Advanced Materials for Future Terahertz Devices, Circuits and Systems (Lecture Notes in Electrical Engineering, 727) [1st ed. 2021] 9813344881, 9789813344884

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Lecture Notes in Electrical Engineering 727

Aritra Acharyya Palash Das   Editors

Advanced Materials for Future Terahertz Devices, Circuits and Systems

Lecture Notes in Electrical Engineering Volume 727

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Naples, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, Munich, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, Humanoids and Intelligent Systems Laboratory, Karlsruhe Institute for Technology, Karlsruhe, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Università di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Department of Electrical Engineering and Information Science, Technische Universität München, Munich, Germany Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martín, Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Sebastian Möller, Quality and Usability Laboratory, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering & Advanced Technology, Massey University, Palmerston North, Manawatu-Wanganui, New Zealand Cun-Zheng Ning, Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Graduate School of Informatics, Kyoto University, Kyoto, Japan Federica Pascucci, Dipartimento di Ingegneria, Università degli Studi “Roma Tre”, Rome, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, Universität Stuttgart, Stuttgart, Germany Germano Veiga, Campus da FEUP, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Beijing, China Junjie James Zhang, Charlotte, NC, USA

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Aritra Acharyya Palash Das •

Editors

Advanced Materials for Future Terahertz Devices, Circuits and Systems

123

Editors Aritra Acharyya Department of Electronics and Communication Engineering Cooch Behar Government Engineering College Cooch Behar, India

Palash Das Department of Electronics and Communication Engineering Cooch Behar Government Engineering College Cooch Behar, India

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-33-4488-4 ISBN 978-981-33-4489-1 (eBook) https://doi.org/10.1007/978-981-33-4489-1 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

The state-of-the-art progress in semiconductor material science along with latest advancement in lithography technologies associated with integrated circuit fabrication has originated astonishing possibilities and huge interest among modern researchers in terahertz (THz) technology for numerous applications in the fields like wireless communication, photonics, remote sensing, health, biotechnology, astronomy, etc. Greater resolution and wider bandwidth are the primary advantages of THz spectrum (0.3–10 THz) over millimeter-wave (30–300 GHz) and microwave (1–30 GHz) frequency spectrums. In order to enhance the efficiency of the sources or sensitivity of the detectors operating at THz regime, the choice of the base material plays the most important role. The search of suitable materials for the generation of THz waves (i.e., for THz sources) as well as its detection purpose (i.e., for THz detectors) is an emerging field of research. This book deals with the vast discussion regarding advanced materials suitable for realizing THz devices, circuits and systems, processing and fabrication technologies associated with those, some measurement techniques exclusively effective for THz regime, newly explored materials and recently developed solid-state devices for efficient generation and detection of THz waves, THz antennas, THz biosensors, etc. The content of this book is focused on the recent advancements and several research issues related to THz materials and devices, and also seeks out theoretical, procedural and validated experimental works dealing with different topics corresponding to THz technologies. This book covers a very vast audience from basic science to engineering and technology experts as well as learners. This could work as a textbook for engineering and science students as well as for researchers. Cooch Behar, India

Aritra Acharyya Palash Das

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Contents

Introduction to the Advanced Materials for Future Terahertz Devices, Circuits and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aritra Acharyya and Palash Das

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Gallium Nitride-Based Solid-State Devices for Terahertz Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aritra Acharyya

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Noncontact Characterization Techniques of GaN-Based Terahertz Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prajukta Mukherjee, Aritra Acharyya, Hiroshi Inokawa, and Arindam Biswas

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A Brief Review on Terahertz Avalanche Transit Time Sources . . . . . . . S. J. Mukhopadhyay, P. Hazra, and M. Mitra

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Terahertz IMPATT Sources Based on Silicon Carbide . . . . . . . . . . . . . S. J. Mukhopadhyay, S. Kanungo, V. Maheshwari, and M. Mitra

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Terahertz Quantum Dot Intersublevel Photodetector . . . . . . . . . . . . . . . Sanjib Kabi

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Graphene—A Promising Material for Realizing Active and Passive Terahertz Radiators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aritra Acharyya

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First-Principle Molecular Dynamics Simulation of Terahertz Absorptive Hydrogenated TiO2 Nanoparticles . . . . . . . . . . . . . . . . . . . . 103 S. Mahata and S. S. Mahato Doping Effects on Optical Properties of Titania Composite in Terahertz Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 S. Mahata and S. S. Mahato

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Silicon Nanowires as a Potential Material for Terahertz Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Shrabani Ghosh, Ankita Chandra, Sourav Sarkar, and K. K. Chattopadhyay Analysis of Optical Performance of Dual-Order RAMAN Amplifier Beyond 100 THz Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Rajarshi Dhar, Arpan Deyasi, and Angsuman Sarkar A Novel Approach Dual Material Double Gate Germanium-Based TFET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Jayabrata Goswami, Anuva Ganguly, Aniruddha Ghosal, and J. P. Banerjee Sources and Security Issues in Terahertz Technologies . . . . . . . . . . . . . 233 Saswati Chatterjee Interferometric Switch Based on Terahertz Optical Asymmetric Demultiplexer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Dilip Kumar Gayen Material Systems for Realizing Heterojunction IMPATT Sources for Generating Terahertz Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Monisha Ghosh and Arindam Biswas Development of an Active MMIC Frequency Tripler System in a Sub-millimeter to Terahertz Region Receiver for Planetary Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Apala Banerjee High-Sensitive Terahertz Biosensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Sandipan Mallik, Prashant Kumar Singh, Gufran Ahmad, Shrabani Guhathakurata, S. S. Mahato, and Nabin Baran Manik Terahertz Antennas for Future Communications . . . . . . . . . . . . . . . . . . 315 Prashant Kumar Singh, Sandipan Mallik, Palash Das, Hare Krishna, and Anjini Kumar Tiwary

Editors and Contributors

About the Editors Dr. Aritra Acharyya is currently working at the Department of Electronics and Communication Engineering, Cooch Behar Government Engineering College, Harinchawra, Ghughumari, West Bengal, 736170, India, as Assistant Professor. He was born in 1986. He received B.E. and M.Tech. degrees from IIEST, Shibpur, India, and Institute of Radio Physics and Electronics, University of Calcutta, India, in the years 2007 and 2010, respectively. Finally, he obtained Ph.D. degree from the Institute of Radio Physics and Electronics, University of Calcutta, in the year 2016. His research interests are high-frequency semiconductor devices, nano-structures, semiconductor physics, transport phenomena, quantum mechanics, optoelectronics, etc. He has published 81 research papers in peer-reviewed national and international journals, 60 research papers in national and international conference proceedings, and several book chapters. He also authored and edited 06 and 02 numbers of books, respectively.

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Dr. Palash Das is currently working at Cooch Behar Government Engineering College as Assistant Professor. He did his M.S. and Ph.D. from IIT Kharagpur and B.Tech. from Kalyani Government Engineering College, West Bengal, India. His current research interest involves GaN optical devices, GaN HEMT, HRXRD of GaN/AlGaN thin film, ideation of new device structures, simulation and modeling, simulation tool development using Visual Basic 6, automated measurement instrument development with embedded hardware, and Visual Basic-based software. He is currently guiding one Ph.D. scholar working on GaN optical devices for Intra Device Communication Applications. He has guided around 15 B.Tech. projects as well. Palash is owning 1 US patent and 3 Indian patents; he authored 11 journal papers, 19 conference papers, and 02 book chapters. He developed a few software to simulate/demonstrate/measure certain semiconductor physical characteristics. He recently developed one measurement instrument product for automated I-V characterization of electronic devices.

Contributors Aritra Acharyya Department of Electronics and Communication Engineering, Cooch Behar Government Engineering College, Harinchawra, Ghughumari, Cooch Behar, West Bengal, India Gufran Ahmad Department of Electrical Engineering, Dayalbagh Educational Institute, Agra, India Apala Banerjee Department of Electrical Engineering, Indian Institute of Technology, Kanpur, Uttar Pradesh, India J. P. Banerjee Institute of Radio Physics and Electronics, University of Calcutta, Kolkata, India Arindam Biswas Centre for Organic Spin-Tronics and Optoelectronics Devices (COSOD), Mining Engineering Department, Kazi Nazrul University, Asansol, Burdwan, West Bengal, India Ankita Chandra School of Materials Science and Nanotechnology, Jadavpur University, Kolkata, India Saswati Chatterjee Department of Computer Science and Engineering, St Mary’s Technical Campus Kolkata, Barasat, West Bengal, India

Editors and Contributors

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K. K. Chattopadhyay School of Materials Science and Nanotechnology, Jadavpur University, Kolkata, India; Thin Film and Nano Science Laboratory, Department of Physics, Jadavpur University, Kolkata, India Palash Das Department of Electronics and Communication Engineering, Cooch Behar Government Engineering College, Harinchawra, Ghughumari, Cooch Behar, West Bengal, India Arpan Deyasi Department of Electronics and Communication Engineering, RCC Institute of Information Technology, Kolkata, India Rajarshi Dhar Department of Electronics and Telecommunication Engineering, IIEST Shibpur, Howrah, India Anuva Ganguly Institute of Radio Physics and Electronics, University of Calcutta, Kolkata, India Dilip Kumar Gayen Department of Computer Science & Engineering, College of Engineering & Management, Kolaghat, KTPP Township, Kolaghat, India Aniruddha Ghosal Institute of Radio Physics and Electronics, University of Calcutta, Kolkata, India Monisha Ghosh Department of Electronics and Communications Engineering, Supreme Knowledge Foundation Group of Institution, Hooghly, India Shrabani Ghosh School of Materials Science and Nanotechnology, Jadavpur University, Kolkata, India Jayabrata Goswami Institute of Radio Physics and Electronics, University of Calcutta, Kolkata, India Shrabani Guhathakurata Department of Electronics Communication Engineering, National Institute of Science and Technology, Berhampur, Odisha, India P. Hazra Indian Institute of Space Science and Technology, Trivandrum Deemed University in Thiruvananthapuram, Valiamala, Kerala, India Hiroshi Inokawa Research Institute of Electronics, Shizuoka University, Hamamatsu, Japan Sanjib Kabi Sikkim Manipal Institute of Technology, Sikkim Manipal University, East Sikkim, Majhitar, Sikkim, India S. Kanungo Department of Electrical and Electronics Engineering, Birla Institute of Technology and Science, Pilani, Hyderabad, Shameerpet, Hyderabad, Telangana, India Hare Krishna RTC Institute of Technology, Ranchi, Jharkhand, India

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S. Mahata National Institute of Science and Technology, Berhampur, Orissa, India S. S. Mahato Department of Electronics Communication Engineering, National Institute of Science and Technology, Berhampur, Odisha, India V. Maheshwari Department of Electronics and Communication Engineering, Bharat Institute of Engineering and Technology Mangalpally (V), Ibrahimpatanam (M), Ranga Reddy, Hyderabad, Telangana, India Sandipan Mallik Department of Electronics Communication Engineering, National Institute of Science and Technology, Berhampur, Odisha, India Nabin Baran Manik Department of Physics, Condensed Matter Physics Research Centre, Jadavpur University, Kolkata, India M. Mitra Department of Electronics and Telecommunication Engineering, Indian Institute of Engineering Science and Technology, Howrah, West Bengal, India Prajukta Mukherjee Department of Electrical Engineering, Cooch Behar Government Engineering College, Harinchawra, Ghughumari, Cooch Behar, India S. J. Mukhopadhyay Department of Electronics and Telecommunication Engineering, Indian Institute of Engineering Science and Technology, Howrah, West Bengal, India Angsuman Sarkar Department of Electronics and Communication Engineering, Kalyani Govt Engineering College, Kalyani, India Sourav Sarkar School of Materials Science and Nanotechnology, Jadavpur University, Kolkata, India Prashant Kumar Singh University College of Engineering and Technology (UCET), VBU, Hazaribag, Jharkhand, India Anjini Kumar Tiwary Birla Institute of Technology, Mesra, Ranchi, Jharkhand, India

Introduction to the Advanced Materials for Future Terahertz Devices, Circuits and Systems Aritra Acharyya and Palash Das

Abstract A brief introduction to different advanced materials for terahertz (THz) devices, circuits and systems has been included in this introductory chapter. The chapter also contains short discussions regarding potential applications of THz waves and different recently developed electronic and optoelectronic devices operating at THz spectrum. Finally, an overview of all the chapters included in this book has been provided at the end of this chapter. Keywords GaN · Infrared · Terahertz · Terahertz antenna · Terahertz gap

1 Introduction Terahertz (THz) frequency spectrum or “terahertz gap” is a frequency regime in between millimeter-wave (mm-wave) and infrared (IR) regimes; the frequency range of 0.1–10 THz is called the terahertz gap (where 1 THz = 1012 Hz), i.e., 3.0–0.03 mm wavelength range. Due to various unique and inherent properties of this spectrum, THz frequency band is in great demand since last two decades for several fascinating electronic as well as photonic applications [1]; some examples of such applications are bio-imaging, bio-sensing, non-contact industrial quality inspection, applications in medical and pharmaceutical areas, astronomy, short-range terrestrial wireless communication systems, airborne radar systems, space communication, remote sensing, spectroscopy, food diagnostics, etc [2–9]. From the prospective of the wireless communication systems, wide bandwidth of this spectrum can be utilized to implement ultra-broadband wireless transmission systems having the data rate up to tens of gigabytes per second. The energy of photon in THz spectrum is lower as compared to the X-ray photons. However, like the X-ray A. Acharyya (B) · P. Das Department of Electronics and Communication Engineering, Cooch Behar Government Engineering College, West Bengal, Harinchawra, Ghughumari, Cooch Behar 736170, India e-mail: [email protected] P. Das e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Acharyya and P. Das (eds.), Advanced Materials for Future Terahertz Devices, Circuits and Systems, Lecture Notes in Electrical Engineering 727, https://doi.org/10.1007/978-981-33-4489-1_1

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beam, THz beam can also pass through most of the nonmetallic substances. The molecules of those substances are ionized due to the interaction with high-energy X-ray photons; this undesirable ionization can be avoided by using low-energy THz photon instead of X-ray photon. As a result, THz waves are significantly less harmful to live animal tissues including the human tissues [10]. Terahertz waves also cause insignificant degrading effects on wide varieties of substances and thus can be highly suitable for non-contact investigation of historical artifacts [11], precious and expensive semiconductor devices [12], historical structures, wall paintings, etc. However, recently the researchers have found slight degrading effect of highly intense THz waves on DNA [13–15]. As a whole, THz waves are much safer than X-ray in most of the areas of application. Therefore, spectroscopy and imaging in THz spectrum are undoubtedly better substitution of X-ray spectroscopy and X-ray imaging tools.

2 State-of-The-Art Terahertz Devices, Circuits and Systems However, from the prospective of imaging, the primary drawback of THz waves is the low resolution. Low resolution is an inherent feature of THz imaging systems due to the relatively larger wavelengths associated with this spectrum as compared to the X-ray spectrum [16]. This drawback is more pronounced for the THz imaging systems working below 5 THz. In order to overcome this shortcoming, use of THz waves having frequency greater than 5 THz (i.e., smaller wavelength, leading to better resolution) is essential. However, the generation of high-power oscillations within 5–10 THz frequency band is a challenging task. The materials required for this purpose must have high electron and hole drift velocities and high breakdown field. Gallium nitride (GaN) is a semiconductor which can fulfill these requirements. Different potential THz sources like quantum cascade lasers (QCLs), heterostructure field-effect transistors (HFETs), negative differential resistance (NDR) diodes, Gunn diodes, impact avalanche transit time (IMPATT) diodes, high electron mobility transistors (HEMTs), antenna-coupled FETs, resonant tunneling diodes (RTDs), avalanche photodiodes (APDs), etc., based on GaN and some heterostructure based on AlGaN/GaN or InGaN/GaN material systems are capable of operating at 5– 10 THz frequency band [17–55]. Recently, some graphene-based avalanche transit time (ATT) sources also show immense potentiality for generating THz waves in the sub-spectrum under consideration (5–10 THz) [56, 57]. However, extraordinary material properties of some wide bandgap semiconductor materials like SiC, type-IIb diamond, etc., also show enormous potentiality to be used as base materials for THz sources [58–60]. On the other hand, another challenging area is to choose materials for implementing THz detectors, especially for longer wavelength detection (wavelength range of 1–3 mm). Several material systems as well as several complicated device structures like multi-quantum well (MQW) have been implemented and investigated by various researchers for obtaining optimum performance of THz detectors [61–65]. Recently, some two-dimensional (2-D) materials like graphene, black phosphorus (BP), transition metal dichalcogenides (TMDCs) and topological insulators

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(TIs) have shown huge prospects for being the base materials of THz detectors [66, 67]. Moreover, the use of metamaterials for implementing THz passive circuits as well as biosensors, use of hydrogenated titanium oxide (TiO2 ) nanoparticles for efficient absorption of THz radiation from sun, uses of graphene and carbon nanotube for fabricating THz antennas, etc., are some astonishing fields of recent development in THz technology. Lastly, modern researchers are also very much curious to know about the future of the most conventional and popular semiconductor material, i.e., silicon (Si) as a base material of THz devices, since Si process technology is still the most advanced one among all other materials and material systems. It is observed that Si has very limited capability for being the base material of THz sources; however, its combined structures with other suitable materials are still very much useful for implementing THz detectors [68].

3 Overview of the Book This book deals with the properties of advanced materials suitable for realizing THz devices, circuits and systems, processing and fabrication technologies associated with those, some measurement techniques exclusively effective for THz regime, newly explored materials and recently developed electronic and photonic devices for generating and detecting THz waves, potentiality of metamaterials for implementing THz passive circuits and biosensors, and finally the future of silicon as the base material of THz devices. The content of this book is focused on the modern advancements and several experimental techniques related to THz materials and devices. The book covers a very wide range of readers from basic science to technological experts as well as students. This book can be considered as a textbook for undergraduate, postgraduate and doctoral students and also for scientists. Chapter-wise organization of the entire book is as follows. Chapter 2 provides the description of GaN-based THz solid-state devices and their future scopes. Chapter 3 summarizes the characterization methods of the GaN-based THz devices. A brief review of the state-of-the-art THz avalanche transit time (ATT) sources is provided in Chap. 4. Again the advantages and possibilities of 4H-SiC-based ATT THz sources are summarized in Chap. 5. In Chap. 6, the method of detection of THz waves via quantum dot intersubband photodetectors has been discussed. The possibilities of THz radiation from graphene-based ATT sources are discussed in Chap. 7. Chapters 8 and 9 are dealing with the molecular dynamic simulation of THz absorptive hydrogenated TiO2 nanoparticles and effects of doping on optical properties of titania composite in THz range, respectively. Chapter 10 provides the insight of the different properties of synthesized Si nanowires and its composites and their applications as THz emitter and detector. In Chap. 11, the analysis of optical performance of dual-order RAMAN amplifier beyond 100 THz is presented. Chapter 12 presents a novel approach of designing and analyzing the dual-material gate germaniumbased THz tunnel field-effect transistor (TFET). Sources and security issues related

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to the modern THz technologies are discussed in Chap. 13. The THz optical asymmetric demultiplexer-based interferometric switch is introduced in Chap. 14. Some material systems for realizing the heterojunction THz ATT sources are introduced in brief in Chap. 15. The method of down-conversion THz signals by using mixers made of active GaAs monolithic microwave integrated circuit (MMIC) realizable by using standard pHEMT technology and suitable antenna and low-noise amplifier arrangements are presented in Chap. 16. Chapter 17 introduced some highly sensitive THz biosensors. Finally, the descriptions of THz antennas for future communication technologies are presented in the last chapter of this book, i.e., in Chap. 18.

