Summary and Future Trends 538Acknowledgment 539Exercises 539Exercise 1–3 539Exercise 4 540References 540Index 547