References 1. P.H. Siegel, Terahertz technology. IEEE Trans. Microwave Theory Tech. 50(3), 910–928 (2002) 2. P. Martyniuk, J. Antoszewski, M. Martyniuk, L. Faraone, A. Rogalski, New concepts in infrared photodeector designs. Appl. Phys. Rev. 1, 041102-1-35 (2014) 3. R.M. Woodward, B.E. Cole, V.P. Wallace, R.J. Pye, D.D. Arnone, E.H. Linfield, M. Pepper, Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue. Phys. Med. Biol. 47, 3853–3863 (2002) 4. M. Nagel, P.H. Bolivar, M. Brucherseifer, H. Kurz, A. Bosserhoff, R. Buttner, Integrated THz technology for label-free genetic diagnostics. Appl. Phys. Lett. 80(1), 154–156 (2002) 5. N. Karpowicz, H. Zhong, C. Zhang, K.I Lin, J.S. Hwang, J. Xu, X.C. Zhang, Compact continuous-wave subterahertz system for inspection applications. Appl. Phys. Lett. 86(5), 054105-1-3 (2005) 6. K. Yamamoto, M. Yamaguchi, F. Miyamaru, M. Tani, M. Hangyo, Non-invasive inspection of c4 explosive in mails by terahertz time-domain spectroscopy. J. Appl. Phys. 43(3B), L414–L417 (2004) 7. K. Kawase, Y. Ogawa, Y. Watanabe, H. Inoue, Non-destructive terahertz imaging of illicit drugs using spectral fingerprints. Opt. Express 11(20), 2054–2549 (2003) 8. C. Joerdens, M. Koch, Detection of foreign bodies in chocolate with pulsed terahertz spectroscopy. Opt. Eng. 47 (3), 037003-1-5 (2008) 9. M. Tonouchi, Cutting-edge terahertz technology. Nat. Photonics 1, 97–105 (2007) 10. J.L. Prince, J. Links, Medical Imaging Signals and Systems, 2nd edn. (Pearson Prentice Hall, Upper Saddle River, 2006). 11. C.L.K. Dandolo, P.U. Jepsen, Wall painting investigation by means of non-invasive terahertz time-domain imaging (THz-TDI): inspection of subsurface structures buried in historical plasters. J. Infrared Millimeter Terahertz Waves 37, 198–208 (2016) 12. X. Wan et al., SEB hardened power MOSFETs with high-K dielectrics. IEEE Trans. Nucl. Sci. 62(6), 2830–2836 (2015) 13. L.V. Titova et al., Intense THz pulses cause H2AX phosphorylation and activate DNA damage response in human skin tissue. Biomed. Opt. Express 4, 559–568 (2013) 14. E.V. Demidova et al., Impact of terahertz radiation on stress-sensitive genes of E. coli cell. IEEE Trans. Terahertz Sci. Technol. 6(3), 435–441 (2016) 15. L.V. Titova et al., Intense THz pulses down-regulate genes associated with skin cancer and psoriasis: a new therapeutic avenue? Sci. Rep. 3, 1 (2013) 16. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd edn. (Wiley, New York, 2007), p. 1200 17. M.S. Shur, AlGaN/GaN plasmonic terahertz electronic devices. J. Phys. 486, 012025-1-6 (2014)

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43. M. Beeler et al., Pseudo-square AlGaN/GaN quantum wells for terahertz absorption. Appl. Phys. Lett. 105, 131106-1-3 (2014) 44. H. Durmaz et al., Terahertz intersubband photodetectors based on semi-polar GaN/AlGaN heterostructures. Appl. Phys. Lett. 108, 201102-1-3 (2016) 45. S. Krishnamurthy et al., Bandstructure effect on high-field transport in GaN and GaAl. Appl. Phys. Lett. 71(14), 1999–2001 (1997) 46. B.E. Foutz et al., Comparison of high field electron transport in GaN and GaAs. Appl. Phys. Lett. 70(21), 2849–2851 (1997) 47. E. Alekseev, D. Pavlidis, GaN Gunn diodes for THz signal generation. IEEE MTT-S Int. Microwave Symp. Digest 3, 1905–1908 (2000) 48. E. Alekseev et al., GaN-based NDR devices for THz generation, in Proceedings of the 11th International Symposium on Space Terahertz Technology (2000), pp. 162 49. D. Veksler et al., GaN heterodimensional Schottky diode for THz detection, in 5th IEEE Conference Sensors (2006), pp. 323–326 50. W.C.B. Peatman, T.W. Crowe, M.S. Shur, A novel Schottky/2-DEG diode for millimeter- and submillimeter-wave multiplier applications. IEEE Electron. Device Lett. 13(1), 11–13 (1992) 51. A. Reklaitis, Monte Carlo study of hot-carrier transport in bulk wurtzite GaN and modeling of a near-terahertz impact avalanche transit time diode. J. Appl. Phys. 95(12), 7925–7935 (2004) 52. A. Reklaitis, L. Reggiani, Giant suppression of avalanche noise in GaN double-drift impact diodes. Solid State Electron. 49, 405–408 (2005) 53. Y. Wang et al., Modulation of the domain mode in GaN-based planar Gunn diode for terahertz applications. Phys. Status Solidi (c) 13(5–6), 382–385 (2016) 54. A. Biswas, S. Sinha, A. Acharyya, A. Banerjee, S. Pal, H. Satoh, H. Inokawa, 1.0 THz GaN IMPATT source: effect of parasitic series resistance. J. Infrared Millimeter Terahertz Waves39(10), 954–974 (2018) 55. A. Acharyya, J.P. Banerjee, Prospects of IMPATT devices based on wide Bandgap semiconductors as potential terahertz sources. Appl. Nanosci. 4, 1–14 (2014) 56. A. Acharyya, Three-Terminal Graphene Nanoribbon Tunable Avalanche Transit Time Sources for Terahertz Power Generation. physica status solidi (a) 216(18), 1900277 (2019) 57. A. Acharyya, 1.0–10.0 THz radiation from graphene nanoribbon based avalanche transit time sources. Phys. Status Solidi (a) 216(7), 1800730 (2019) 58. M. Ghosh, S. Ghosh, A. Acharyya, Self-consistent quantum drift-diffusion model for multiple quantum well IMPATT diodes. J. Comput. Electron. 15(4), 1370–1387 (2017) 59. M. Ghosh, S. Ghosh, P.K. Bandyopadhyay, A. Biswas, A.K. Bhattacharjee, A. Acharyya, Noise performance of 94 GHz multiple quantum well double-drift region IMPATT sources. J. Act. Passive Electron. Devices 13(2/3), 195–207 (2018) 60. A. Acharyya, S. Banerjee, J.P. Banerjee, Potentiality of semiconducting diamond as base material of millimeter-wave and terahertz IMPATT devices. J. Semicond. 35(3), 034005-1-11 (2013) 61. A. Acharyya, S. Ghosh, Dark current reduction in nano-avalanche photodiodes by incorporating multiple quantum barriers. Int. J. Electron. 104(12), 1957–1973 (2017) 62. S. Ghosh, A. Biswas, A. Acharyya, Optical properties of multiple quantum barrier nano-scale avalanche photo diodes. Int. J. Nanopart. 12(1–2), 1–15 (2019) 63. S. Ghosh, A. Acharyya, Multiple quantum barrier nano-avalanche photodiodes—part I: spectral response. Nanosci. Nanotechnol.-Asia 9(1), 172–184 (2019) 64. S. Ghosh, A. Acharyya, Multiple quantum barrier nano-avalanche photodiodes—part II: excess noise characteristics. Nanosci. Nanotechnol. -Asia 9(1), 185–191 (2019) 65. S. Ghosh, A. Acharyya, Multiple quantum barrier nano-avalanche photodiodes—part III: time and frequency responses. Nanosci. Nanotechnol.-Asia 9(1), 192–197 (2019) 66. S. Ahmed, J. Yi, Two-dimensional transition metal dichalcogenides and their charge carrier mobilities in field-effect transistors. Nano-Micro Lett. 9(50), 1–23 (2017)

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67. J. Yang, H. Qin, K. Zhang, Emerging terahertz photodetectors based on two-dimensional materials. Opt. Commun. 406, 36–43 (2018) 68. J. Marczewski, D. Coquillat, et al., THz detectors based on Si-CMOS technology field effect transistors—advantages, limitations and perspectives for THz imaging and spectroscopy. OptoElectron. Rev. 26(4), 261–269 (2018)

Gallium Nitride-Based Solid-State Devices for Terahertz Applications Aritra Acharyya

Abstract Some exclusive material properties of gallium nitride (GaN) such as extraordinary transport, breakdown and thermal properties lead to highest combined frequency-power performance of GaN-based solid-state devices among all devices based on conventional semiconductors. Future needs of low-cost, compact and highly efficient terahertz (THz) systems are greatly endorsing the usage of GaN for realizing next-generation THz devices like quantum cascade lasers (QCLs), plasma THz heterostructure field-effect transistors (HFETs), negative differential resistance (NDR) diodes, GUNN diodes, impact avalanche transit time (IMPATT) diodes, high electron mobility transistors (HEMTs), antenna-coupled FETs, resonant-tunnelling diodes (RTDs), etc. This chapter deals with a comprehensive review of the abovementioned GaN-based electronic and photonic devices since their inception to the state-of-the-art status of those; the chapter also discusses the impact of the recent developments of those devices on the future THz systems. Keywords GaN · HEMT · HFET · GUNN · IMPATT · QCL · Thz · RTD

1 Introduction Since the last three decades, the advancement of processing and fabrication technologies of gallium nitride (GaN) leads to enormous progress in solid-state lighting technology. The blue and white light emissions from GaN and its ternary allows (e.g., InGaN) based light emitting devices have bought revolutionary improvement in display systems for cell phones, televisions, computer monitors, etc., as regards quality of display as well as power consumption. Moreover, GaN-based light-emitting diodes (LEDs) are slowly replacing incandescent bulbs due to very low power consumption, high reliability and long life span of those. The state-of-theart GaN technology has achieved such an extraordinary progress that its reach now A. Acharyya (B) Department of Electronics and Communication Engineering, Cooch Behar Government Engineering College, West Bengal, Harinchawra, Ghughumari, Cooch Behar 736170, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Acharyya and P. Das (eds.), Advanced Materials for Future Terahertz Devices, Circuits and Systems, Lecture Notes in Electrical Engineering 727, https://doi.org/10.1007/978-981-33-4489-1_2

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broadens far beyond optoelectronics and lighting. Recent advancement of advancement of this technology has enabled the modern industries and research and development sectors to replace microwave amplifiers, millimetre wave (mm-wave) communication modules, etc., by using their GaN counterparts due to higher frequency and power handling capability of this material. Some extraordinary material properties of GaN like wide bandgap (WBG) energy (E g ≈ 3.4 eV at 300 K in its wurtzite phase, i.e. Wz-GaN), high electron saturation velocity, high thermal conductivity, etc., lead to highest combined frequency-power performance of GaN-based solid-state devices amount all devices based on conventional semiconductors. Terahertz (THz) spectrum, which exists between mm-wave and IR frequency regimes, possesses the frequency range of 0.1–10 THz, i.e. corresponding wavelength range of 3.0–0.03 mm. Some fascinating electronic and photonic applications of THz spectrum are bio-imaging, bio-sensing, non-contact industrial quality inspection, medical and pharmaceutical applications, THz astronomy, short-range wireless communication, space communication, air-borne radar communication, food diagnostics, THz spectroscopy, remote sensing, etc. [1–9]. The huge demand of the above-mentioned THz frequency band originates extreme stipulation of THz devices such as THz sources and detectors. The exclusive and favourable material properties of GaN make it highly suitable candidate for implementing semiconductor devices based on it for possible THz applications. Some important aspects like high-frequency capability, power handling capability, on-state resistance, switching speed, power switching product, etc., of semiconductor devices are usually compared by computing the figure of merit (FOM) of those. The FOM is a parameter which is used to characterize the performance of a device, system or method compared to its alternatives. The FOM reflects the relative advantages of a particular material for a specific application over other materials. However, the FOM can be defined in many ways and forms depending on the field of application. Some very popular FOM and their corresponding application areas are given below: (a) Johnson’s Figure of Merit (JFOM): Measure of ultimate high-frequency capability [10], (b) Baliga’s Figure of Merit (BFOM): Measure of on-state resistance [11], (c) FET Switching Speed Figure of Merit (FSFOM): Measure of FET switching speed, (d) Bipolar Switching Speed Figure of Merit (BSFOM): Measure of BJT switching speed, (e) FET Power Handling Figure of Merit (FPFOM): Measure of FET power handling capability, (f) FET Power Switching Product (FTFOM): Measure of FET power switching speed product, (g) Bipolar Power Handling Capability Figure of Merit (BPFOM): Measure of BJT power handling capability, (h) Bipolar Power Switching Product (BTFOM): Measure of BJT power switching speed product.

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The normalized FOM values of GaN and GaAs with respect to Si have been shown in Table 1 for the sake of comparison of the high frequency-power capabilities of semiconductor devices based on GaN and conventional semiconductors like Si and GaAs [12]. It is highly fascinating to observe from Table 1 that the narrow bandgap (NBG) semiconductors like Si (E g ≈ 1.12 eV at 300 K) and GaAs (E g ≈ 1.43 eV at 300 K) as regards high-frequency capability, on-state resistance, switching speed, power handling capability and power switching product of the device. The electric field-dependent parameters like drift velocity (vn,p ), ionization rate (α n,p ) of electrons and holes as well as field-independent parameters like bandgap (E g ), relative permittivity (εr ), density of state effective mass (md * ), intrinsic carrier concentration (ni ), breakdown field (ξ c ), effective density of states in conduction and valence bands (N c and N v ), mobility (μn,p ), diffusivity (Dn,p ) and diffusion length (L n,p ) of charge carriers in gaN can be compared with conventional semiconductors like Si and GaAs from Figs. 1 and 2; Table 2. Significantly, high saturation drift velocity (vsn,sp ) and mobility (μn,p ) of charge carriers in GaN as compared to Si and GaAs ensure the higher frequency capability of GaN, whereas smaller ionization rate of charge carriers (α n,p ) and greater breakdown field (ξ c ) in GaN indicate the higher power handling capability of it as compared to Si and GaAs. The favourable material properties of GaN as mentioned here make it highly suitable for implementing several THz devices mentioned earlier. This chapter deals with a comprehensive review of some prospective TH electronic and photonic devices based on GaN since their inception to the state-of-the-art status of those. The chapter also includes appropriate discussion regarding the impact of the recent developments of those devices on the future THz systems. From the subsequent sections, i.e. from Sect. 2–9, the detailed review of GaN-based potential THz devices has been presented. Finally, a brief summary of the entire chapter has been presented in Sect. 10. b εs = εr ε0 is the permittivity of the semiconductor; where ε0 = 8.85 × 10–12 F −1 m is the vacuum permittivity. Table 1 Figure of merits (FOMs) [12]

FOM

Si

GaAs

Wz-GaN

JFOM

1.0

1.8

215.1

BFOM

1.0

14.8

186.7

FSFOM

1.0

11.4

65.0

BSFOM

1.0

1.6

52.5

FPFOM

1.0

3.6

30.4

FTFOM

1.0

40.7

1973.6

BPFOM

1.0

0.9

10.7

BTFOM

1.0

1.4

560.5

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A. Acharyya

Fig. 1 Drift velocity of a electrons and b holes in GaN, GaAs and Si versus electric field plots at 300 K [15–19]

Fig. 2 Ionization rate of a electrons and b holes in GaN, GaAs and Si versus electric field plots at 300 K [20–22]

Gallium Nitride-Based Solid-State Devices for Terahertz … Table 2 Electric field independent material parameters of Si, GaAs and GaN [13, 14] at 300 K

13

Material parameter

Si

E g (eV)

1.0465

1.3271

3.4691

am * d bε r

0.1370

0.0370

1.5000

11.7000

13.1000

10.4000

859.5800

3.2393

3.6114 × 10–17

(×m0 )

ni (×1013 m−3 )

GaAs

Wz-GaN

Nc

(×1025

m−3 )

6.9318

0.0965

0.2234

Nv

(×1025

m−3 )

3.9131

2.0460

4.6246

μn (m2 V−1 s−1 )

0.0500

0.4000

0.1000

μp (m2 V−1 s−1 )

0.0180

0.0200

0.0034

Dn (×10–4 m2 s−1 )

11.0000

17.2000

2.6000

Dp (×10–4 m2 s−1 )

1.8900

8.6250

0.8798

L n (×10–6 m)

35.4000

70.0000

6.5000

L p (×10–6 m)

10.0000

50.0000

2.1000

ξ c (×105 V m−1 )

– –

5.8000

50.0000

am

0

= 9.1 × 10–31 kg is the electronic rest mass,

2 Quantum Cascade Lasers Quantum cascade lasers (QCLs) have become most widely used THz radiators since its inception in 1994 [23]. The wavelength of the emitted photons from conventional semiconductor lasers depends on the energy bandgap of the base material, i.e. λ = hc/E g , where λ is the wavelength associated with the emitted photons, E g is the bandgap of the semiconductor material, h = 6.62 × 10–34 J s is the Planck’s constant, and c = 3.0 × 108 m s−1 is the velocity of light in vacuum. However, radiation of photons in THz frequency range requires very narrow bandgap semiconductor material. Therefore, the fabrication of THz lasers is limited by the technological constraints associated with the narrow bandgap semiconductor materials. Easier technique to generate THz photons is introduction of intersubband transition of electrons by realizing quantum wells (QWs) in the conduction band. Intersubband transition of electrons in the conduction band of a forward biased QCL structure and generation of THz wave has been demonstrated via band diagrams presented in Fig. 3. The QCL structure is nothing but the repeated periods of QWs which can be fabricated by using molecular beam epitaxy (MBE) technique [23]. The first report on QCL based on GaAs ~ AlGaAs material system was published by Köhler et al. in the year 2002 [24]. However, it was operational only at very low temperature (~50 K), but capable of radiating pulsed power of around 2 mW at 4.4 THz [24]. Later in the year 2005, the first continuous wave (CW) QCL was reported, which was also based on GaAs ~ AlGaAs heterostructures [25]; however, the operational temperature remains well below the room temperature in this case also. The room temperature operation of QCLs can be achieved by using GaN ~ AlGaN material systems instead of using GaAs ~ AlGaAs material system, since

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Fig. 3 Schematic energy band diagram of the conduction band of a QCL structure illustrating the intersubband transition of electrons and emission of THz wave. Redrawn from Ref. [23]

the longitudinal-optical (LO) phonon energy for GaN is located at 92 meV which is much higher than that of GaAs (36 meV) [26]. Rigorous research carried out by several researchers on these two material systems reveal the fact that dependence of gain coefficient on temperature is much smaller in case of GaN ~ AlGaN QWs as compared to their GaAs ~ AlGaAs counterparts. This fact ensures the room temperature operation of GaN ~ AlGaNbased QCLs; i.e., the use of cryogenic cooling can be avoided [27–29]. Moreover, GaN-based QCLs can emit THz waves within much higher frequency range of 5–10 THz, which is un-achievable by using GaAs-based QCLs. Initially, during early 2000s, the THz emission was obtained from multi-quantum well (MQW) lasers based on InGaN ~ GaN heterostructures [30, 31]. Later, during the mid of this decade, AlGaN ~ GaN-based QCLs have been realized which are capable of radiating significantly high CW power at 5.5 and 7.0 THz. The schematic shown in Fig. 4 illustrates the AlGaN ~ GaN heterostructure-based QCL structure. Afterwards, several researchers and research groups have reported GaN-based QCLs operational at room temperature [32–34], which is turned out to be the most promising THz wave generator among all solid-state alternatives.

Gallium Nitride-Based Solid-State Devices for Terahertz …

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Fig. 4 Schematic of GaN ~ AlGaN heterostructure-based QCL structure. Redrawn from Refs. [35, 36]

3 High Electron Mobility Transistors High electron mobility transistors (HEMTs) are one of the best THz wave detectors; these are operational at room temperature. Suitable material and structural design of HEMTs make those being capable of detecting very low intensity THz waves. The HEMTs are nothing but the field-effect transistors (FETs) based on high-mobility two-dimensional electron gas (2DEG). Optical lithography technique was first used to fabricate GaN ~ AlGaN HEMT operational at room temperature, which is capable of detecting THz waves by using self-mixing technique; the highest responsivity was reported to be 3600 V W−1 [37]. Later, the same research group has developed a quasistatic self-mixing model for interpreting the characteristics of the THz detector [38]. Figure 5 illustrates the basic structure of GaN ~ AlGaN HEMT THz detector. Later, in the year 2015, Bauer et al. reported an antenna coupled field-effect transistor for detecting THz radiation within the frequency range of 0.4 to 1.18 THz; this detector was based on GaN ~ AlGaN material system-based HEMT [39]. Next year (2016), Hou et al. proposed a quasi-static self-mixing model of GaN HEMT detector, which is capable of explaining both the magnitude and polarity of the photocurrent [40]. They introduced novel asymmetric pads in GaN HEMTs instead of using conventional

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Fig. 5 Schematic of GaN ~ AlGaN heterostructure-based HEMT THZ detector. Redrawn from Ref. [38]

symmetric pads, which, in turn, improved the THZ detection responsivity of the device by around one order of magnitude.

4 Resonant-Tunneling Diodes Resonant-tunneling diodes (RTDs) are highly suitable for several applications at submm-wave and THz frequency bands. The GaN ~ AlGaN material system is highly suitable for realizing RTDs for THz applications. The vertical transport in 2D GaN ~ AlGaN heterostructure is practically very difficult to realize due to the presence of high density of threading dislocations (~1012 m−2 ) as a result of a large lattice mismatch between conventional substrates like sapphire, Si, etc., and the epitaxial layers. First few attempts of realizing double barrier (DB) RTDs based on GaN ~ AlGaN heterostructure were not achieved much success, since many device samples failed to reproduce the negative differential resistance (NDR) effect [41–46]. The current–voltage characteristics of the above-mentioned devices show hysteresis and NDR found to be absent during the backward sweep of the hysteresis loop of the current–voltage curve. This effect arises due to the presence of (i) deep traps in the barrier material (AlN) due to the threading dislocations [47], (ii) leakage current [48] and additional scattering [49]. However, these problems have been recently solved by using GaN ~ AlN nanowire (1-D) RTDs [50–52], in which higher order of lattice mismatch can be accommodated without forming dislocations. However, this RTD action can be reproduced in GaN ~ AlN RTDs up to the temperature of 250 K [50].

Gallium Nitride-Based Solid-State Devices for Terahertz …

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5 Plasma Heterostructure Field-Effect Transistors The plasma heterostructure field-effect transistors (pl-HFETs) are special kind of plasmonic electronic devices which show immense potentiality in generating, detecting and mixing of THz waves [53]. Generally, group III nitrides based 2DEG structures are utilized to implement pl-HFETs. The fundamental plasma frequency associated with a pl-HFETs is given by ω0 = π v/2L, where L and v are the length of the channel and speed of propagation respectively. Since the eigen modes of the plasma oscillation are associated with the odd harmonics of ω0 , the plasma mode of HFETs is ensured by keeping the L well below the critical channel length (L cr ), i.e. L  L cr = vμn mn * /r, where μn and mn * are the mobility and effective mass of electrons in conduction band and r is any odd integer, respectively. The afore-said condition is satisfied for ω0  ωcr = 1/τ, where ωcr is the critical plasma frequency and τ is the momentum relaxation time. Now, it is well verified that the ωcr value of GaN falls in the THz regime for wide range of temperature above room temperature [54]. The GaN can be considered as the most promising material for realizing pl-HFETs. Figure 6a, b illustrates the operation of a FET in both conventional regime as well as plasmonic regime, respectively. First pl-HFET based on AlGaN ~ GaN heterostructure was fabricated in the year 1997 by Lu et al. [55] for detecting THz waves. They achieved finite responsivity of the detector up to 0.2 THz under non-resonance mode of the device [55]. The responsivity of GaN-based pl-HFETs is further enhanced in non-resonance mode of operation up to 0.6 THz later in the year 2002 [56]. Generally, the HFETs operate in non-resonance mode at low frequencies below ωcr ; maximum responsivity of 600 V W−1 has been observed practically under this mode within the frequency range of 0.05 to 20 GHz. Resonance occurs at the critical frequency (ωcr ), and device enters to the resonance mode. Therefore, HFETs operates at any frequency above ωcr which can be considered to be as pl-HFETs. The resonance mode of plHFET was first fabricated in the year 2006, by Fatimy et al. [57]. They achieved peak responsivity of 200 mV W−1 at 0.2 THz at room temperature [57].

6 GUNN Diode Oscillators The GUNN diode oscillators show NDR due to inter-valley transfer of electrons in conduction band; that is why these are also know and transfer electron device (TED). Group III-V direct bandgap semiconductors like GaAs, InP, etc., are the very popular materials for fabricating GUNN diodes. However, due to larger energy relaxation time in GaAs (~10 ps), the GaAs-based GUNN oscillators cannot operate beyond 100 GHz. However, bulk NDR can be achieved in GaN above the threshold field of 8.0 × 106 V m−1 , and due to much shorter energy relaxation time in GaN, GaN NDR diode oscillators can operate at THz frequencies at room temperature [59,

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A. Acharyya

Fig. 6 a Conventional and b plasmonic regime operations of FET. Redrawn from Ref. [58]

60]. Moreover, higher electron drift velocity in GaN as compared to other group IIIV compound semiconductors ensures the THz operation of GaN-based NDR diode oscillators. The THz radiation up to 1 THz has been achieved via inter-valley transferbased GaN NDR diode oscillator, whereas up to 4 THz radiation was achieved from inflection-based NDR diode oscillators during early 2000s [61, 62]. Moreover, due to the much higher breakdown field and greater bandgap energy, the GaN-based NDR oscillators can deliver almost 3–4 times higher power output as compared to their GaAs counterparts. In the year 2016, Wang et al. proposed the planar GUNN diode structure based on GaN, capable of generating THz waves [63]. The proposed structure has been illustrated in Fig. 7. The dead zone length is narrowed down in the proposed structure by decreasing the recess layer near the cathode. Consequently, the output power increases significantly [63]. Donor traps are reduced near cathode in order to reduce the dead zone length, which leads to increase in electron concentration of that region as compared to other regions; thus, the region near the cathode behaves as the n+ -layer and results in GUNN operation at THz regime.

Gallium Nitride-Based Solid-State Devices for Terahertz …

19

Fig. 7 Schematic of AlGaN ~ GaN heterostructure-based planar GUNN diode. Redrawn from Ref. [63]

7 Antenna-Coupled Field-Effect Transistors Antenna-coupled field-effect transistors are also known as teraFETs. This device can be fabricated by using standard CMOS technology, and it is very much useful for realizing low cost THz camera for several THz imaging applications. Asymmetric coupling can be utilized in this device for optimizing the THz power detection capability. The first teraFETs were fabricated by using standard AlGaN ~ GaN process technology (0.25 µm), which were capable of detecting frequencies up to 0.59 THz by utilizing plasmonic detection technique [64]. The structure of teraFET has been illustrated in Fig. 8.

8 Hetero-dimensional Schottky Diode High 2DEG concentration of AlGaN ~ GaN heterojunction results in very high cut-off frequency and reduced parasitic series resistance in AlGaN ~ GaN heterostructure-based THz devices. Hetero-dimensional Schottky diodes (HDSDs)

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A. Acharyya

Fig. 8 Schematic showing the structure of a AlGaN ~ GaN heterostructure-based teraFET. Redrawn from Ref. [64]

are very promising device for detecting waves, first AlGaN ~ GaN heterostructurebased HDSD devices was realized by Veksler et al. in 2006 [65]. The schematic of the proposed HDSD structure has been illustrated in Fig. 9.

Fig. 9 Schematic of AlGaN ~ GaN heterostructure-based hetero-dimensional a lateral and b vertical Schottky diodes. Redrawn from Ref. [65]

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9 Avalanche Transit Time Devices Impact avalanche transit time (IMPATT) diodes are the most promising two-terminal devices among the avalanche transit time (ATT) family members for generating microwave (1–30 GHz) and mm-wave (30–300 GHz) frequencies [66, 67]. Recent studies reveal that the IMPATT diode oscillators based on some WBG semiconductors like SiC, GaN, diamond, etc., are capable of radiating THz waves with sufficiently high efficiency [68, 69]. Among all WBG semiconductors, GaN-based IMPATT oscillators are found to be the most favourable for THz wave generation up to 5 THz frequency [68]. Moreover, the AlGaN ~ GaN heterostructures in IMPATT diodes can be used to reduce the avalanche noise level of the THZ oscillators [70]. Figure 10 illustrates the structure of a GaN-based double-drift IMPATT structure optimized for 1 THz operation [71]. The mm-wave, THz and noise performance of GaN-based IMPATT sources are demonstrated and compared with other semiconductor-based IMPATT sources in the performance curves presented in Figs. 11, 12 and 13.

Fig. 10 Optimized GaN IMPATT structure for 1.0 THz operation [71]

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Fig. 11 Variations of power output of Si, 4H-SiC, diamond and Wz-GaN-based IMPATT sources versus frequency curves obtained from simulation and experimental measurements [67, 72–78]

10 Summary This chapter deals with a comprehensive review of some GaN-based electronic and photonic devices like quantum cascade lasers (QCLs), plasma heterostructure fieldeffect transistors (pl-HFETs), negative differential resistance (NDR) diodes, GUNN diodes, high electron mobility transistors (HEMTs), antenna coupled FETs, resonanttunneling diodes (RTDs), impact avalanche transit time (IMPATT) diodes, etc., since their inception to the state-of-the-art status of those. The future needs of economical, compact and highly efficient THz systems are vastly endorsing the usage of GaN for realizing next generation THz devices due to the favourable material properties of GaN. The chapter also discusses the impact of the recent developments of those devices on the future THz systems.

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Fig. 12 Variations of efficiency of Si, 4H-SiC, diamond and Wz-GaN-based IMPATT sources versus frequency curves obtained from simulation [72]

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Fig. 13 Variations of noise measure of Si, 4H-SiC, diamond and Wz-GaN-based IMPATT sources versus frequency curves obtained from simulation and experimental measurement [79]

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Noncontact Characterization Techniques of GaN-Based Terahertz Devices Prajukta Mukherjee, Aritra Acharyya, Hiroshi Inokawa, and Arindam Biswas

Abstract The fresh developments in the area of terahertz (THz) devices and systems based on gallium nitride (GaN) have lifted the requirement of the state-of-the-art noncontact characterization techniques. In this chapter, three major noncontact characterization techniques used for characterizing GaN-based THz devices have been described in details; those are (i) THz time-domain spectroscopy, (ii) laser-induced THz emission spectroscopy, and (iii) THz electromodulation spectroscopy. These noncontact characterization techniques have been established as potential alternatives of conventional contact measurement techniques due to their accuracy, reliability, and capability of providing noteworthy amount of visually interpretable information. Keywords GaN · Noncontact characterization · Thz measurements · Thz spectroscopy

1 Introduction The frequency spectrum ranging from 0.1 to 10 THz is known as terahertz (THz) spectrum or more popularly recognized as THz-gap. It is a useful frequency gap in P. Mukherjee (B) Department of Electrical Engineering, Cooch Behar Government Engineering College, West Bengal, Harinchawra, Ghughumari, Cooch Behar 736170, India e-mail: [email protected] A. Acharyya Department of Electronics and Communication Engineering, Cooch Behar Government Engineering College, West Bengal, Harinchawra, Ghughumari, Cooch Behar 736170, India H. Inokawa Research Institute of Electronics, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu 432-8011, Japan e-mail: [email protected] A. Biswas Centre for Organic Spin-Tronics and Optoelectronics Devices (COSOD), Mining Engineering Department, Kazi Nazrul University, Asansol, Burdwan, West Bengal 713340, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Acharyya and P. Das (eds.), Advanced Materials for Future Terahertz Devices, Circuits and Systems, Lecture Notes in Electrical Engineering 727, https://doi.org/10.1007/978-981-33-4489-1_3

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between the widely used millimeter wave (mm-wave) and infrared (IR) frequency spectrums. The wavelength range of the THz-gap, i.e., 3.0–0.03 mm, finds numerous electronic as well as photonic applications. Some of those applications are biosensing and imaging, remote sensing, remote quality inspection of industrial products, astronomy, wireless communication, spectroscopy, food diagnostics, medical and pharmaceutical applications, etc. [1–9]. Day by day, the demand of THz spectrum is increasing, due to its harmlessness, high reliability, and accuracy in various fields of applications as mentioned earlier. This huge demand of the THz spectrum is supported by current progress in different THz sources, detectors, and systems [10]. It has already observed that some wide bandgap materials like GaN and some of its ternary alloys such as InGaN, AlGaN have already shown immense potentiality to realize THz devices and systems based on those [10]. Some of the potential GaNbased THz devices are quantum cascade lasers, plasma heterojunction field effect transistors, resonant tunneling diodes, GUNN diodes, impact avalanche transit time diodes, high electron mobility transistors, etc. [11–59]. The extraordinary progress in the field of the GaN-based THz devices in recent years is not only occurred due to the exceptional advancements in the area of GaN process technology but also due to the amazing advancements in THz measurement techniques. The performance of a THz system could not be verified, evaluated, or compared with existing systems unless advanced THz characterization techniques are available. In this chapter, some important noncontact characterization techniques of GaNbased devices are described. The characterization of GaN at THz frequencies requires accurate spectroscopic measurement technique. Three major noncontact characterization techniques, i.e., (i) THz time-domain spectroscopy (THz-TDS), (ii) laserinduced THz emission spectroscopy (LTEM), and (iii) THz-electromodulation spectroscopy (THz-EMS) techniques have been described in brief in this chapter. Elaborated literature review and descriptions of the said characterization techniques are presented in the successive sections.

2 THz Time-Domain Spectroscopy The wavelength associated with the THz-gap, i.e., 3.0–0.03 mm, is very much important to study the low-frequency modes in molecular crystals. These wavelengths are also important for vibrational spectroscopy as well as low-frequency dielectric relaxation of liquids [60, 61]. Basically, the transient electric field of time-domain THz signal can be directly calculated by using THz-TDS method. During the decade of 1980s of the earlier century, the TDS was applied to different systems using different emitters [62–78]. When an input electromagnetic pulse is propagated through a sample under test, it changes its shape as per the nature of the sample. Thus, after the propagation, a changed shaped pulse is detected at the output. The TDS technique measures both the input and output pulse shapes. The absorption and dispersion properties of the sample can be calculated as functions of frequency by using the suitable frequency domain analysis of the input and output pulses. The duration of the input

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pulse and the time resolution of the detection process determine the frequency range of this process. When the said frequency range falls in the THz spectrum, then the TDS technique is called THz-TDS technique. Currently, the THz-TDS has emerged as a significantly valuable characterization method in the fields of material science, pharmaceutical applications, engineering, chemistry, and many other applications [62–70]. In the year 1989, THz-TDS was first used by M. V. Exter and D. Grischkowsky of IBM Research Division, to ensure the absorption as well as dispersion properties of both n and p type Si having different doping levels at moderate range at 0.1–2 THz frequency regime [79]. They had carried out the measurements at 80 K and room temperature (i.e., 300 K) and obtained the accurate view of carrier dynamics of moderately doped Si via the measured values of absorption, dispersion parameters, and complex conductivity; the measured data are well fitted with an extended Drude model considering and energy-dependent carrier relaxation rate. The antenna structure and a schematic illustration of generation and detection of THz pulses used in the said experiment have been shown in Fig. 1. Later in the year 1990, the same research group measured the absorption dispersion properties of some widely used dielectric like sapphire, quartz, fused silica, and some popular semiconductors such as Ge,

Fig. 1 Schematics of a antenna structure and b experimental setup for generation and detection of THz pulses. Redrawn from Ref. [79]

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Si, and GaAs within 0.1–2 THz [80]. They observed that their measured absorption and dispersion parameters at THz regime are in good agreement with simple Drude theory [80]. Two years later in the year 1992, the researchers of IBM Watson Research Center reported the absorption, refraction index, and complex conductance of n and p type GaAs at the frequency range of 0.1–4 THz [81]; they had also used the same THz-TDS characterization technique and found that the measured data are agreeing with the Drude’s model [81]. For all of these three cases, the experimental setup shown in Fig. 1 was used. The epitaxial films based on GaN were first characterized by using THz-TDS by Y. Bu et al. in the year 1995 [82]. They studied the far-IR transmission in GaN films grown on sapphire substrate and measured absorption coefficient, electron and hole densities and corresponding mobility in the range of 1–3 THz frequencies [82]. Later, during early 2000s (i.e., in the year 2002), Nagashima et al., a research group from Osaka University, Japan, reported the noncontact measurement of electrical properties of GaN by using THz-TDS [83]. They have carried out their experiments on GaN thin film samples and measured carrier density, mobility of charge carriers in GaN and DC resistivity of GaN films within the frequency range of 0.1–1 THz [83, 84]. Their experimental data were well fitted with the Drude model and also very close to the experimental data measured earlier through conventional contact measurements. The complex conductivity as well as the dielectric function of GaN were first measured by Zhang et al. in the year 2003 [85]. They had used 0.1–4 THz frequency range in their THz-TDS measurement [85]. In the year 2005, Tsai et al. used THz-TDS characterization technique to measure the index of refraction as well as complex conductivities of n-type GaN film; they had used 0.2–2.5 THz frequency range for their measurement [86]. The results were in good agreement with the Kohlrausch stretched exponential model [86]; this agreement not only provides the carrier mobility in GaN film, but also provides the estimation of both the relaxation time distribution function and average relaxation time. Recently, in the year 2013, Fang et al. measured the dielectric functions of GaN over the frequency range of 0.3–1 THz by using THz-TDS characterization technique [87]; the measurements were carried out within a wide range of temperatures (10– 300 K). They observed oscillations in the dielectric functions of GaN at different frequencies which are basically corresponding to the resonant states of the point defects in GaN. Experimental as well as fitting dielectric functions of GaN at 10 and 300 K temperatures with frequency are shown in Fig. 2. The combined simple Drude model and classical damped oscillation model shows best fit with the experimentally measured data. All of these THz-TDS characterizations of GaN reveal the fact that this technique is a highly promising and accurate technique which is noncontact in nature and more convenient than the conventional contact measurement technique [88].

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Fig. 2 Real and imaginary parts of dielectric functions of GaN obtained from experimental data as well as fitting at 10 and 300 K. Redrawn from Ref. [87]

3 Laser-Induced THz Spectroscopy Another alternative approach of optical as well as electrical characterization of semiconductor materials is laser-induced THz emission spectroscopy (LTEM). This noncontact characterization technique was first deployed by Kondo et al. in the year 1999, in an undoped (111)-oriented InAs surface [89]. The 1.55 μm wavelength femto-second laser pulses were used to excite the InAs surface in order to study the THz radiation from the surface. However, the THz radiations from different materials were reported earlier by different research groups [90–92]. But in most of the cases, the experimentalists had used 800 nm wavelength femto-second laser pulses for exciting the materials [90–92]; this wavelength is very near to the first window wavelength of optical communication. However, taking into account the modern trends in optical communication systems, the thirds optical window wavelength, i.e., 1.55 μm wavelength, has greater technological significance. Therefore, the use of LTEM characterization technique used by Kondo et al. was a path breaking milestone [89]. The experimental setup used by Kondo et al. has been shown in Fig. 3. Later, it was found that LTEM technique is highly suitable for inspecting the faults and defects in semiconductor materials as well as in integrated circuits [93, 94]. The

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Fig. 3 Schematic diagram of the experimental setup used by Kondo et al. [89]. Redrawn from Ref. [89]

experimental setup of the LTEM system, used by Yamashita et al. in the year 2004, is shown in Fig. 4 [95]. The LTEM characterization of GaN surface was first reported by Sakai et al. [96] in the year 2015. They had measured the defect density and surface potential of GaN surface by using the said technique. Ultraviolet femto-second laser pulses were used to excite the GaN surface. They observed the defects corresponding to the yellow luminescence are primarily responsible for the enhancement in THz radiation from GaN surface. The non-radiative defects are generally understandable by using photoluminescence. But LTEM characterization technique is capable of evaluating the distributions of non-radiative defects in semiconductor surfaces. Some results obtained by Sakai et al. are illustrated in forms of LTEM images and graphs in Figs. 5 and 6.

4 THz-Electromodulation Spectroscopy The THz-TDS technique effectively reduces the carrier mobility in the material under test; therefore, this technique is not suitable for measuring the transport characteristics of semiconductor materials especially at low doping levels. Better technique

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Fig. 4 Experimental setup of LTEM system used by Yamashita et al. [95]. Redrawn from Ref. [95]

which can be used for this purpose is the THz-electromodulation spectroscopy (THzEMS). The THz-EMS characterization technique is highly suitable for measuring the transport characteristics at doping levels where classical techniques become inefficient. By using this technique, the measuring frequency range can be extended up to 2.8 THz. The charge transport in n-type GaN was first investigated by Engelbrecht et al. in the year 2015, by using THz-EMS [97]. They have used a few samples of GaN grown on sapphire substrate by using MOVPE technique for their measurement [97]. They have realized Schottky contacts on GaN surface for fulfilling the prerequisite of electron sheet density switching in the semiconductor material which is essential for THz-EMS. The relaxation time and the effective mass of conductivity of electrons in GaN had been determined by them by using THz0TDS measurements. The experimental setup used by them has been shown in Fig. 7.

5 Summary The fresh growths in the area of THz devices, systems, and technologies based on GaN have raised the demand of state-of-the-art noncontact characterization techniques. In this chapter, three major noncontact characterization methods like THzTDS, LTEM, and THz-EMS used for characterizing GaN-based THz devices have been described in details. These noncontact characterization techniques have been established as potential alternatives of conventional contact measurement techniques

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Fig. 5 a LTEM image of n-type GaN surface using 260 nm excitation wavelength, b THz waveforms at different two points, c PL spectra at two characteristic points, and d PL 2-D mapping. Redrawn from Ref. [96]

due to their accuracy, reliability, and capability of providing noteworthy amount of visually interpretable information.

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Fig. 6 a LTEM image of n-type GaN at different excitation wavelengths, b THz waveforms at the LDD region and the HDD region, and c peak-to-peak amplitude of the THz emissions at each excitation wavelength. Redrawn from Ref. [96]

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Fig. 7 Schematic of the device at equilibrium used by Engelbrecht et al. [97] for their experiment. Redrawn from Ref. [97]

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A Brief Review on Terahertz Avalanche Transit Time Sources S. J. Mukhopadhyay, P. Hazra, and M. Mitra

Abstract During last few years, numerous researches have been processed for the growth of reliable sources in the terahertz (THz) frequency regime. Among different solid-state sources, impact ionization avalanche transit time (IMPATT) diode is the most promising one for THz wave generation. Here, a selective review has been carried on THz IMPATT diode, which helps in detailed understanding of device operation in this domain. The paper mainly deals with several terahertz properties based on DC, noise, small and large-signal simulation of IMPATT devices. This study reveals the potency of this device in many THz applications. Keywords Diamond · Si · Double-drift IMPATT diode · Terahertz

1 Introduction The terahertz (THz) range is of 0.1–10 THz, and related wavelength area is 3.0 and 0.03 mm. This frequency band is in enormous demand for a variety of applications like imaging [1], spectrum analysis [2], nanoelectronic [3], inspection services [4–6], drug industry [7, 8], space research [9], etc. Though much application possibility, this field is not fully exercised for non-access of potential sources that may generate terahertz waves. Though lot of technical advantages prevail the great challenge today, it is the development of portable high-power THz radiators. Very recently, a number of solid-state physics research group worldwide have been highlighting their attention to S. J. Mukhopadhyay (B) · M. Mitra Department of Electronics and Telecommunication Engineering, Indian Institute of Engineering Science and Technology, Shibpur, P.O.: Botanic Garden, Howrah, West Bengal 711103, India e-mail: [email protected] M. Mitra e-mail: [email protected] P. Hazra Indian Institute of Space Science and Technology, Trivandrum Deemed University in Thiruvananthapuram, Valiamala Road, Valiamala, Kerala 695547, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Acharyya and P. Das (eds.), Advanced Materials for Future Terahertz Devices, Circuits and Systems, Lecture Notes in Electrical Engineering 727, https://doi.org/10.1007/978-981-33-4489-1_4

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improve semiconductor devices which can yield THz oscillator. In early nineties, brilliant idea of using plasma waves in two-dimensional (2D) electron gas (2DEG) was thought. Nowadays, experimental observations and theoretical studies have focused on plasma oscillations in the electron channel of field-effect transistor (FET). The other shining THz emitters are quantum cascade lasers (QCLs). In the year 1994, this was first demonstrated on the basis of cascaded quantum wells made utilizing molecular beam epitaxy (MBE) technique. Though in the infrared (IR) region, these devices are in the process of improvement for more than 10 years, still very recently the foremost THz laser was realized at 4.4 THz. It is evident that recent commercially existing THz emitters are compound and heavy. If THz waves could be produced from a single solid-state source, then this would be more prolific. Out of all the solid-state sources, it is eminent that impact ionization avalanche transit time (IMPATT) devices have revealed the ability of yielding sufficient THz power. IMPATT devices are mainly p–n junction semiconductor diode which operates under reverse-biased condition when avalanche breakdown occurs. These diodes can produce oscillation at microwave frequencies and find applications in satellite communication system, radars and missile guidance as sources in transmitter section. The microwave oscillation from IMPATT diode arises from its negative resistance which will be maximum when the phase delay between input voltage and terminal current is around 180°. This phase delay consists of an avalanche delay of 90° to produce avalanche growth of either electrons or holes or both and a transit time delay of about 90° to move through the drift space. If the net phase difference between the voltage and current is between 90° and 270°, the negative resistance is produced in IMPATT diode. Homojunction IMPATT is formed by using same semiconducting material, on either side of the junction. On the other hand, a heterojunction IMPATT is realized by using different semiconductors on either side of the junction. If the dopants are of same type on both sides of the junction, then the heterojunction formed is called isotype such as n–n/p-p heterojunction. On the other hand if the dopants are of different types on either side of the junction, i.e. n-P/p-N, then anisotype heterojunction is formed. It has been mentioned previously that heterojunction IMPATTs have more privileged than that of homojunction in respect of lower noise output [10]. IMPATT structure chosen for all the studies here is a double-drift region (DDR) p+ -pn–n+ structure whose junction is located almost at the central region of the depletion layer. The main objective of this paper is to focus on simulation studies on terahertz (THz) properties based on DC, noise small and large-signal simulation of both homoand heterojunction IMPATT devices.

2 Theory The phase difference between current and voltage is created because of the inherent time delay in the build-up of the avalanche current and by the transit time delay

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witnessed by the drifting charge carriers. One can consider the structure proposed by Read [11] to discuss the two principal effects that contribute to the negative resistance in IMPATT devices. The Read structure consists of two distinct regions: (i) avalanche region around the junction where electric field is maximum and in which impact ionization takes place, and (ii) a drift region where carriers drift at saturated velocity without any further multiplication. The electron–hole pairs (EHPs) which are generated in the avalanche region drift in opposite directions. While holes are immediately collected at the p+ -terminal, the electrons are injected into the drift region and they are collected at the n+ -substrate terminal. Miswa first considered p-i-n diode, in which the avalanching and drifting of charge carriers take place simultaneously over the entire active layer of the device and calculated the diode impedance [12, 13]. The Read diode has large negative conductance in a very narrow band, whereas the Miswa diode has small negative conductance, but the band is broad and flat extending to zero frequency. Several researchers have also accomplished large-signal simulation of SDR and DDR IMPATTs [14–16]. Their analysis showed that the negative conductance is reduced with the rise of voltage swing. Efficiency (η) of an IMPATT source is obtained from the semi-quantitative relation [14] given below η=

VD VD × 100, × 100 = π VB π (VD + VA )

(1)

where V D , V A and V B are drift, avalanche voltage drops and breakdown voltage, respectively. In IMPATT, the frequency of operation is determined by the carrier transit time. The width of the active region, voltages and output power reduce with the rise of operational frequency. The transit time limitation imposes a power (P0 ) frequency trade-off in IMPATT diode and is given by the expression [17] P0 f 02 X D = C,

(2)

where X D is the device impedance at the frequency f 0 and the constant (C) depends on the specific material properties of the semiconductor used to fabricate IMPATT diode.

3 Early Developments In 1970, Scharfetter et al. [18] proposed a DDR structure where both electrons and holes travel in opposite directions under reverse bias and reach their respective terminals. They showed that output power and conversion efficiency of the DDR IMPATT improved considerably over the conventional SDR IMPATT. The DDR p+ -p-n–n+ IMPATT’s structure, doping and field profile are shown in Figs. 1a–c.

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Fig. 1 a DDR IMPATT diode structure, b doping profile and c field profile showing the avalanche and drift regions

Although from a theoretical standpoint, the output power from a DDR IMPATT diode is expected to be four times more than that from a SDR diode, experimental result does not meet the expectation exactly. In practice, the power output from a DDR diode is about 2–2.7 times higher than that from an SDR diode. Scharfetter et al. [18] demonstrated the millimetre-wave power generation capability of DDR silicon IMPATTs in 1970 for the first time. In the next year, Seidel et al. [19] experimentally demonstrated improved power output of DDR Si IMPATTs with respect to SDR Si IMPATTs for CW operation at 50 GHz. They reported that a flat profile ion-implanted DDR Si IMPATT diode delivers 1 W power with 14.2% conversion efficiency while SDR Si IMPATT diode delivers RF power of 0.53 W with 10.3% efficiency at 50 GHz. The superior RF performance of DDR IMPATTs over their SDR counterparts as regards both output power and conversion efficiency was undoubtedly established. In 1973, Su and Sze [20] showed analytically that a modification of doping profile through incorporation of impurity bumps in IMPATT diode leads to considerable

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47

improvement of its DC to RF conversion efficiency. Such modified structures having impurity bumps are usually of two types: (i) lo-hi-lo (‘clump’ type) and (ii) hi-lo structures designed by three- and two-step doping, respectively. These structures are also called quasi-Read IMPATT structures since some of the essential properties of a Read diode such as a confined avalanche zone are maintained in these structures. Experimental reports have established that quasi-Read IMPATT diode provides high power of the order of 1 W [21] at 94 GHz. Dalle and Rolland [22] carried out theoretical studies on the RF performance of different quasi-Read and flat profile Si diodes at 94 GHz. Their results do not show any improvement of RF performance of quasi-read Si IMPATTs as regards maximum attainable RF power levels over flat profile counterparts at 94 GHz. Earlier in 1977, Chang et al. [23] proposed a double-drift quasi-Read LHL Si IMPATT diode. In the following year, they reported large-signal analysis of the proposed diode and showed that a high efficiency of 19% can be realized from the device at 50 GHz [15]. Later in 1991, Banerjee et al. [24] carried out theoretical as well as experimental studies on the DC and RF characteristics of double-drift (DD) flat profile and low high low (LHL) Si IMPATTs at V-band (60 GHz) first time. Experimentally, the epitaxial layers of complex LHL DDR with p+ -layer were developed by Si MBE machine. The results show that the power output from circular mesa of DD LHL Si diode having a diameter of 54 micron is 1.26 W with 11.6% efficiency. Further improvement of efficiency at V-band was shown by Luy et al. [25]. Above 100 GHz, the active layer of diodes becomes very narrow and peak field at the junction increases above 1MV/cm. Under this situation, band-to-band tunnelling generation of carriers takes place along with avalanche generation of carriers. W. T. Read [11] reported that tunnelling limits the conversion efficiency of the source. Tunnelling current was theoretically studied by Kwok and Haddad [26] and Chive et al. [27]. Elta and Haddad [28, 29] identified three modes of operation for various ranges of breakdown field and generation region widths. These modes are (i) normal IMPATT mode, (ii) MITATT mode where both tunnelling and avalanche breakdown take place and (iii) TUNNETT mode where pure tunnelling breakdown occurs. Elta and Haddad [30] showed from large-signal analysis that with increase of frequency the efficiency of GaAs Read-type TUNNETT devices initially increases to reach a peak value and then decreases. They observed a peak efficiency of 6% at 100 GHz. They also reported that frequencies above which Si and GaAs IMPATTs exhibit pure TUNNETT mode are 400 GHz and 75 GHz, respectively. Heterojunctions formed by two semiconductors of different bandgaps can be used advantageously to obtain improved RF and noise characteristics of IMPATT diode. The important feature of heterojunction IMPATT device is conduction band discontinuity and sharpness of electric field at the junction. Various reports [31–35] have established significant performance improvements of heterojunction IMPATT devices. Considering no interface charge, the maximum field at the interface would always be larger for a GaAs/Al0.3 Ga0.7 As heterojunction than for a standard GaAs homojunction [36]. The reports available in the literature show that the noise performance of InP/GaInAs (Ga0.47 In0.53 As) and InP/GaInAsP (Ga0.33 In0.67 As0.7 P0.3 ) DDR

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heterostructure is superior compared to their homojunction counterparts [37]. Mishra et al. [38] theoretically studied heterojunction IMPATTs and reported that these devices excel their homojunction counterparts as regards efficiency and noise.

4 Terahertz IMPATTs The structures reviewed here are mainly concerned with DDR homojunction/heterojunction IMPATTs. The layer widths (W n , W p ) and corresponding doping densities (N D , N A ) of DDR IMPATT devices are designed to operate at terahertz frequencies based on transit time formula [39] and simulated using static [40] and high-frequency [41] analysis methods. Different simulated results have been published on terahertz homojunction/heterojunction IMPATTs. Last ten years’ research work on homojunction/heterojunction IMPATTs in terahertz domain is shown in Fig. 2. In the year of 2007, Mukherjee carried out simulation on 4H-SiC diode operating at 0.5 THz [42]. The study highlights that 4H-SiC IMPATT has produced high RF power (PRF ) of about 2.70 W at 0.515 terahertz with 12% conversion efficiency. In the same year, she reported the dynamic characteristics of InP diode at 0.5 THz [43] through simulation analysis. The study reveals that InP source can deliver 27 mW power with an efficiency of 6.3%. Later in the year of 2009, Mukherjee [44] carried out simulation on 4H-SiC DDR IMPATTs at 0.7 THz. In the year of 2010, M. Mukherjee et al. [45] carried out a comparative study between groups IV-IV- and III-V-based DDR IMPATTs through modelling and simulation at 0.3THz. Later in the year of 2011, A. Acharyya et al. [46] studied the effect of tunnelling on THz performance of Si IMPATTs. In the year of 2014, A. Acharyya et al. [47] carried out Fig. 2 Last ten years’ research work on homojunction/heterojunction DDR IMPATTs

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49

simulation using various substances like GaAs, Si, InP, 4H-SiC and Wz-GaN for the operation at terahertz frequencies. The study indicates that Wz-GaN DDR IMPATT is the potential source to generate high conversion efficiency and sufficiently high RF power output at THz frequencies up to 5.0THz because of less avalanche response time. In the year of 2013, A. Acharyya et al. [48] performed characterization of DDR Si IMPATTs operating up to 0.5 THz via large-signal simulation. In the year of 2014, A. Acharyya et al. [49] also performed large-signal characterization of DDR THz frequencies. It is already known to us that at higher mm-wave regime, the depletion layer width of the device gets narrowed down and the junction electric field rises to a high value. The thinner depletion layer and higher junction field create a favourable situation for carrier generation by band-to-band tunnelling. Under this situation, the device is said to operate in MITATT mode, as previously discussed already. Many researchers have been reported on heterostructure IMPATTs in terahertz domain. In the year of 2008, Xiaochuan et al. [50] analysed the design trade-offs between Si and SiGe heterostructure MITATT diodes. It is seen that SiGe heterostructure MITATT produces 42 mW power at 200 GHz, i.e. around 63% higher than that of Si diode. Later in the year of 2013, Banerjee et al. [51] studied the noise performance of Si ~ Si1-x Gex anisotype heterojunction DDR MITATT device at W-band. In the same year [52], she carried out large-signal modelling and simulation of anisotype heterojunction 3C-SiC/Si diodes at 0.3 and 0.5 THz. Later in 2015, they also characterized Alx Ga1-x N/GaN diodes at 1.0 THz [53].

5 Characteristics According to previously published data, a comparative analysis has been made based on the figure of merits like RF performance, conversion efficiency and noise performance of various semiconducting substance-based homojunction and heterojunction DDR IMPATTs in THz frequency domain, as shown in Table 1. It is seen from Table 1 that Wz-GaN diodes appear as the potential substance to generate high conversion efficiency and sufficiently high THz power up to 5.0 THz. But it is also observed that up to 1.0 THz, the RF performance of SiC-based homojunction IMPATT is superior than Wz-GaN-based homojunction IMPATT. It is also revealed from the table below that Si-based DDR homojunction performs better in IMPATT mode rather than in MITATT mode. Another thing is that n-Si/p-(3C)SiC- and n-Alx Ga1-x N/p-GaN-based DDRs excel their homojunction counterparts, THz power and noise performance.

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Table 1 Comparative analysis among various homojunction/heterojunction DDR IMPATTs Device

DC to RF power output PRF (W)

Efficiency (η(%))

Noise measure (dB)

Si HMDDR IMPATT 0.3 [46]/0.3 [52]

0.138 [46]/0.173 [52]

6.55 [46]/3.97 [52]

20.5 [52]

0.5 [47]/0.5 [52]

0.136 [47]/0.101 [52]

4.59 [47]/2.49 [52]

15.5 [52]

0.5 [42]

2.70 [42]

12 [42]

0.7 [44]

2.80 [44]

10.5 [44]

0.3 [45]

20 [45]

15 [45]

1.0 [47]

1.982 [47]

9.38 [47]

SiC(3C) HMDDR IMPATT

0.3 [45]/ [52]

11.5 [45]/2.453 [52]

12.5 [45]/3.14 [52]

25.5 [52]

0.5 [52]

0.957 [52]

1.68 [52]

25.0 [52]

SiC(6H) HMDDR IMPATT

0.3 [45]

7.5 [45]

12 [45]

GaN(Wz) HMDDR IMPATT

0.3 [45]

6.23 [45]

15.47 [45]

0.5 [47]

1.162 [47]

14.56 [47]

1.0 [47]/1.0 [53]

0.504 [47]/0.411 [53]

13.32 [47]/17.34 [2015]

1.5 [47]

0.192 [47]

12.27 [47]

2.0 [47]

0.047 [47]

11.46 [47]

5.0 [47]

0.007 [47]

5.88 [47]

InP HMDDR IMPATT

0.5 [43]

0.027 [43]

6.3 [43]

1.0 [47]

0.072 [47]

7.82 [47]

NA

Si HMDDR MITATT

0.2 [50]

0.0260 [50]

3.7 [50]

NA

0.3 [46]

0.120 [46]

5.89 [46]

SiGe HTDDR MITATT

0.2 [50]

0.0428 [50]

4.6 [50]

n-(3C)SiC/p-Si HTDDR IMPATT

0.3 [52]

0.578 [52]

7.83 [52]

15.1 [52]

0.5 [52]

0.383 [52]

5.80 [52]

10.5 [52]

n-Si/p-(3C)SiC HTDDR IMPATT

0.3 [52]

0.680 [52]

8.49 [52]

15.0 [52]

0.5 [52]

0.413 [52]

7.22 [52]

10.4 [52]

n-Alx Ga1-x N/p-GaN HTDDR IMPATT

1.0 [53]

0.610 [53]

22.94 [53]

7.3 [53]

n-GaN /p-Alx Ga1-x N 1.0 [53] HTDDR IMPATT

0.537 [53]

21.23 [53]

7.2 [53]

SiC(4H) HMDDR IMPATT

Peak operating frequency f p (THz)

9.5 [53]

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6 Summary The homojunction Wz-GaN- and 4H-SiC-based DDR IMPATTs are most suitable semiconductors for THz IMPATT action as regards the high power output and efficiency. As noise performance is considered, heterojunction DDR IMPATTs excel over homojunction IMPATTs in terahertz frequencies. The terahertz characteristics of the IMPATT based on that said substances have been explored using the computer simulation method. The simulation results and corresponding designs would be useful for realizing the THz IMPATTs by using either MBE or metal–organic chemical vapour deposition (MOCVD) techniques.

References 1. W.L. Chan, J. Deibel, D.M. Mittleman, Imaging with terahertz radiation. Rep. Prog. Phys. 70, 1325–1379 (2007) 2. D. Grischkowsky, S. Keiding, M. Exter, C. Fattinger, Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors. J. Opt. Soc. Am. B. 7, 2006–2015 (1990) 3. C. Debus, P.H. Bolivar, Frequency selective surfaces for high sensitivity terahertz sensing. Appl. Phys. Lett. 91, 184102–184103 (2007) 4. T. Yasui, T. Yasuda, K. Sawanaka, T. Araki, Terahertz paintmeter for noncontact monitoring of thickness and drying progress in paint film. Appl. Opt. 44, 6849–6856 (2005) 5. C.D. Stoik, M.J. Bohn, J.L. Blackshire, Nondestructive evaluation of aircraft composites using transmissive terahertz time domain spectroscopy. Opt. Express. 16, 17039–17051 (2008) 6. C. Jordens, M. Koch, Detection of foreign bodies in chocolate with pulsed terahertz spectroscopy. Opt. Eng. 47, 037003 (2008) 7. A.J. Fitzgerald, B.E. Cole, P.F. Taday, Nondestructive analysis of tablet coating thicknesses using terahertz pulsed imaging. J. Pharm. Sci. 94, 177–183 (2005) 8. P.H. Siegel, Terahertz technology in biology and medicine. IEEE Trans. Microwave Theory Tech. 52, 2438–2447 (2004) 9. P.H. Siegel, THz Instruments for Space. IEEE Trans. Antenn. Propag. 55, 2957–2965 (2007) 10. S. Banerjee, A. Acharyya, J.P. Banerjee, Noise performance of heterojunction DDR MITATT devices based on Si~Si1-x Gex at W-Band. Act. Passive Electron. Compon. 1–7 (2013) 11. W.T. Read, A proposed high frequency negative resistance. Bell Syst. Tech. J. 37, 401 (1958) 12. T. Misawa, The negative resistance in p-n junction under avalanche breakdown conditions. part-I, IEEE Trans. Electron Devices ED 13, 137 (1966a) 13. T. Misawa, The negative resistance in p-n junction under avalanche breakdown conditions. part-II, IEEE Trans. Electron Devices ED 13, 143 (1966b) 14. D.L. Scharfetter, H.K. Gummel, Large signal analysis of a silicon Read diode oscillator. IEEE Trans. Electron devices ED 18, 1137 (1978) 15. L.C. Chang, D.H. Hu, Large signal analysis of Lo-Hi-Lo double drift silicon Impatt at 50 GHz. IEEE Trans. Electron. Devices ED 25, 1137 (1978) 16. P.A. Rolland, C. Dalle, M.R. Friscourt, Physical understanding and optimum design of high power millimeter wave pulsed Impatt diode. IEEE Electron Device Lett. 17(5), 221 (1991) 17. Jr. B.C. Deloach, Recent advances in solid state microwave generators. in Advances in Microwaves, vol. 2. (Academic Press, New York, 1967), p. 43 18. D. L. Scharfetter, W.J. Evans, H.L. Johnson, Double drift region p+ pnn+ avalanche diode oscillators. Proc. IEEE Lett. 50, 1131 (1970)

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19. T.E. Seidel, R.E. Davis, D.E. Iglesias, Double-Drift-region ion implanted millimetre wave IMPATT diodes. Proc. IEEE 59, 1222 (1971) 20. S. Su, S.Sze, Design considerations of high efficiency GaAs impatt diodes. IEEE Trans. Electron. Devices ED 20, 541 (1973) 21. J.F. Luy, E. Kasper, W. Behr,Semiconductor structures for 100 GHz Silicon Impatt diodes. Proc. 17th European Microwave Conference (Rome), 820 (1987) 22. C. Dalle, P.A. Rolland, Read versus flat doping profile structures for the realization of reliable high-power, high-efficiency 94 GHz IMPATT Sources. IEEE Trans. Microwave Theory Tech. MTT 38, 366 (1990) 23. L.C. Chang, D.H. Hu, C.C. Wang, Design considerations of high efficiency double drift silicon IMPATT diodes. IEEE Trans. Electron. Devices ED-24,655 (1977) 24. J.P. Banerjee, J.F. Luy, F. Schaffler, Comparison of theoretical and experimental 60 GHz silicon Impatt diode performance. Electron. Lett. 27, 1049 (1991) 25. J.F. Luy, F. Schaffler, M. Schlett, 17.6% conversion efficiency at 60 GHz with IMPATT diodes, in Proceedings of 22nd European Microwave Conference, p. 485 (1992) 26. S.P. Kwok, G.I. Hadded, Effects of tunnelling on an IMPATT oscillator. J. Appl. Phys. 43, 3824–3860 (1972) 27. M. Chive, E. Constant, M. Lefebvre, J.P. Ribetich, Effect of tunneling on high efficiency Impatt avalanche diode. Proc. IEEE (Lett.) 63, 824–826 (1975) 28. E.M. Elta, G.I. Hadded, Mixed tunneling and avalanche mechanisms in pn junctions and their effects on microwave transit-time devices. IEEE Trans. Electron Devices ED 25(6), 694–702 (1978) 29. E.M. Elta, G.I. Hadded, High frequency limitations of IMPATT, MITATT and TUNNET mode devices. IEEE Trans. MTT. 27, 442 (1979a) 30. E.M. Elta, G.I. Hadded, Large-signal performance of microwave transit-time devices in mixed tunneling and avalanche breakdown. IEEE Trans. Electron Device. 26, 941 (1979) 31. J.C. De Jaeger, R. Kozlowski, G. Salmer, High efficiency GaInAs/InP heterojunction Impatt diodes. IEEE Trans. Electron Devices ED 30,790 (1983) 32. D. Lippens, J.L. Nieruchalski, E. Constant, Multilayered heterojunction structure for millemeter wave Impatt devices .Physics 134 B, 72 (1985) 33. N.S. Dogan, J.R. East, M. Elta, G.I. Haddad, Millimeter wave heterojunction MITATT diodes. IEEE Trans. Microwave Theory Tech. MTT 35, 1304 (1987) 34. M.J. Kearney, N.R. Couch, J. Stephens, R.S. Smith, Heterostructure impact avalanche transit time diodes grown by molecular beam epitaxy. Semicond. Sci. Tech. 8, 560 (1993) 35. G.N. Dash, S.P. Pati, Computer aided studies on the microwave characteristics of InP/GaInAs and GaAs/GaInAs heterostructure single drift region impact avalanche transit diodes. J. Phys. D. Appl. Phys. 27, 1719 (1994) 36. M.J. Bailey, Hetrojunction IMPATT diodes. IEEE Trans. Electron. Devices 39, 1829 (1992) 37. P. Weissglas, Avalanche and barrier injection devices, in Microwave Devices, Device-Circuit Interactions, vol. 41. ed by M.J. Howes, D.V. Morgan, Wiley (1976) 38. J.K. Mishra, A.K. Panda, G.N. Dash, An extremely low-noise heterojunction IMPATT. IEEE Trans. Electron. Devices ED-44(12), 2143–2148 (1997) 39. S.M. Sze, R.M. Ryder, Microwave avalanche diodes. Proc. IEEE Special Issue Microwave Semicond. Devices 59, 1140–1154 (1971) 40. S.K. Roy, M. Sridharan, R. Ghosh, B.B. Pal, Computer method for the dc field and carrier current profiles in the IMPATT device starting from the field extremum in the depletion layer. in Proceedings of the 1st Conference on Numerical Analysis of Semiconductor Devices (NASECODE I), ed. ByJ.H. Miller (Dublin, Ireland, 1979), pp. 266–274 41. S.K. Roy, J.P. Banerjee, S.P. Pati, A Computer analysis of the distribution of high frequency negative resistance in the depletion layer of IMPATT Diodes, in Proceedings 4th Conference on Numerical Analysis of Semiconductor Devices (NASECODE IV) (Dublin, Ireland, 1985), pp. 494–500 42. M. Mukherjee, N. Mazumder, Optically illuminated 4H-SiC terahertz IMPATT device. Egypt. J. Solids 30, 87–101 (2007)

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43. M. Mukherjee, N. Mazumder, K. Goswami, S.K. Roy, An opto-sensitive InP based Impatt diode for application in Terahertz regime, in Physics of Semiconductor Devices, IWPSD (2007). 44. M. Mukherjee, N. Mazumder, S.K. Roy, Prospects of 4H-SiC double drift region IMPATT device as a photo-sensitive high-power source at 0.7 terahertz frequency regime. Act. Passive Electron. Compon. 2009, 1–9 (2009) 45. M. Mukherjee, S. Banerjee, J.P. Banerjee, Dynamic characteristics of III-V and IV-IV semiconductor based transit time devices in the terahertz regime: a comparative analysis. Terahertz Sci. Technol. 3, 98–109 (2010) 46. A. Acharyya, M. Mukherjee, J.P. Banerjee, Influence of tunnel current on DC and dynamic properties of silicon based terahertz IMPATT source. Terahertz Sci. Technol.4(1), 26–41 (2011) 47. A. Acharyya, J.P. Banerjee, Prospects of IMPATT devices based on wide bandgap semiconductors as potential terahertz sources. Appl. Nanosci. 4, 1–14 (2014) 48. A. Acharyya, J. Chakraborty, K. Das, S. Datta, P. De, S. Banerjee, J.P. Banerjee, Large-signal characterization of DDR silicon IMPATTs operating up to 0.5 THz. Int. J. Microwave Wirel. Technol. 5(5),567–578 (2013) 49. A. Acharyya, A. Mallik, D. Banerjee, S. Ganguli, A. Das, S. Dasgupta, J.P. Banerjee, IMPATT devices based on group III–V compound semiconductors: prospects as potential terahertz radiators. HKIE Trans. 21(3), 135–147 (2014) 50. Bi Xiaochuan, East R. Jack, Ravaioli Umberto, G.I. Haddad, A Monte Carlo study of Si/SiGe MITATT diodes for terahertz power generation. Solid State Electron 52, 688–694 (2008) 51. S. Banerjee, A. Acharyya, J.P. Banerjee, Noise performance of Heterojunction DDR MITATT Devices Based on Si~Si1-x Gex at W-Band. Act. Passive Electron. Compon. [USA] 2013, 1–7 (2013) 52. S. Banerjee, A. Acharyya, M. Mitra, J.P. Banerjee, Large-signal properties of 3C-SiC/Si heterojunction DDR IMPATT devices at terahertz frequencies, in 34thPIERS in Stockholm, Sweden 12–15 Aug 2013, , pp. 462–467 53. S. Banerjee, M. Mitra, Heterojunction DDR THz IMPATT diodes based on Alx Ga1-x N/GaN material system. J. Semicond. 36(6) (2015)

Terahertz IMPATT Sources Based on Silicon Carbide S. J. Mukhopadhyay, S. Kanungo, V. Maheshwari, and M. Mitra

Abstract In this paper, detailed study has been explored on Si and SiC(4H) based avalanche transit time (ATT) sources for operation at frequencies under millimeterwave and terahertz (THz) regimes. Drift–diffusion model has been used here to scrutinize the high frequency features of the device. Also, corresponding avalanche response time ("T A ) as well as transit time ("T T ) has been ascertained to investigate device performance. The simulation studies show that the upward cut-off frequency levels of Si and SiC(4H) double-drift region (DDR) ATTs are 500 GHz and 1.0 THz, respectively. The finding here is that SiC (4H) upon IMPATTs are highly favorable for generation of power with significant efficiency at higher frequencies due to smaller value of avalanche response time. Keywords Si · IMPATTs · SiC(4H) · Double-drift · Millimeter-wave · Terahertz

1 Introduction The ATT devices, especially impact ATT (i.e., IMPATT) devices have shown possibility of radiating alternating power within the large frequency regime extending from microwave to THz band [1–6]. The THz band has several applications such as S. J. Mukhopadhyay (B) · M. Mitra Department of Electronics and Telecommunication Engineering, Indian Institute of Engineering Science and Technology, Shibpur, P.O.: Botanic Garden, Howrah, West Bengal 711103, India e-mail: [email protected] S. Kanungo Department of Electrical and Electronics Engineering, Birla Institute of Technology and Science, Pilani, Hyderabad, Shamirpet-Keesara Road, Jawahar Nagar, Shameerpet, Hyderabad, Telangana 500078, India e-mail: [email protected] V. Maheshwari Department of Electronics and Communication Engineering, Bharat Institute of Engineering and Technology Mangalpally (V), Ibrahimpatanam (M), Ranga Reddy, Hyderabad, Telangana 501510, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Acharyya and P. Das (eds.), Advanced Materials for Future Terahertz Devices, Circuits and Systems, Lecture Notes in Electrical Engineering 727, https://doi.org/10.1007/978-981-33-4489-1_5

55

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spectrum analysis, nano-electronics, inspection services, space research, imaging, and drug industry [7–15]. Single-drift (SDR) and DDR silicon diodes are highly suitable for generating high RF power with high conversion efficiency at millimetric wave frequencies [12–18]. Wide bandgap (E g > 3.0 eV) semiconductors specially two hexagonal polytypes of SiC, i.e., 4H and 6H, referred to as α-SiC appeared as brilliant substance for the growth of high-power IMPATT devices [19]. Although these two polytypes possess similar properties, the 4H-SiC is mostly preferable to 6H-SiC for its isotropic carrier mobility. Moreover, the overall features like direct bandgap structure, high electric breakdown field, and high thermal conductivity are very favorable for realizing it as a high-power device. Besides, considerable breakthrough is also arrived in 4H-SiC development, processing, and characterization very recent. A co-relative research is being carried out between Si and SiC(4H) at various millimeter-wave and THz frequency bands to explore the potency of SiC(4H) IMPATT as a suitable source at THz regime.

2 Materials and Design Ionization rate, saturation drift velocity, and other material parameters of Si and SiC(4H) are taken from the published literature [20–24]. The DDR IMPATT structures are firstly designed for a frequency from the relation furnished by Sze et al. [25]. As focused earlier [26], the electric field profile is obtained from simulation strategy. High frequency analysis method is elaborated elsewhere [27, 28] is used to get the admittance profile of the device based on Gummel–Blue technique [29]. The design parameters of Si and SiC(4H) diodes are given in Tables 1 and 2. Table 1 Design parameters of Si Substrate

Design frequency, f d (GHz)

W n (nm)

W p (nm)

ND (×1023 m−3 )

NA (×1023 m−3 )

N Sub (×1026 m−3 )

Si

94

400.0

380.0

1.20

1.25

1.00

140

280.0

245.0

1.80

2.10

1.00

220

180.0

160.0

3.95

4.59

1.00

300

132.0

112.0

6.00

7.30

1.00

500

72.0

70.0

15.0

16.2

1.00

Terahertz IMPATT Sources Based on Silicon Carbide

57

Table 2 Design parameters of SiC(4H) Substrate

Design frequency, f d (GHz)

W n (nm)

W p (nm)

ND (×1023 m−3 )

NA (×1023 m−3 )

N Sub (×1026 m−3 )

SiC(4H)

94

580.0

580.0

2.80

2.90

1.00

140

400.0

400.0

4.90

5.00

1.00

220

300.0

300.0

6.90

7.00

1.00

300

250.0

250.0

9.50

10.5

1.00

500

160.0

160.0

14.5

16.5

1.00

1000

90.0

90.0

37.0

43.0

1.00

3 Analysis One-dimensional reverse-biased model of double-drift IMPATT structure is considered for analysis, as shown in Fig. 1. By solving some basic device equations mentioned in Fig. 2, we have obtained E- field and normalized current density profiles. DC simulation technique had been depicted earlier. Outline of the DC simulation program including boundary condition is shown in Fig. 2. The device efficiency is η(%) = (1 × Vd )/(π × VB )

(1)

where V d and V B are drift and breakdown voltage drop, respectively. The data derived from DC simulation is utilized in the high frequency analysis [29]. Outline of the small-signal simulation program has been exhibited in Fig. 3. The optimum power output is computed by the equation, PRF = (VRF )2 (|G p |)A j /2,

Fig. 1 1D schematic of DDR diode

(2)

58

Fig. 2 Outline of the DC simulation program

Fig. 3 Outline of the small-signal simulation program

S. J. Mukhopadhyay et al.

Terahertz IMPATT Sources Based on Silicon Carbide

59

where V RF is the RF swing, Gp is negative conductance, and Aj is the area of the diode.

4 Results and Discussion The E-field (ζ p ), break down voltage (V B ), efficacy, avalanche layer width (x A ), "T A , and "T T of DDR Si and SiC(4H) IMPATTs are received from the DC simulation. The variation in ζ p , V B , and efficiency with operating frequency are depicted in Figs. 4, 5, and 6. The DC properties of Si and SiC(4H) diodes are given in Tables 3 and 4 at different operating frequencies. Figure 5 exhibits that the V B of SiC(4H) diodes is higher as compared to that of Si diodes. It is observed from Table 4 that "T A for SiC(4H) based IMPATT is much lower than the corresponding "T T , which is the primary condition to produce oscillation at high frequencies. It is also noticed from tables below that "T A of SiC(4H) IMPATT is considerably lower (order of 10–15 s) at any operating frequency than Si IMPATT (order of 10–12 s) under consideration. For smaller avalanche response time ("T A ), SiC(4H) IMPATT device is able to operate up to 1.0 THz. The parameters obtained from small-signal simulation are optimum frequency (f p ), peak negative conductance (Gp ), susceptance (Bp ), quality factor (Qp ), negative resistance (Z R ), and RF power output (PRF ). These parameters of DDR Si and SiC(4H) IMPATTs are given in Tables 3 and 4. Since the power output is dependent on Z R , consequently it is slashed down with frequency as depicted in Fig. 7. RF

Fig. 4 Peak electric field variation with frequency of DDR Si and SiC(4H) IMPATTs

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Fig. 5 Breakdown voltage versus optimum frequency plots for DDR Si and SiC(4H) IMPATTs

Fig. 6 Efficiency versus optimum frequency plots for DDR Si and SiC(4H) IMPATTs

power of around 136 mW and 1982 mW are derived from Si and SiC(4H) diodes at 0.5 THz and 1.0 THz, respectively. Experimentally measured power from 94 and 140 GHz Si sources are 600 mW [2] and 300 mW [3], as plotted in Fig. 7. At higher frequencies, power output is much less in Si diodes (as depicted in Fig. 7) which

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Table 3 Characteristics of DDR Si IMPATTs Design frequency (f d )

94 GHz

140 GHz

220 GHz

300 GHz

500 GHz

ζ p (×107 V/m)

5.93

6.65

8.19

9.36

12.16

Breakdown voltage (V B )

25.50

18.93

13.73

11.30

8.93

Efficiency (%)

10.52

8.88

7.99

6.70

4.25

x A (nm)

378

274

170

130

90

T A (×10–12 s)

2.03

1.60

1.07

0.854

0.613

T T (×10–11 s)

1.06

0.709

0.456

0.326

0.189

Gp (×107 Sm−2 )

−4.72

−8.04

−18.03

−26.50

−68.12

Bp (×107 Sm−2 )

5.47

15.89

38.78

82.62

253.05

Z R (×10−9 m−2 )

−9.03

−2.53

−0.985

−0.352

−0.099

Quality factor (−Q)

1.15

1.97

2.15

3.11

3.71

PRF (mW)

708.43

446.35

334.23

184.59

136.10

Table 4 Characteristics of DDR SiC(4H) IMPATTs Design f (f d )

94 GHz

140 GHz

220 GHz

300 GHz

500 GHz

ζ p (×107 V/m)

35.79

38.71

40.64

42.63

45.11

51.85

Breakdown voltage (V B )

228.25

156.33

127.87

107.27

88.42

55.44

Efficiency (%)

16.29

15.14

14.74

13.92

13.25

11.32

x A (nm)

380

260

208

176

146

90.0

T A (×10−12 s)

2.35

1.57

1.22

1.01

0.785

0.424

T T (×10−11 s)

1.02

0.675

0.450

0.325

0.206

0.100

Gp (×107 Sm−2 )

− 5.69

− 9.25

− 17.61

− 54.07

− 84.42

Bp (×107 Sm−2 )

1.69

4.56

9.72

18.86

29.49

131.47

Z R (×10−9 m−2 )

−16.13

−8.69

−4.35

−1.64

−1.05

−0.373

Quality factor (−Q) 0.29

0.49

0.55

0.34

0.34

PRF (mW)

16,180.81

13,315.09

13,130.85

9,355.78

30,290.98

1000 GHz

− 108.09

1.21 1,982.31

validate analysis technique. Until now, at millimetric or THz frequencies, experimental investigation on RF performance of the SiC(4H) IMPATT is not available, and therefore, comparison cannot be carried out with the simulation. It is also noticed from Tables 3 and 4 that SiC(4H) based diodes excel over Si in terms of Q-factor. The G-B profile for Si and SiC(4H) IMPATTs are depicted in Figs. 8 and 9.

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Fig. 7 Variation of RF power output with peak operating frequency for Si and SiC(4H) DDR IMPATTs

Fig. 8 G-B plot for 94, 140, 220, 300, and 500 GHz DDR Si IMPATTs

5 Summary Here, a co-relative research is being made on IMPATT diodes based on Si and SiC(4H) as substrate for operation at millimetric and THz frequency regimes. The upward frequency limitation of Si and SiC(4H) diodes are examined from the avalanche response time of the diodes operating at aforesaid frequencies. The simulation studies exhibit that upward cut-off frequency level of Si and SiC(4H) IMPATTs

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Fig. 9 G-B plot for 94, 140, 220, 300, 500, and 1000 GHz DDR SiC(4H) IMPATTs

is 0.5 THz and 1.0 THz, respectively. It is also noticed that SiC(4H) IMPATTs are highly suitable source for radiation THz power with significant efficacy at higher frequencies due to lesser magnitude of avalanche response time. Therefore, it may be concluded that DDR SiC(4H) IMPATTs arrive as potential resource for generating THz frequencies.

References 1. T.A. Midford, R.L. Bernick, Millimeter -wave CW IMPATT diodes and oscillators. IEEE Trans. Microw. Theo. Tech. 27, 483–492 (1979) 2. W. Behr, J.F. Luy, High power operation mode of pulsed Impatt diodes. IEEE Electron Dev. Lett. 11, 206–208 (1990) 3. Y. Chang, J.M. Hellum, J.A. Paul, K.P. Weller, Millimeter-wave IMPATT sources for communication applications, in IEEE MTT-S International Microwave Symposium Digest (1977), pp. 216–219 4. W.W. Gray, L. Kikushima, N.P. Morentc, R.J. Wagner, Applying IMPATT power sources to modern microwave systems. IEEE J. Solid-State Circ. 4, 409–413 (1969) 5. H. Eisele, G.I. Haddad, GaAs TUNNETT diodes on diamond heat sinks for 100GHz and above. IEEE Trans. Microw. Theo. Tech. 43, 210–213 (1995) 6. H. Eisele, C.C. Chen, G.O. Munns, G.I. Haddad, The potential of InP IMPATT diodes as highpower millimeter-wave sources: first experimental results. IEEE MTT-S Int. Microw. Symp. Digest 2, 529–532 (1996) 7. W.L. Chan, J. Deibel, D.M. Mittleman, Imaging with terahertz radiation. Rep. Prog. Phys. 70, 1325–1379 (2007) 8. D. Grischkowsky, S. Keiding, M. Exter, C. Fattinger, Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors. J. Opt. Soc. Am. B 7, 2006–2015 (1990)

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9. C. Debus, P.H. Bolivar, Frequency selective surfaces for high sensitivity terahertz sensing. Appl. Phys. Lett. 91, 184102–184103 (2007) 10. T. Yasui, T. Yasuda, K. Sawanaka, T. Araki, Terahertz paintmeter for noncontact monitoring of thickness and drying progress in paint film. Appl. Opt. 44, 6849–6856 (2005) 11. C.D. Stoik, M.J. Bohn, J.L. Blackshire, Nondestructive evaluation of aircraft composites using transmissive terahertz time domain spectroscopy. Opt. Express 16, 17039–17051 (2008) 12. A.J. Fitzgerald, B.E. Cole, P.F. Taday, Nondestructive analysis of tablet coating thicknesses using terahertz pulsed imaging. J. Pharm. Sci. 94, 177–183 (2005) 13. P.H. Siegel, Terahertz technology in biology and medicine. IEEE Trans. Microw. Theo. Tech. 52, 2438–2447 (2004) 14. P.H. Siegel, THz Instruments for Space. IEEE Trans. Antenn. Propag. 55, 2957–2965 (2007) 15. C. Dalle, P. Rolland, G. Lieti, Flat doping profile double-drift Silicon IMPATT for reliable CW high-power high efficiency generation in the 94GHz window. IEEE Trans. Electron Dev. 37, 227–236 (1990) 16. J.F. Luy, A. Casel, W. Behr, E. Kasper, A 90-GHz double drift IMPATT diode made with Si MBE.IEEE Trans. Electron Dev. 34, 1084–1089 (1987) 17. M. Wollitzer, J. Buechler, F. Schaffler, J.F. Luy, D-band Si-IMPATT diodes with 300mW CW output power at 140GHz. Electron. Lett. 32, 122–123 (1996) 18. D. Ghoshal, Measurement of electrical resistance of Silicon Single Drift Region IMPATT diode based on the study of the device and mounting circuit at threshold condition. J. Electron Dev. 11, 625–631 (2011) 19. M. Mukherjee, N. Majumder, Effects of charge bump on high frequency characteristics of α-SiC based double drift ATT diodes at millimeter wave window frequencies. IETE J. Res. 55, 118–127 (2009) 20. W.N. Grant, Electron and hole ionization rates in epitaxial silicon. Solid State Electron. 16, 1189–1203 (1973) 21. A.O. Konstantinov, Q. Wahab, N. Nordell, U. Lindefelt, Ionization rates and critical fields in 4H-silicon carbide. Appl Phys Lett 71, 90–92 (1997) 22. C. Canali, G. Ottaviani, A.A. Quaranta, Drift velocity of electrons and holes and associated anisotropic effects in Silicon. J. Phys. Chem. Solids 32, 1707–1720 (2007) 23. K.V. Vassilevski, A.V. Zorenko, K. Zekentes, K. Tsagaraki, E. Bano, C. Banc, A. Lebedev, 4H-SiC IMPATT diode fabrication and testing, inTechnical digest of international conference on SiC and related materials. (Tsukuba, Japan, 2001), pp 713–714 24. Electronic Archive: New semiconductor Materials, Characteristics and Properties: http;//www. ioffe.ru/SVA/NSM/semicond 25. S.M. Sze, R.M. Ryder, Microwave avalanche diodes. Proc. IEEE Spec. Issue Microw. Semicond. Dev. 59, 1140–1154 (1971) 26. S.K. Roy, M. Sridharan, R. Ghosh, B. Pal, Computer methods for the dc field and carrier current profiles in impatt devices starting from the field extremum in the depletion layer, in Proceedings of NASECODE-I Conference on Numerical Analysis of Semiconductor Devices (Boole Press, Dublin, 1979), pp. 266–274 27. S.K. Roy, J.P. Banerjee, S.P. Pati, A computer analysis of the distribution of high frequency negative resistance in the depletion layers of impatt diodes, in Proceedings of NASECODE-IV Conference on Numerical Analysis of Semiconductor Devices (Boole Press, Dublin, 1985), pp. 494–500 28. A. Acharyya, J.P. Banerjee, Analysis of photo-irradiated double-drift region silicon impact avalanche transit time devices in the millimeter- wave and terahertz regime. Terahertz Sci. Technol. 5, 97–113 (2012) 29. H.K. Gummel, J.L. Blue, A small-signal theory of avalanche noise in IMPATT diodes. IEEE Trans. Electron. Dev. 14, 569–580 (1967)

Terahertz Quantum Dot Intersublevel Photodetector Sanjib Kabi

Abstract A terahertz photodetector receives terahertz frequency in the range of ~0.3 to ~30 THz from a source in the input terminal and transforms the input signal, typically into an electrical signal. In general, a terahertz detector can be able to differentiate photons of different energies. A broad energy response is desirable from a detector, though a narrowband with minimal FWHM is desirable in some applications. In this chapter, the author is interested of the kind of detectors where the terahertz radiation interacts with the bound carriers in a heterostructure and presented desired transition. The quantum dot intersublevel photodetector (QDIP) is such kind of detector which creates a great interest among the researchers. Room-temperature terahertz detection has been reported with QDIPs by various groups. THz QDIP works on the principle of carrier transitions from lower subband to excited sate while interacting with a photon of required energies. The photons may be absorbed by exciting carriers in the valance or conduction band of a dot and excited to higher state from the ground state. Quantum dot size and shape doping concentration affected the absorption coefficient and in turn overall output of the detectors. Inherent properties of QDIPs such as normal incidence interaction of light and enhanced lifetime of photo-excited electrons are few crucial advantages for such structures. There are several valuable reports on QD working as a detector with minimal dark current attributed to the 3D quantum confinement and diminished thermionic emissions. Detectivity and responsivity are the two quantities which define the reliability and quality of a detector. Ideally, a terahertz detector should have large value for responsivity following the interaction of individual terahertz photons with the confined carriers. The dependency of the absorption coefficient and transition energies on the QD size and size distribution of the QD system has already been explained by the author in his earlier work. In this chapter, the author discussed the basic working principle of the QDIP while explaining the overall sensitivity of QDIP changes depending on the QD morphology and choice of materials. The chapter concludes by taking S. Kabi (B) Sikkim Manipal Institute of Technology, Sikkim Manipal University, East Sikkim, Majhitar, Sikkim 737136, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Acharyya and P. Das (eds.), Advanced Materials for Future Terahertz Devices, Circuits and Systems, Lecture Notes in Electrical Engineering 727, https://doi.org/10.1007/978-981-33-4489-1_6

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notes of the drawbacks of QDIPs in terahertz detection and a scientific approach to overcome those issues. Keywords Quantum dot · Terahertz · Intersubband · Exciton · Detectivity · Dark current

1 Introduction Photodetectors are the most abundant types of technology use in daily life of present world. Photodetector usage ranges from automatic door to receivers on remote controls of our television. Photodiodes are used in fiber optical communication, whereas array of such detector helps to differentiate radiation from distant universe. In the field of commerce, industry, entertainment, or research, photodetectors find its way to make itself essential and useful [1–5]. For different purposes, photodetectors comprise any device for measuring photon frequencies from radio frequencies to far infrared and up to gamma rays. In this article, a detailed survey of the main types of applications that use photodetectors to detect terahertz signals is presented. Photodetectors convert incident light photons into current. The generated electrical pulse in terms of photocurrent or a photovoltage from a photodetector is proportional to the power of the input optical signal. Photodetectors are categorized into two classes: photon detectors and thermal detectors, depending on the difference in the conversion process. The photoelectric effect is the key mechanism by which a photon detector converts a photon into an emitted electron or an electron–hole pair. In case of a photon detector, the responsivity of the detector depends upon the number of photons absorbed by the unit area of the device. Thermal detector working principle is based on conversion of optical energy to heat energy via photothermal effect. Output characteristics such as detectivity and responsivity of a thermal detector are defined by the incident optical energy rather than the number of photons absorbed by the photon detector. The response of a photon detector depends on optical wavelength, while characteristics of a thermal detector are wavelength independent. The long-wavelength cutoff of a photon detector determines its response to a particular spectral band, which usually includes near ultraviolet to the terahertz region. These characteristics make photon detectors suitable for sensing optical signals in photonic systems, whereas thermal detectors are usually dealt with optical power measurement or infrared imaging. Technological advances on terahertz frequency electromagnetic radiation in the range 0.3–30 THz have been advanced rapidly over the last few decades [2, 6–8]. Astronomers and some spectroscopists use terahertz radiation for their research to gather information about the outer space. In this chapter, the basic technological and physical aspects of semiconductor photon detectors are discussed with special emphasis on photonics applications in the terahertz wavelength region. Different compound semiconductor material systems reported by researchers for terahertz detection will be discussed. Experimental results

Terahertz Quantum Dot Intersublevel Photodetector

67

as well as theoretical modeling to enhance the capabilities of different terahertz detectors are reported by various groups assembled here for a better understanding of the device. Recently, quantum dot structures of various materials, e.g., III–V or graphene QD (GQD), received some serious attention to improve detector capabilities, especially in the terahertz range [9–11]. We categorically look into the advancement of different quantum dot terahertz photodetectors and discuss the future prospects of this device system.

1.1 Significance of Terahertz Frequency The terahertz frequency electromagnetic radiation in the range 0.3–30 THz has quite a few unique characteristic features [12–14]. Terahertz frequency band range can be assessed consistently even not employing an interferometer. The scientific methods using THz are well suited for understanding the material properties or physical phenomenon under extreme conditions of applied electric field, system temperature, and applied magnetic field. Different nanostructural systems with 1D, 2D, or 3D confinement have electronic excitations in the THz regime. Single-particle excitations are possible using THz frequency which in turn provides information about many important physical properties such as control of carrier injection by doping, the dependence of the energy level on the geometry of the system, line widths of transitions between different available states, and spin excitations. Researchers are interested about the interaction of THz frequencies with semiconductor nanostructures. The interaction provides important information about the orbital and spin states of carriers. The physical properties of semiconductor nanostructures at visible or near-IR wavelengths can also be engineered with THz radiation. Superconducting “sheets” in layered superconductors show propagation of Cooper pairs producing plasma resonance. In a variety of layered superconductors, this mode falls in THz frequency range [15]. THz spectroscopy can also be used to extract information about protein structure and dynamics of a biological system. It is obvious from the above discission that THz band of the electromagnetic spectrum is effective means to understand the basic properties of different existing form matters. It is further noticeable that in terms of development THz technology is still not at par with other similar filed and requires attention of the scientific community.

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2 Semiconductor Photodetectors Photodetector is a special type of P–N junction diode operating in reverse-bias mode and produces current when exposed to light of certain wavelengths. It is also known as photosensor. Figure 1 shows the symbolic representation of a photodiode in photoconductive mode: A photodetector works on the principle of photoelectric effect. Photodetector or photodiode is a two-terminal device as shown in Fig. 2. The current constitutes across the active P–N junction as it is illuminated with certain wavelength of light. In reverse-bias condition, only minority current flows through the device.

2.1 General Characteristics of Semiconductor Photodetectors Photodiode operates in two modes: Photovoltaic mode: In photovoltaic mode of operation, the zero-bias P–N junction conducts current in the circuit due to flow of minority carrier, when the device is illuminated to light of appropriate wavelength. Fig. 1 Symbolic representation of an illuminated P–N junction photodiode with corresponding band structure

Terahertz Quantum Dot Intersublevel Photodetector

69

Fig. 2 Schematic of P–N junction in reverse-bias mode under illumination

Photoconductive mode: In photoconductive mode of operation, the reverse-bias P–N junction starts conducting when exposed to light. The depletion region increases with the increasing reverse voltage. Even in the non-illumination condition, the reversebias device is conducting. The small reverse current flows through the device in that condition dubbed as dark current. Figure 2 illustrates a schematic of an illuminated P–N junction diode in reversebias condition. The electrons and hole are minority carriers in the P side and N side of the diode, respectively. The minority carriers are present in the P and N side of the reverse-bias device experiencing repulsion force from the battery, moved toward the junction, and form the dark current. The mixture of electron and hole at the junction creates neutral atom at the depletion region which restricts any further flow of current. In illuminated condition, as the light of certain wavelength falls on surface of the junction, energy of the junction gets increased and causes the electron and hole to get separated from each other. The separated carriers get attracted toward the opposite potential of the battery and generate high reverse current through the device. The increasing intensity of the light proportionately generates enough charge carriers to produce a large electric current through the device. The device becomes nonconducting; i.e., no current flows through it only in a proper positive-biased condition. In photovoltaic mode of operation, the incident light generates a reverse photocurrent, which passes through a resistor, and the voltage measured across the load resistor. In photoconductive mode of operation, the P–N junction is reverse biased. The photon flux is incident on the P–N junction, generates additional carriers flowing, and results in additional current because device increased conductivity. The photoconductive mode of operation is a high-speed mode of operation because there is a field which is already applied and separates the carriers in the corresponding direction immediately. In all high-speed applications with special emphasis on optical communication or any signal processing, it is the photoconductive mode of operation which is employed. Figure 3 shows the constructional aspects of a photodiode.

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Fig. 3 Schematic showing the basic constructional details of a photodetector

The P–N junction photodiode is packaged inside a transparent material such that the incident light easily passes through it without reflecting or absorbed. The typical dimension of an overall detector unit is of very small about 2.5 mm.

2.2 Figure of Merits of Semiconductor Photodetectors There are four general characteristics which define the operating characteristics of a photodetector. I.I.I. Quantum efficiency (η) II.II.II. Responsivity of the detector (R) III.III.III. Rise time of the detector (t r )/bandwidth of the detector (the rise time or impulse response will determine what is the bandwidth of the detector, how fast the detector can respond) IV.IV.IV. Dark current (I dark ) or noise power (N pr ). In general, for detection of light the quantum efficiency and responsivity of the detector are of outmost importance, but in the case of high-speed communications, the rise time and the noise power are very important. Quantum efficiency (η) of a detector is defined as the number of carriers generated per incident photon per unit area of the device. If the photon flux is φ on a photodetector at a certain time, optical power is Pop P and energy of one photon is given as hν, then photon flux is given by φ = hν , i.e., the optical power divided by energy of one photon. The is the number of electron– hole pairs which contribute to the photocurrent ip , so generated carrier flux due to the i incident photon is ( ep ). It is to be understood that all the electron–hole pairs generated need not contribute to the current in the external circuit as well as all incident photons will not generate electron–hole pairs. Now the quantum efficiency can be written as

Terahertz Quantum Dot Intersublevel Photodetector

 η=

71

 i p e Pop hν

(1)

If every incident photon will generate one electron–hole pair which contributes to the current such as in the case of an ideal device, then ideally η can be unity. In real-case scenario, quantum efficiency (η) should be less than 1. Responsivity (R) of a detector is defined as generated photocurrent ip for a given optical power.   i So, R = Popp in units of (A/W). Thus, the responsivity will give the information on how much current will be generated for certain amount of applied optical flux. Responsivity is very important to design the electronic photodetector circuit. We can express the responsivity (R) as:   i R = Popp ; now using Eq. (1), we can write R= Or R =

 ηe  hν

;

ηλ(inμm) 1.24

(2) (3)

where wavelength (λ) of the incident light of photon is in μm. Figure 4 depicts the variation of the responsivity and quantum efficiency with the incident wavelength of light for different semiconductor materials. From Eq. (2), we find that, if to maximize the responsivity of a detector, quantum efficiency of the device needs to be maximum. Let us consider a semiconductor photodetctor with a thickness d hit by a light with photon flux φ. If we consider the system is such that the refractive index outside is 1, and inside the detector material is, e.g., 3.5, then a fraction of the light, hence the photon flux, is reflected in effect of variation of the refractive index. If Ref is the reflectivity of that material, then φ (1 − Ref ) will enter the detector material. The photon flux will decrease exponentially inside the material, defined by the absorption coefficient α. The amount of photons absorbed is φ(1 − Ref ) (1 − e−αd ). The absorbed photons in the device will generate carrier pairs, which will contribute to the current in the circuit. Now out of this, a fraction say ζ of them will contribute to the generated current in the external circuit. If N number of photons is absorbed, ζ · N will contribute to external current. It has two components. One out of all the photons which are absorbed may lead to generation of electron–hole pairs and rest of them may just generate phonons, so they can give energy to the lattice. Some of the photons may get absorbed in traps. The generated e–h pairs may immediately recombine due to defects or surface states. The generated electron–holes may immediately recombine due to the presence of surface states or defect states in the medium, and they are no more contributing to this. So, ζ is less than 1.

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Fig. 4 Variation of the quantum efficiency and responsivity with the incident wavelength of light for different semiconductor materials. Dotted line shows the different values of quantum efficiency [16]

So, from this we get   η = (1 − Re f ) 1 − e−∝d ζ

(4)

The bandwidth of a detector is the determining figure for how fast it responds to a modulated optical input. There are two main factors affecting the bandwidth of a detector: the transit time and the RC parasitic response. The transit time is defined by the time taken by the optically generated carriers to be removed out of the detector’s active region. However, not all the carriers arrive at the electrodes at once. Instead, there is a range of times in which the carriers generated from an incident pulse will arrive at the electrodes of a detector. Transit time depends on the mobility of the electrons and holes, subject to change depending on the materials of the detector. When biased with a high enough electric field, the carriers will reach a saturation velocity, vsat . The mobility is thus modified to be μ  2 1 + μE vsat

μsat =

(5)

An instantaneous pulse of light hits the detector creating carriers. To collect the full charge, the holes and electrons must both travel the full height (h). The bandwidth is then given by

Terahertz Quantum Dot Intersublevel Photodetector

73

f transit = 0.38

vsat h

(6)

The second factor in determining the bandwidth of a detector is the electrical impedance characteristic of the detector circuit and is given by f t RC =

1 2π RC

(7)

The total bandwidth which includes both RC and transit time effects is given by:

f =

1 2 f RC

+

1

− 21

2 f transit

(8)

As a DC offset, the dark current can be subtracted from the total current to calculate the photocurrent signal. However, sufficient levels of dark current can contribute to the noise of a detector. There are two factors that contribute to the total dark current: bulk generation and surface generation. Bulk generation is a volume-dependent mechanism that is shown to result predominantly from the Shockley–Read–Hall process [17]. The large lattice mismatch between silicon and germanium causes threading dislocations, which allow for the existence of mid-bandgap states. At a low electric field, the bulk current density is relatively constant. However, as the electric field increases, band bending will result in a higher bulk current density that increases exponentially with the applied electric field; surface generation is the second contributor to the dark current and is a result of surface defects such as dangling bonds. Surface passivation is more difficult with germanium than silicon as germanium is not fully passivated by silicon dioxide. Other materials such as germanium oxide have been used for passivation with some success [18]. The total dark current is given by √ Idark = Jbulk · A + JSurface 4π A

(9)

If we assume that bulk current dominates, the dark current scales with detector area. Experimental results for Ge detectors are shown in Fig. 7.5, indicating an approximately linear increase of dark current with the area of the detector. The inverse of the noise equivalent power (NEP) provides the value of specific detectivity D* for detectors. The detector measurement bandwidth (f) and its surface morphology determine the NEP of the device. Thus, the specific detectivity D* is given by √ D∗ =

A f NEP

(10)

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S. Kabi

3 Quantum Well (QW)-Based Photodetector: Terahertz Applications 3.1 Basic Working Principle of QWP A quantum well (QW) is a few nanometers of thin layer sandwiched between a layer of a different material. This QW thin layer can confine carriers (electrons or holes) in the perpendicular direction to the layer surface. The movement of the carrier remains unhindered in the other dimensions. The quantum confinement in a QW has substantial effects on the density of states for the confined particles. It is significant that the two-dimensional density of states in a QW does not depend on energy, and it remains invariant within a certain energy interval. A quantum well is often constructed with a thin layer low bandgap semiconductor material sandwiched between other wider bandgap semiconductor layers. The thickness of such a quantum well is of the order of ≈ 5–20 nm. Epitaxial and vapor deposition techniques such as MBE and MOCVD, and few advanced technologies are used to fabricate thin layers of the QW structures. The working principle of a quantum well detector is established on fact of carrier confinement in nanostructures. The detection energy of a detector is the small confinement energies, ranging from 4 to 20 meV for the THz region, a value that is equivalent with the normal thermal energy of the carriers depending on the temperature of the device. Semiconductor THz quantum well photodetector (QWP) depends on the intersubband transitions upon interaction with light within either the conduction band (n-type) or the valence band (p-type). The wide bandgap materials used for construction of QWPs do not absorb in the MWIR to THz radiation in their bulk condition or via interband transitions. However, carrier transition may take place between the ground state and excited state in a conduction or valence band quantum well structure (see Fig. 5). These intersubband absorption energies are in the MWIR to THz regions make it possible to realize the nanostructure intersubband devices [19]. The detection capability, i.e., the photocurrent of QWP, depends on the amount of escaped photo-excited carriers from the potential well of the designed quantum well structure. The detected peak energy and cutoff wavelength of a QWP can be continuously tailored within a range by varying quantum well width and mole fraction of the barrier which change the band offset, i.e., barrier depth of the structure. The choice well and barrier material decide the detection energy range of a QWP.

Terahertz Quantum Dot Intersublevel Photodetector

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Fig. 5 Schematic showing different interband and intersubband transition in a quantum well

3.2 Progress in QW-Based Terahertz Photodetectors Quantum well infrared photodetector is a matured technology, whereas THz QWPs are much less established, having been only recently validated experimentally [17, 18, 20]. Terahertz detection deals with energy range of few meV which is not to be realized from the interband transition originated from available narrow bandgap materials. There are no terahertz photodetectors constructed on basis of interband transitions in a heterostructure [6]. Researchers reported mainly working on two different types of terahertz QWP depending on the detection criterion [21, 22]. Photon detectors made from lowtemperature superconductors are in the category of pair-breaking detector [21], whereas detector fabricated by extrinsic semiconductors based on Ge, Si, GaAs, GaP, etc., depends on detection of the electrons bounded by shallow-impurity centers [22]. Lewis et al. reported high-speed THz detection QWP with short carrier lifetimes. Li et al. detected response of 1 AW−1 and NEP of 10−13 WHz−1/2 in a device working at a very low temperature of 5 K [23]. In THz QWIPs, the depth of the potential well called band offset of the structure should be very low to provide the confinement energies in few tens of meV range. Liu et al. in the year 2004 proposed a structure using very thick barriers (50–90 nm) for QWP structure with t peak detected around 9.3, 6.0, 3.3 THz, for BLIP temperatures of 17, 13, and 12 K, respectively [24]. Castellano et al. [18] in their multiphoton design of semiconductor-based terahertz photodetectors established increased TBLIP with reduced dark current by employing quantum wells with more than one confined states.

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Yu et al. offer an interesting observation of improvement of the THz response in the presence of the magnetic field for GaAs/AlGaAs quantum well photodetector [25]. THz QWP often deals with the deficiency of absorption in the active region of the device. In case of QWP, the Fermi level surpasses the confinement energy of the device structure and cannot be perfectly optimized with value of K B T. However, doping concentration can change the photocurrent peak due to many body effects which alter the band structure such that second subband takes part in the transitions [26]. The significance of many body effects has been reported by Jordens et al. [27], where authors explore the effect of many body interactions in photoresponse peak positions. All types of THz detectors have a major problem, which is the intrinsically low power levels of thermal radiation emitted in the THz band. Castellano et al. experimentally show that exchange–correlation and depolarization effects exhibit limited background detection though it is only achievable at very low temperature (|2  |< k|eiq·r k  > 8πe2    1 − N N + N − N , (1 ) k k+q k k + q2 E k+q − E k− E k+ − E k− k

(4)

k

where k  ≡ k +q −(2K F )(k +q)/|k +q|, q is a wave number and N is the occupation number for the states k and k + q. This model is good for small values of wave number (q). It does not consider the degeneracy that may occur in the Brillouin zone.

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7.3 Alternate Approaches Gupta and Ravindra [157, 158] redefine the relation: n = K 1 − K 2 E g + K 3 E g2 − K 4 E g3 ,

(5)

After calculating the values of K, the equation reduces to n = 4.16 − 1.12E g + 0.31E g2 − 0.08E g3 ,

(6)

for optical range Herve and Vandamme proposed [158]  n=

 1+

A Eg + B

2 ,

(7)

where A is the hydrogen ionization energy ~13.6 eV and B is 3.47 eV.

8 Computational Study Computational study provides one of the strongest supportive information to predict the effect of different modifications on expected properties of the materials. Hydrogenation at the surface of TiO2 cluster and reduction of titanium (Ti4+ to Ti3+ ) modifies overall property of the material significantly. Drastic increase in photocatalytic properties and noteworthy improvement in microwave absorption are some of them. Hydrogenation is a reductive process for adsorption of H on reducible oxides like TiO2 . In the hydrogenation process, hydrogen atoms attached to O-atoms on surface producing –OH groups. This part explain the effect of hydrogenation on electronic properties with the help of density functional theory. Concerning their exciting performance in solid-state calculations, the density functional theory (DFT) approaches have been effectively applied to study the electronic properties of various materials of interest. Discussion on electronic band structure, density of states (DOS) and charge distribution on optimized structure of hydrogenated rutile TiO2 have been done. The density functional theory (DFT) based on the pseudo-potential method has been applied with the help of BURAI interfacing of Quantum Espresso (QE) calculations. Present discussion is QE and ORCA formalism-based DFT approach, to put highlights on effect of hydrogenation on rutile TiO2 . In the literature, this type of calculations has been performed with Kohn–Sham model [159] considering the generalized gradient approximation (GGA) proposed by Perdew and Wang [160, 161] and ultra-soft pseudo-potentials have been applied [162, 163] along with basis sets of plane waves. It has been considered that the interactions have been described by the norm-conserving pseudo-potentials as supplied in the package’s database. As

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usual, O-atoms have been treated by 2s and 2p states, Ti atoms by 3s, 3p, 4s and 3d orbitals and H-atoms by 1s states. Band structures and DOS of H-TiO2 have been calculated along high-symmetry points of Brillouin zone. Geometry optimization is carried out using associated basis sets for all the clusters. This basis set offers a good compromise between calculation time and accuracy. The basis set is commonly used nowadays to investigate these types of nanoparticles though it is computationally and experimentally very challenging. DFT calculation of different H-TiO2 clusters gives the refractive index of the different clusters as a function of band gap of the material, which correlated to the HOMO–LUMO energy separation. The presence of H-atom on the surface is due to the interactive combination between basic O-surface atoms when H-atom placed on the external anion surface anions and Ti4+ reduced to Ti3+ . According to DFT calculations this transformation is favourable and two H-atoms attached to two different external surface O-atoms reduces two Ti4+ to Ti3+ . According to the literature, this kind of reduction of surface occurs through polarization of spin where H-atoms do not transfer complete electronic charge to that of the surface. The charge distribution on different HOMO–LUMO orbitals has been discussed for different hydrogenated clusters.

8.1 DFT Study of Density of State for Hydrogenated Rutile TiO2 Computational studies have been discussed for different size model systems of hydrogenated (TiO2 )n .xH varying n from 1 to 11 and x = 1 and 2 with different TiO2 : H ratios, i.e. (TiO2 )4 -H, (TiO2 )7 -H, (TiO2 )11 -H, (TiO2 )4 -2H, (TiO2 )7 -2H and (TiO2 )11 . Pure rutile TiO2 has a tetragonal crystal structure with 15 atoms in the unit cell (six molecules/cell), and it belongs to the P42 /mnm space group. Crystal class of this phase is di-tetragonal and di-pyramidal (4/mmm) having H-M symbol: (4/m 2/m 2/m), and crystal habit is acicular to prismatic crystal, elongated and striated parallel to [001] surface. Twinning of the crystal is common on {011} or {031} as contact twin with two, six or eight individuals, cyclic, polysynthetic. Regarding cleavage, {110} is good and {100} is moderate parting on {092} and {011}. The experimental unit cell dimensions are a = b = 4.584 Å and c = 2.953 Å. Density functional theory-based studies reveal good interaction of hydrogen to that of TiO2 surface (110) with the appearance of new states and new bands in the calculated density of states and band structure of H-TiO2 . Literature reported on hydrogenation resultant shell becomes disordered and forms O–H as well as Ti-H bonds, all of which leads to the formation of mid-gap states. This change in band gap also relates consequently and affects optical properties like refractive indices, absorption coefficient, dielectric constant, conductivity, etc., of TiO2 that can be calculated from quantum calculations based on DOS and band structure study. Moreover, the obtained DOS and band structures confirm that the valence and conduction bands of H-rutile TiO2 are mainly formed by O2p and Ti3d , H1s states, respectively. This substantiates the existence of

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Fig. 1 DOS of a H-(TiO2 )4 cluster, b 2H-(TiO2 )4 cluster and c (TiO2 )4 cluster

interactions between H-atom and rutile TiO2 surface. The large optical anisotropy has been studied through the calculation of the band structure and DOS. Density of states of different clusters is evaluated in detail. The DOS for pure (TiO2 )4 cluster of rutile TiO2 and H-rutile TiO2 is presented in Fig. 1, (TiO2 )7 cluster in Fig. 2 and (TiO2 )11 cluster in Fig. 3. All the presented figures (Figs. 1, 2 and 3) represent DFT calculated data and show very well agreement with each other. Clear observations of the figures show that for all the clusters band gap value decreases on hydrogenation. This is in well agreement with the previous reports by Leconte et al. [164]. Figure 1 shows clear extension of HOMO and LUMO band in H-(TiO2 )4 cluster compared to that of pure (TiO2 )4 cluster in Fig. 1c, whereas Fig. 1b shows clear appearance of new states in 2H-(TiO2 )4 cluster. Extension of HOMO as well as LUMO band supports decrease in band gap of H-(TiO2 )4 cluster compared to that of pure (TiO2 )4 cluster. Clear appearance of a new energy band in between valence band (VB) and conduction band (CB) in all H-(TiO2 )n clusters strongly not only supports the decrease in band gap but subsequently leads to very low refractive index loss, and H-TiO2 cluster shows exceptional behaviour with respect to its pure counterpart. Refractive index loss, absorption coefficient, dielectric constant and the conductivity of materials are very much depended on their band gap as already discussed in Sect. 7. All the structures are found to be energetically stable. The increase in refractive index of H-rutile TiO2 material in the terahertz range can be well explained with supporting values of related parameters. This is an excellent addition to the existing literature supporting significant refractive index loss on H-TiO2 . This remarkable behaviour in

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Fig. 2 DOS of a H-(TiO2 )7 cluster, b 2H-(TiO2 )7 cluster and c (TiO2 )11 cluster

Fig. 3 DOS of a H-(TiO2 )4 cluster, b 2H-(TiO2 )7 cluster and c (TiO2 )11 cluster

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the optical properties of these hydrogenated clusters makes it feasible as a potential candidate in the field of terahertz applications. Apart from these, it has been noticed that thermodynamic stability significantly enhanced with the increase in the size of the clusters. In the case of the nanoparticles, the RIs of the x and y directions differ from each other, although the basic form of the RIs is quite similar. This is obviously due to changes in the crystal structure due to the finite size of the particles and an increase in surface-to-bulk ratio, which has been already established in the analysis of relaxation of the particle models. It is very important to understand that somehow the underestimation of the band gap energy to some extent is principally because of the well-known problem of DFT.

8.2 DFT Study of Band Structure for Hydrogenated Rutile TiO2 Band gap of material can also be determined from band structure of the material. In this part, structural analysis of the relaxed structures and contribution of hydrogenation on the optoelectronic properties of TiO2 semiconducting clusters have been reported based on DFT calculations. Band structure is calculated for all above clusters, i.e. (TiO2 )n .xH varying n from 4 to 11 and x = 1 and 2 with different TiO2 : H ratios, i.e. (TiO2 )4 -H, (TiO2 )7 -H, (TiO2 )11 -H, (TiO2 )4 -2H, (TiO2 )7 -2H and (TiO2 )11 . The band structure for pure rutile (TiO2 )4 cluster and H-rutile TiO2 is presented in Fig. 4, for (TiO2 )7 cluster in Fig. 5 and for (TiO2 )11 cluster in Fig. 6. All the structures are in very well agreement with the results obtained from density of state calculation data. Band structures also well supports that band gap decrease on hydrogenation from pure rutile TiO2 to H-rutile TiO2 . Density functional theory-based studies reveal good interaction of hydrogen to that of TiO2 surface (110) with the appearance of new bands in the calculated band structure of H-TiO2 . This band structure data excellently supports the previous reports by Leconte et al. that refractive index loss of materials is very much depended not only on band gap but also on band structures. Figure 1a, b clearly shows addition of new band between HOMO and LUMO for all H-(TiO2 )n and 2H-(TiO2 )n cluster compared to that of pure (TiO2 )n cluster in Fig. 1c. Appearance of new band in HOMO as well as LUMO band structure supports decrease in band gap of H-(TiO2 )n and 2H-(TiO2 )n cluster compared to that of pure (TiO2 )4 cluster. Clear appearance of a new energy band in between valence band (VB) and conduction band (CB) in all H-(TiO2 )n clusters not only strongly supports decrease in band gap but subsequently leads to very low refractive index loss, and H-TiO2 cluster shows exceptional behaviour with respect to its pure counterpart. Furthermore, the appeared DOS and band structures ascertain that the VB and CB of rutile TiO2 are predominantly formed by O2p and Ti3d, H1s states, respectively. It may be suggested that hydrogenation changes charge distribution on the two Ti atoms near to it and as a result of which occupied states appeared near the conduction band. This validates the presence of good interactions between H-atom and TiO2 surface. Large optical

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Fig. 4 Band structure of a H-(TiO2 )4 cluster, b 2H-(TiO2 )4 cluster and c (TiO2 )4 cluster

anisotropy is also studied with the help of band structure. Resulting outcomes are in good correlation with previous experimental and theoretical findings. Generally, the RIs of nanoparticles clearly show blue shift, but in this set of model structures, do not show any size-dependent shift by the increase in cluster size. All the figures show that the shape and structure of the particle can have more pronounced effect on the RI than the actual particle size in the area of small crystals. This is certainly attributed to the relatively small particle size variation in the test set. But represented figures support the previously reported facts that changes in the gap width of the nanoparticles significantly affect the RI of the particles. It has been established that the bottom of the CB appeared to the top of the VB. This important observation substantiates that tetragonal rutile phase is a wide direct band gap semiconductor even after hydrogenation. Close observations of the figures confirm that in the case of H-TiO2 cluster band gap is lowest. Hydrogenated cluster shows significantly dense band structure. This is obvious due to the changes in band structure on hydrogenation of TiO2 .

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Fig. 5 Band structure of a H-(TiO2 )7 cluster, b 2H-(TiO2 )7 cluster and c (TiO2 )7 cluster

8.3 DFT Study of HOMO–LUMO Band Gap for Hydrogenated Rutile TiO2 TiO2 is a promising material for optoelectronic devices, and recently it has been the topic of intensive research in the field of terahertz applications. Recently, DFT and ab initio methods have been used to calculate different optoeletronic properties of hydrogenated TiO2 . Conformational stability of H-(TiO2 )n clusters is established by structural optimizations. In this study under the def2-SVP basis set, the outermost valence electrons 3d2 4s2 for Ti, 1s1 for H and 2s2 2p4 for O are defined and their core electrons are not taken into account. The H-states are hybridized with the Ti and O-states, to form different hybrid orbitals. Hydrogenation plays a significant role in positive and negative charge distribution in HOMO and LUMO orbitals. It also considerably affects the position of HOMO and LUMO orbitals resulting in noticeable effects on its band gap. This final section interprets HOMO–LUMO charge distribution and band gap calculations under the formalism of density functional theory for hydrogenated (TiO2 )n (n = 2, 4 and 8) cluster based on ORCA computational calculations. All the structures are again found to be energetically stable. The results are analysed with increase in cluster size. The clusters show well agreement with respect to its other counterparts. The remarkable changes in refractive index is well supported by the decrease in band gap and proves it as a potential candidate in

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Fig. 6 Band structure of a H-(TiO2 )11 cluster, b 2H-(TiO2 )11 cluster and c (TiO2 )11 cluster

the field of high frequency terahertz absorption. Apart from these, it has been noticed that thermodynamic properties are significantly enhanced with the increase in size of the cluster. To comprehend the association between the electronic structure and the optical property of TiO2 nanoclusters, highest occupied molecular orbitals (HOMOs) and lowest un-occupied molecular orbitals (LUMOs) are plotted by ORCA simulations as shown in Figs. 7, 8, 9, 10, 11 and 12. Subsequently, all titanium, hydrogen and oxygen atoms do not have equivalent positions in the (TiO2 )n nanocluster. For all the (TiO2 )n nanoclusters, the HOMO and LUMO orbital electrons are more widely distributed on different atoms compared to the localized distribution of electrons. We find that all structures (Figs. 7, 8, 9, 10, 11 and 12) have the same description.

9 Summary Hydrogenated TiO2 is one of the promising and emerging materials attracting pronounced research attention in the field of nanomaterials research and different fields of applications. Various aspects of dramatic improvements in properties and

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Fig. 7 HOMO orbital charge distribution in H-(TiO2 )2 cluster (HOMO to HOMO-4 are presented in sequence)

Fig. 8 LUMO orbital charge distribution in H-(TiO2 )2 cluster (LUMO to LUMO-4 are presented in sequence)

remarkable enhancement in terahertz absorption have made H-TiO2 a potential material for future. Dramatic improvement in terahertz absorption occurs due to significant alteration in structural and physicochemical properties of H-TiO2 . Alteration of dielectric constant and refractive index of material associated with enhanced electric loss are major contributing factors towards significant improvement in their properties, and hydrogenated TiO2 nanoparticles may provide an easier solution for different applications. Ongoing extensive research provides new insights into the photo-activity of H-TiO2, improved microwave absorption etc., and paves the way for further studies of other hydrogenated metal oxides for potential applications. As HTiO2 shows drastic improvement in terahertz absorption efficiency boldly competing

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Fig. 9 HOMO orbital charge distribution in H-(TiO2 )4 cluster (HOMO to HOMO-4 are presented in sequence)

Fig. 10 LUMO orbital charge distribution in H-(TiO2 )4 cluster (LUMO to LUMO-4 are presented in sequence)

with other promising materials and newly developed technology, this discussion opens a new horizon for future applications of hydrogenated TiO2 . This chapter discusses challenges and recent advancement of H-TiO2 , different methods for the development of H-TiO2 , factor which affects the properties, various applications and computational study to observe effect on electronic properties on hydrogenation. Finally, the chapter highlights effect of hydrogenation on increased refractive index of H-TiO2 clusters with the help of density functional theory. Hope this chapter will motivate more advance research in this field in coming future.

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Fig. 11 HOMO orbital charge distribution in H-(TiO2 )8 cluster (HOMO to HOMO-4 are presented in sequence)

Fig. 12 LUMO orbital charge distribution in H-(TiO2 )8 cluster (LUMO to LUMO-4 are presented in sequence)

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Doping Effects on Optical Properties of Titania Composite in Terahertz Range S. Mahata and S. S. Mahato

Abstract Terahertz materials, with its absorption span in the infrared and microwave region, have been payed significant attention throughout the world, and day by day, new materials are being developed having potential applications in the terahertz range. While naturally occurring materials hardly respond to THz radiation, extensive research efforts established numerous materials as high absorbers in the THz domain. Terahertz radiation, with its wide range absorption ability, has been studied thoroughly for numerous futuristic applications. The THz band straddling from 0.1 to 10 THz has also eye-catching usability in the field of life sciences, material characterizations, industrial applications, security, etc. Owing to such miscellany use, cost-effectiveness and low-weight THz integrated circuits are of being high technological demand in present global scenario. Carbon-based graphene nanotubes, etc., have been established for those applications. Recently, rutile phase of titania has also attracted huge interest in the area of metamaterials which are considered as good terahertz absorber and open ups new potential application opportunity for TiO2 nanomaterial. This chapter focusses on one of the recently discovered promising material rutile phases of TiO2, which can be potentially used for terahertz applications. The study highlights on effect of Sb and Bi doping on refractive index of rutile TiO2 clusters considering density functional theory. Keywords Bi- and sb-doped TiO2 · Effect on band gap · Oxygen vacancy · THz absorption · DFT calculation

1 Introduction The THz part of EM spectrum embraces amazing prospects for future science and technology owing to its several exciting and distinctive spectral signatures which is S. Mahata (B) · S. S. Mahato National Institute of Science and Technology, Palur Hills, Berhampur, Odisha 761008, India e-mail: [email protected] S. S. Mahato e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Acharyya and P. Das (eds.), Advanced Materials for Future Terahertz Devices, Circuits and Systems, Lecture Notes in Electrical Engineering 727, https://doi.org/10.1007/978-981-33-4489-1_9

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advantageous for both fundamental investigations as well as real-world applications. The spectral connotation of THz waves was well known for years. Recently, this field encompasses an extensive range of applications in interdisciplinary areas including photonics, spintronics, astronomy, materials spectroscopy, biomedical diagnosis, imaging, sensing, nonlinear applications, metrology, wireless communication and many more. Terahertz radiation, with its wide range absorption span in the infrared and micro-waves, has been investigated thoroughly for many futuristic applications. The THz band straddling from 0.1 to 10 THz has also eye-catching usability in the field of life sciences, material characterizations, industrial applications, security, etc. Owing to such miscellany use, cost-effectiveness and low-weight THz integrated circuits are of being high technological demand in present global scenario. While naturally occurring materials hardly respond to THz radiation, extensive research efforts have been dedicated to make absorbers in the THz region. Carbon-based graphene nanotubes, etc., have been established for those applications. However, THz devices applications are inadequate from the point of developmental complexity. The working of those devices is controlled by the electrical and optical performance of the materials which can be tuned by impurity concentration or by functionalization of the materials. Recently, rutile phase of titania has also attracted huge interest in the area of metamaterials which are considered as good terahertz absorber. This chapter focusses on one of the easily developed structurally modified material which is also a potential candidate to address the challenges in the terahertz range applications. It is obvious that the optical characteristics of nano-TiO2 have considerable prominence concerning the light and EM radiation in such a media. This is a new potential application opportunity for TiO2 nanomaterial. TiO2 nanomaterials have been extensively considered as a promising photocatalyst having wide band gap and extensively dedicated towards solar-driven clean energy generation as well as environmental applications owing to its promising optical properties. Recent research activities demonstrate structural modifications of titania can effectively leads to dramatic changes in their microstructural, optical, storage capacity, photocatalytic, electronic, field emission and microwave absorption properties. Doping assimilated into their lattice introduces structural changes on their surface, extend their optical absorption and shows promising microwave absorbing capabilities. Optical and electrical performances of semiconductor devices are determined mainly by band gap and refractive index. M. Mumtaz et al. [1,2] have shown optical properties of rutile titanium dioxide in the terahertz region improves on Sb and Bi doping. This chapter highlights on effect of Sb and Bi doping on increasing refractive index of rutile TiO2 clusters considering density functional theory. With the advancement of recent technologies, novel semiconducting materials having potential optoelectronic properties find widespread applications in electronic, like laser diodes (LD), light-emitting diodes (LED), photodetectors (PD), integrated circuits (IC), nanotechnology, hetero-structure lasers and good refractive material in the terahertz region [3-8]. Transparent conducting semiconductor oxide (TCO) materials are imperative for the fabrication of optoelectronics devices and solar cells owing to their transparency and conductivity [9, 10]. Generally, TiO2 -based TCO are considered for photocatalysis and photovoltaics [11-15]. According to the recent

Doping Effects on Optical Properties of Titania Composite … Table 1 Structural, optical and electrical properties of the TiO2 crystal

Property

143 Value

Flexural strength

140 MPa

Compression strength

680 MPa

Poisson’s ratio

0.27

Fracture toughness

3.2 MPa.m1/2

Modulus of rigidity

90 GPa

Elastic modulus

230 GPa

Microhardness (HV0.5)

880 VHN

Resistivity (25°C)

1012 O.cm

Resistivity (700°C)

2.5 × 104 O.cm

Dielectric constant (1 MHz)

85

Dissipation factor (1 MHz)

5 × 10−4

Dielectric strength

4 kVmm−1

Transmission range

0.43 to 5.0 μm

Reflection loss

30% at 2μ (2 surfaces)

Refractive index

2.52 (Anatase) 2.72(Rutile)

Density

3.89 g/cc (Anatase) 4.25 g/cc (Rutile)

development, they also have prospective usability for the fabrication THz wave guides [16, 17] and metamaterials [18]. Good work has been done on Sb-doped TiO2 which expands its absorption from UV-region towards visible region [19, 20]. This is an imminent effect on materials properties enhancing its photochemical, photocatalytic and photoelectro-chemical properties developed by different methods [21-24] and magnify the competence of the abovementioned devices. Modified transparency and conductivity of TiO2 broaden its applications in the THz region using time-resolved terahertz spectroscopy (THz-TDS) techniques. For example, mobility study of the photogenerated electrons in porous and bulk TiO2 and temperature-based electron– phonon scattering analysis [25, 26], conductivity tuning studies of Nb-doped anatase TiO2 nanoparticles of [27], thin film depolarization effect investigation [28] have been well reported. Majority of these literature focused on realizing the mechanism behind charge transport of TiO2 . However, effect of band gap, density of states and band structure on increasing refractive index and mechanism of conductivity in the THz region has not yet been reported. This chapter explains this part in details with the help of quantum calculations.

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1.1 Applications of TiO2 Nanomaterials in Terahertz Range Anti-reflective coating is an indispensable constituent of photovoltaic which potentially reduces the well-known difficulty in light reflection. Deposited on the Si-wafers, these type of thin film considerably dedicated to raise the solar cells efficiency. For this purpose, different dielectric materials are used, namely titanium dioxide TiO2 . In last few decades, the use of nanomaterials is expanding exponentially. Various nanomaterials are being used in several consumer products. Nanomaterials having less than 100 nm length in at least one dimension have attracted wide attention due to their unique properties compared to the bulk materials. In spite of some restrictions, nanosize materials are commonly used in the light scattering measurements. TiO2 is one of the potential materials that are developed and used as an engineered nanomaterial in large scale. Addressing numbers of major challenges, it is quite essential to extend significant research and development in the field of advanced nanomaterials to formulise the refractive index (RI) on crystal properties of the materials. Applications of THz devices depends on the miniaturized-scaled and high density planner integration. Substrate-integrated advanced technologies are possibly the best promising answer for on-chip THz devices in this purpose. Dispersionless dielectric properties of substrate materials are advantageous for THz devices, like attenuators, antenna, isolator, modulators, filters, waveguides, etc. Not only the selection of materials but the dielectric, optical and conductive behaviour of these media and their tunability in terahertz frequency range are of major challenge. TiO2 has attained substantial prominence for its low-loss characteristics, high permittivity and wide band gap. Titanium dioxide (TiO2 ) has already been utilized for designing terahertz devices like THz wave guides [29], filters [30, 31] and metamaterials [32, 33]. The working principal of those devices is comprehensively guided by the optical and electronic properties of TiO2 which can be improved by modification of the material, i.e., impurity doping. Sb and Bi in TiO2 has upraised the photocatalytic activity and dielectric behaviour in KHz region [34-36], but its effects on dielectric and optical characteristics in THz region are unmapped. Optical characteristics such as refractive index can be estimated from wavelengthdependent intricate dielectric function based on the ordinary and extraordinary polarization directions. Moreover, the band structures, DOS and HOMO–LUMO position explorations, have high potentials to fall lights on refractive index loss of materials in the terahertz range. Optical anisotropy has been calculated through band diagram and DOS. Experimental results are somehow in good harmony with different theoretical and experimental data. In different reported literature, the terahertz transmission measurement technology has been employed to analyse different structures of TiO2 like nanospheres, nanowires, etc., under various conditions. The analysis made can be explicated with the help of new phonon bands shifting due to polymorphism. Mainly, Kramers Kronig dispersion model has been used to determine the wavelength-dependent refractive index of the samples, having well-known thickness, with the help of absorbance data.

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In this part, the refractive index of Bi and Sb doping rutile titanium dioxide in the terahertz region has been discussed. The properties of doped rutile titanium dioxide in the terahertz region have been highlighted with the help of optimized structures, band diagram and DOS of rutile phase of titanium dioxide (TiO2 ) clusters. Several ab initio computations have been done for obtaining the dependence of the RI of TiO2 on the crystal or on the cluster size, for small size particles. But for greater size of crystal calculations has not been done due to the unbearable increase in computational time. However, this chapter analyses DFT calculation results up to (TiO2 )11 cluster of rutile TiO2 . The crystal-size, density of states, band structure and band gap-dependent-RI up to (TiO2 )11 cluster have been tried to well explain. These calculations are done on optimized model constructions of the clusters. Results of HOMO–LUMO charge distribution has been parallelly explained with the help of ORCA calculation based on def2-SVP basis set. Density of states (DOS) as well as band structure developed with the help of BURAI interfacing platform of quantum expresso excellently supports the low refractive index loss of rutile TiO2 in the terahertz range. The chapter is organized as follows: firstly, importance of TiO2 nanomaterials as a potential candidate for terahertz range applications. Next, different theories and empirical formulas were developed in the literature on characterizations of high refractive index of terahertz materials. Finally, the high refractive index of rutile TiO2 in the terahertz range has been supported with the theoretical modelling followed by the summery and references.

1.2 Brief Overview of General Properties of Titanium Dioxide From long back, TiO2 is a potential material for optical coatings in the visible range. It is considered to be the highest index material for the visible range and is hard as well as stable as a composite with other oxides. Application of TiO2 as a high-index material extends from heat-reflecting mirrors, cold mirrors, beam splitters and AR on different substrates. Unfortunately, its typical absorbance in less than 450 nm range restricts the applications to the visible and near-IR regime. Its multilayer film in combination with other oxide films potentially displays outstanding durability but low mechanical stress owing to the fact that tensile stress of TiO2 layers is well-adjusted by the compressive stress from the other metal oxide layers. Titanium dioxide is well known for large band gap and has received a lot of attention due to its exceptional characteristics. It is transparent in the 380-750 nm, but absorbs strappingly in the UV region. TiO2 is stable white pigment and chemically resistant with other substances. In nature, TiO2 occurs in three polymorphs: anatase, rutile and brookite; the main source of industrially manufactured TiO2 is ilmenite FeTiO3 . Nano-titania (n-TiO2 ) has many attractive properties as compared to traditional titania ceramics. N-TiO2 is attracting academic and industrial community for its properties and high-tech applications. The nanoparticle of TiO2 is very useful as it results in significant improvement of surface properties. Nano-titania (n-TiO2 ) has potential as electroceramics due to its high conductivity, enhanced ductility, toughness and

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formability than its counterparts. It has also an applicant of good implant materials for dental, orthopedic and osteo synthesis for its chemical stability, non-toxicity and biocompatibility. Generally, TiO2 is used in different fields like pigment, catalysts, aeronautics, ceramics and structural composite materials. A thin film coating of n-TiO2 has a wide range of applications in photocatalysis, photo-electrocatalysis, self-cleaning, etc. Recent studies show that the photocatalytic activity of TiO2 mainly depends on crystal structure, surface area, crystallinity, particle size and porosity [3744]. Transparent single crystals/thin films of TiO2 host high refractive index make it promising for optical applications, especially dye-sensitized solar cell (DSSC). Most commercially available TiO2 powders are either in anatase or rutile phase are mixture of the two.

1.2.1

TiO2 Crystal Structures

Titanium dioxide exists in a number of naturally occurring crystalline forms. At ambient conditions, three structures are known: rutile, anatase, brookite which are thermodynamically most stable forms. Further most common structures are anatase and rutile. Rutile can exist at any temperature less than 1800°C, at which point TiO2 becomes liquid. Though temperatures above 750°C, the anatase converts to the rutile phase but different researcher. TiO6 octahedra is the basic block for the polymorphicstructured TiO2 . The polymorphs are differing from each other. The largest useful form of TiO2 is anatase though it is rarely available in ore form. Compared to the rutile phase, anatase phase is always less stable and transforms to rutile instinctively at any temperatures more than 750°C. The stable form of titania is rutile which has a crystal form similar to anatase, but octahedra connects through four edges as a place of four corners. These results of chain formation can successively have arranged in a fourfold symmetry. For rutile crystal, each octahedron is linked to ten neighbouring octahedron, sharing edge with 2 of them and corner with 8 of them. The edgesharing octahedron are positioned along the [001] direction. Naturally occurring rutile crystals host mainly (110) surfaces and the (110) surface is of utmost stability. The unit crystal of rutile host 2 Ti atoms positioned at (0, 0, 0) and (1/2, 1/2, 1/2), and 4 oxygen atoms. Four oxygen atoms surround Ti-cation in a distorted octahedron having denser structure than anatase. Both the crystal forms are represented as chains of TiO6 octahedron, each Ti 4+ ion encircled by six O2− ions. Rutile crystal exhibits slightly orthorhombic distortion but considerably distorted octahedron in anatase has low symmetry. Ti–Ti distances are greater in anatase, but Ti-O distances are smaller compared to that of rutile. Substantial variances in crystal structures significantly alter their electrical, mechanical, electronic properties. Different properties of the TiO2 crystals are tabulated below. Due to its good mechanical properties, it has been used in electronic devices. It is being extensively used in high-frequency appliances like radar, broadcast emitters, high-frequency welding machines, etc. By scaling down the size to the material nanoscale domain, properties changes drastically and extends its application towards large possible fields. Remarkable

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changes in surface-to-volume ratio, mechanical strength, electrical conductivity, thermal conductivity, optical and electronic properties occur in this nanoscale domain. Drastic changes in optical properties make TiO2 a transparent UV radiation blocker than opaque but TiO2 . Developed wonderful properties in the nanoscale dimensions have tremendous potential to be used in several fields in the future.

1.2.2

Rutile Titanium Dioxide (TiO2 )

Rutile is an ore mainly consisting of TiO2 and is the maximum stabilized form of TiO2 . Among all polymorphs of TiO2 , rutile is one of the utmost refractive index materials at visible range compared to any known crystal and also parallelly exhibits large birefringence as well as high dispersion making it highly important for the development of numbers of optical components. Rutile available in nature sometimes hosts up to 10% of Fe and appreciable amount of Nb and Tm. Rutile originates its name from Latin word rutilus, which means red, with reference to its deep red colour appearing in some samples when observed via transmitted light [45]. Rutile was first introduced by A. G. Wernerin in 1803. The conversion of less stable TiO2 polymorphs to rutile is irreversible. Rutile is a widely available in high-temperature and high-pressure metamorphic and igneous rocks.

1.2.3

Refractive Index of TiO2 –Rutile

Very high refractive index (RI) of TiO2 has led its potential application towards thinfilm optics. Technology based on designing high and low TiO2 RI thin films modifies optical interference and optic’s spectral reflectance outline. This is a wonderful technology to be applicable for developing reflectors, optical filters and antireflection coatings on different glasses and lenses. Generally, SiO2 -TiO2 combination is a potential candidate as low RI material. RI of TiO2 can be potentially varied based on several advanced technologies resulting in thin film with large density variations. Applications of advanced technologies, wide variations of process parameters result in development of different phases of TiO2 having different properties and applicable in wide range of fields. For a typical sample of TiO2 –Rutile the refractive index at 632.8 nm is 2.8736.

1.2.4

Semiconducting Properties

TiO2 is a high band-gap semiconductor (3.2 eV). A semiconductor is characterized by a conduction band and a valence band separated by a smaller energy gap resulting in electrical conductivity considerably greater than that of an insulator where the thermal energy unable to stimulate electrons from the valence to conduction band. But the electrical conduction in semiconductor is significantly lower than that of a conductor.

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Photocatalysis is defined by the reaction which occurs on the surface of a semiconductor thin film in the presence of a certain range of wavelength. Technically, all semiconductors can indicate photocatalytic activities, but significantly better results usually oxides and compound semiconductors have demonstrated predominantly. Since the beginning of photoinduced water splitting on TiO2 electrode by Fujishima and Honda 1972 [46], TiO2 photosemiconductor have appealed great consideration as a substitute material for water purification. When illuminated below near UV-light, n-TiO2 generates hydroxyl radicals (OH· ) in the valence band, whereas O2− ions are in the conduction band which are responsible for photoactivity and superhydrophilicity.

Electrical Properties TiO2 has many usability in electronics and optoelectronics for its high permittivity and refractive index. The charge transport in TiO2 is highly responsive to O-vacancy defects. The majorority of the electrical transport experimental material and defects of TiO2 is limited to the range of partial pressure of oxygen (PO2 ) at which TiO2 material exhibits n-type properties. The metastable phase anatase differs from stable phase rutile. However, the electric activity and chemical reactivity of O-vacancies create problems for material reliability. Consequently, fabrication of highly conductive TiO2 remains a challenge for device architecture.

Optical Properties Dielectrics of anatase and rutile single crystals are very interesting, and lot of research has been done on its optical properties. Even though both type of TiO2 absorb UV, rutile-TiO2 can absorb closer to visible range. But, anatase-TiO2 show higher photocatalytic action than rutile as the band gap of anatase-TiO2 is 3.20 eV while rutileTiO2 is 3.0 eV. Anatase dielectric has been calculated by Hosaka et al. [47]. Jellison et al. and Tanemura et al. calculated optical constants of natural anatase crystal and thin films [48,49].

2 Potential Materials in Terahertz Domain Science and Technology Several literatures are available on the exhilarating works that leads toward the mesmerizing science and overabundance of technological improvements being brought out in technologically important terahertz part of EM radiation. A newfangled and sensational development of multi-dimensional crystal along with their sources are fixed to contribute the unique expansion and revolutions in the field of

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terahertz. Over the years, potential implications of terahertz waves are a well-known in science. However, its strong absorbance in atmosphere was one of the major challenge towards its practical applications in various fields. Though ground breaking work in this domain was started long back by Auston with the implementation of terahertz switches, but real revolutionary work in this beautiful and potentials field has potentially emerged in the recent future. For a long time, a substantial amount of terahertz research was dedicated towards the development of strong-THz emission system using laser-driven advanced material and broadband wave that have impending usefulness in the field of THz spectroscopy [50-51]. THz generation via optical refinement procedures in electro-optical materials is one of the amazing techniques strongly guided by currents in optically excited plasma. Tremendous breakthroughs have been happened on intense sources, detectors, optical components, etc., which is removing all technological barriers in terahertz technological and shaping their independency in the present and future leading-edge technologies. Artificially designed terahertz microcavities developed from metamaterials have paid huge attention in the terahertz photonics owing to their tailorable and impending optical behaviour. Their ability of enhancing terahertz fields confinement in a small volume makes them potential candidate for nonlinear devices, ultrasensitive sensors, resonant modulators, phase shifters, etc. Potential of terahertz emissivity attracted incredible attention in non-invasive and ultrafast detection of important properties in the complex interrelated systems of high-temperature superconductors, numerous transition metal oxides, etc., as described by different authors [52-53]. C. In and H. Choi [54] have nicely reported in their review work on Dirac materials like graphene and topological insulators. One of the wondering materials in nanoscale technology graphene has also considerably attracted as promising and potential material in terahertz range. It has potential applications in the field of optoelectronic and nonlinear optics. Different authors have also reported the charge injection processes in two-dimensional graphene-Si interface, and MoS2 -Si interfaces show low-threshold, efficient and extremely fast terahertz modulators. Two-dimensional materials demonstrate exhilarating potentials as highly advanced terahertz devices to efficiently increase the terahertz conductance of semiconductor materials [55]. Y. Zeng et al. [56] have used innovative terahertz cavities to on-chip communication networks.

3 Terahertz Time-Domain Spectroscopy (THz-TDS) THz-TDS is a well-recognized phase-sensitive spectroscopic technique for material optical and electrical analysis without physical contacts in THz wavelengths [57, 58]. It has been used widely to investigate the semiconductors in the form of bulk [59, 60], nanocrystals [61–66] and thin films [67, 68]. In the presence of THz pulse, charge carriers of semiconductor get stimulated which causes collective excitations [61]. By the help of Fourier transformation and spectral-frequency-dependent electrical conductivity, charge carrier’s dynamics can be explained effectively in the form

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of surface plasmons and free carriers. THz-TDS has been employed to explore the carrier positions in dye sensitized nano-TiO2 [69], electron–phonon scattering, depolarization effects in thin film [70] and mobility of photogenerated electrons in TiO2 [71, 72].

4 Theory: Refractive Index of Doped TiO2 4.1 Moss Model Absorption of photons in semiconductors is determined by the energy gap; on the other hand, refractive index is an ability of its transparency to incident wavelength. In 1950, with the help of photoconductivity theory, Moss [73] developed a basic relationship between these. According to it, by absorbing of an optical quantum, electrons move to an excited state and thermal energy push them to CB. This type of photoeffect in crystal defects at few lattice points leads effective dielectric constant, εEff , scaled down by 1/ε2Eff which approximately corresponds to the square of the refractive index, n. Energy required to an electron to go to an excited state given by the Bohr formula for the ionization energy, E, of the hydrogen atom, E = 2π2 m*e4 /ε2 h2 , where m* = electron effective mass, e = electronic charge, ε = relative permittivity and h = Plank constant. Thus, the Moss relation was defined as [73]: n4 = 77/μm, λe

(1)

where n = RI and le = wavelength corresponding to the absorption edge. In terms of energy gap, this is n 4 E g = 95eV,

(2)

where Eg is the band gap of the material

4.2 Penn Model In 1962, Penn [74] proposed a simple model with electrons in a sphere of momentum space. The energy, E, and wave function, w, with respect to the state k for this model are given by, E k±

  1   1 0 0 0 0 2 2 /2 = Ek + Ek ± Ek − Ek + E g , 2

(3)

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  2 1  ψk = eik.r + αk± eik .r /1 + αk± 2 ,

(4)

    ˆ Here, E = electron where αk± ≡ 21 E g / E k± − E k0 E k0 ≡ 2 /2m k 2 k  ≡ k − 2K F k. energy, α = averaged Jones boundary. k = wave vector and KF = Fermi wave vector Penn describes the dielectric function as: ,

(6)

where k  ≡ k + q − (2K F )(k + q)/|k + q|, q = wave number, N = occupation number for the states k and k + q. This model is good for lower values of q without considering Brillouin zone degeneracy.

4.3 Alternate Approaches Gupta and Ravindra [75-76] redefine the relation: n = K 1 − K 2 E g + K 3 E g2 − K 4 E g3 ,

(7)

After calculating the values of K the equation reduces to n = 4.16 − 1.12E g + 0.31E g2 − 0.08E g3 ,

(8)

for optical range Herve and Vandamme proposed [77],

n=

 1+

A Eg + B

2 ,

(9)

where A ~ 13.6 eV and B is 3.47 eV.

5 Computational Study TiO2 clusters are promising due to its very high refractive index. The density functional theory (DFT) based on the pseudo-potentials method has been implemented with the help of first principle-based Quantum ESPRESSO (QE) calculations. For local density approximation (LDA) [69], ground-state energy has been calculated by self-consistent method. DFT has been used to the study of various phases of TiO2 and projected augmented wave (PAW) for three polymorphs of TiO2 [70] with the help of QE and ORCA. Here O atoms is considered by 2 s and 2p states, and Ti atoms by 3 s, 3p, 4 s, and 3d orbitals [80-82]. All calculations described here are performed

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using the BURAI interfacing of Quantum EXPRESSO and ORCA platform. This is a computationally and experimentally very challenging area of nanoparticles applications based on their properties. The DFT implementation for different clusters gives the RI of the different clusters as a function of the band gap of the cluster, which can also be correlated with HOMO–LUMO energy separation.

5.1 DFT Study of Density of State for Bi- and Sb-Doped Rutile TiO2 Bulk rutile-TiO2 has 15 atoms in the unit cell (six molecules/cell), and it associates to the P42 /mnm space group. Crystal class of this phase is di-tetragonal di-pyramidal (4/mmm) having H-M symbol: (4/m 2/m 2/m), and crystal habit is acicular to prismatic crystal, elongated and striated parallel to [001] surface. Twinning of the crystal is common on {011}, 0r {031} as contact twin with two, six, or eight individuals, cyclic, polysynthetic. Regarding cleavage {110} is good, {100} is moderate parting on {092} and {011}. The cell dimensions are a = b=4.584Å and c = 2.953Å. Optical properties such as dielectric constant, refractive index, absorption coefficient and the conductivity of TiO2 can be calculated from quantum calculations based DOS and band structures. Moreover, the obtained DOS and band structures prove that VB and CB rutile-TiO2 are mainly created by O2p and Ti3d states correspondingly. The DOS for the un-doped, Sb-doped and Bi-doped (TiO2 )4 cluster structures is presented in Figs. 2 − 4, for the un-doped, Sb-doped and Bi-doped (TiO2 )7 clusters are presented in Figs. 5 − 7, and the same for (TiO2 )11 clusters are presented in Figs. 7 − 10. All the presented figures (Fig. 2-10) compared with quantum calculated data shows very well agreement with each other. Density of states of different clusters is evaluated in details. Clear observations of the figures show that for different clusters band gap value decreases with Sb and Bi doping. This is in well agreement with the previous reports by M. Mumtaz et al. The high reflection loss stable rutile-TiO2 structures in the terahertz range can be well explained with supporting values of related parameters. The Bi-doped TiO2 cluster shows special performance with other counterparts. Clear appearance of a new energy band in between valence band (VB) and conduction band (CB) in all Bi-doped clusters strongly supports the decrease in band gap subsequently leading to very low refractive index loss. This is an excellent addition to the existing literature supporting significant refractive index loss on Bi doping. The properties of these clusters in terms of abovementioned parameters may be a reason behind considerable potential of these materials to be used in terahertz range applications with increasing thermodynamic stability proportional to cluster size.

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Fig. 1 TiO2 crystals

Fig. 2 Cluster (TiO2 )4

5.2 DFT Study of Band Structure for Bi- and Sb-Doped Rutile TiO2 Band gap of material can also be determined from band structure of the material. Here, the structural analysis and DFT calculated results have been interpreted. The band structures for the un-doped, Sb-doped and Bi-doped (TiO2 )4 cluster structures are presented in Figs. 11 − 13, and the same for (TiO2 )7 clusters are presented in Figs. 14 − 16. All the structures are in very well agreement with the results obtained from density of states calculation data. Band structures data excellently supports the previous data that clusters band gap value decreases with doping which further decreases from Sb to Bi doping. This band structure data is also in well agreement

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Fig. 3 Cluster Sb-(TiO2 )4

Fig. 4 Cluster Bi-(TiO2 )4

with previous reports by M. Mumtaz et al. that refractive index loss of materials is very much depended not only on band gap but also on band structures. Furthermore, the appeared DOS and band structures ascertain that the VB and CB of rutile TiO2 are predominantly formed by O2p and Ti3d states correspondingly validating Ti-O interactions. For small crystals, RI mainly depends on shape and structure rather than size of the crystal. Tauc Plot analyses in the literature have also correlated band gaps data with RI analysis. Figures 11 − 16 show the band structure of the nanoparticles significantly changes compared to that of bulk rutile. By observing CB minima and VB maxima, it is confirmed that tetragonal rutile phase is a direct band gap semiconductor. The results compared with earlier work on Sb- and Bi-doped

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Fig. 5 Cluster (TiO2 )7

Fig. 6 Cluster Sb-(TiO2 )7

rutile TiO2 . Close observations of the figures prove that un-doped cluster band gap is highest which gradually decreases with Sb and Bi doping. The un-doped cluster shows significantly less dense band structure.

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Fig. 7 Cluster Bi-(TiO2 )7

Fig. 8 Cluster (TiO2 )11

5.3 DFT Study of Effect of Oxygen Vacancy on Density of States for Bi- and Sb-Doped Rutile TiO2 Computationally investigated dispersion of O-vacancies in the small TiO2 cluster surface of rutile phases has been simulated. The results depict the O-vacancies distribution in different size cluster forms of rutile phases. For the defective structures, one oxygen elimination creates ~ 6.25% of the O-vacancy. To understand the Ovacancy impact on structure, density of states DOS was determined using the DFT method. The DOS for the un-doped, Sb-doped and Bi-doped (TiO2 )4 clusters with

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Fig. 9 Cluster Sb-(TiO2 )11

Fig. 10 Cluster Bi-(TiO2 )11

first oxygen vacancy is presented in Figs. 17 − 19, for the un-doped, Sb-doped and Bi-doped (TiO2 )7 clusters are presented in Figs. 20 − 22, and for the un-doped, Sb-doped and Bi-doped (TiO2 )11 clusters are presented in Figs. 23 − 25. Again all the figures (Fig. 17-25) are very well agreement with each other. But one important observation is that for (TiO2 )7 clusters, the additional band between VB and CB is absent here resulting in larger band gap of Bi-doped cluster than Sb-doped clusters. All structures clearly confirm creation of oxygen vacancy leads to decrease in RIs as confirmed by the decrease in band of on vacancy creation. Heedful observation of the clusters without oxygen vacancy shows decrease in the band gap after Sb-doping which further decreases on Bi doping.

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Fig. 11 Cluster (TiO2 )4

Fig. 12 Cluster Sb-(TiO2 )4

5.4 DFT Study of Effect of Oxygen Vacancy on Band Structure for Bi- and Sb-Doped Rutile TiO2 Single O-vacancies and their effects on band structure of (TiO2 )4 , (TiO2 )7 and (TiO2 )11 clusters are computationally studied and compared with doped structures [83-84]. The band structure for the un-doped, Sb-doped and Bi-doped (TiO2 )4 cluster structures is presented in Figs. 26 − 28, and the same for (TiO2 )7 clusters with one oxygen vacancy is presented in Figs. 29-31. Results revealed all these figures are in

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Fig. 13 Cluster Bi-(TiO2 )4

Fig. 14 Cluster (TiO2 )7

well agreement with the previous outcomes and interpretation obtained from density of states calculation data for TiO2 clusters without vacancy. Same trend in results also supports that refractive index loss of materials is very much depended on band gap and DOS due to the O-vacancy creation. DOS images of doped and un-doped clusters show that doping has prominent effect on the RI than particle size for small crystals after oxygen vacancy creation also. Figures show the band structure of the nanoparticles significantly changes on oxygen vacancy creation in rutile phase of TiO2 . The un-doped cluster shows significantly different band structure. Close observations of

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Fig. 15 Cluster Sb-(TiO2 )7

Fig. 16 Cluster Bi-(TiO2 )7

the figures confirm the appearance of some new band in the band structure of the doped clusters but creation of vacancy leads to decrease in refractive index loss which gradually decreases with Sb and Bi doping. But as observed in the previous section, here also the additional band between VB and CB is absent and results in smaller band gap of Bi-doped cluster than Sb-doped clusters.

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Fig. 17 Cluster (TiO2 )4 with 1 oxygen vacancy

Fig. 18 Cluster Sb-(TiO2 )4 with 1 oxygen vacancy

5.5 DFT Study of HOMO–LUMO Band Gap for Bi and Antimony-Doped Rutile TiO2 DFT and ab-inito methods used here to compute different opto-eletronic properties of TiO2 . Conformation stability of (TiO2 )n clusters established by structural optimizations. The VB and CB are primarily created by O2p and Ti3d states correspondingly. Under def2-SVP basis set, the electrons 3d2 4s2 for Ti and 2s2 2p4 for O are considered. The Ti-states are strongly hybridized with the O-states, to form different hybrids orbitals. Doping plays major role in positive and negative charge distribution in HOMO and LUMO orbitals. It also considerably affects the position of HOMO

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Fig. 19 Cluster Bi- (TiO2 )4 with 1 oxygen vacancy

Fig. 20 Cluster (TiO2 )7 with 1 oxygen vacancy

and LUMO orbitals resulting in noticeable effects on its band gap. This section interprets HOMO–LUMO charge distribution, band gap calculations for (TiO2 )n (n = 4 & 8) cluster based on ORCA computational calculations. HOMOs and LUMOs of TiO2 cluster are plotted by ORCA simulations as shown in Fig. 32-39. Subsequently, the all titanium and oxygen atoms do not have equivalent positions in the (TiO2 )n nanocluster. For all the (TiO2 )n nanoclusters, the LUMO electrons are more widely distributed compared to localized distribution of electrons on HOMO orbitals. We find that all structures (Fig. 32-39) have the same description. The effect of HOMO– LUMO charge distribution, density of states (DOS) and band structure of [TiO2 ]n (n

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Fig. 21 Cluster Sb-(TiO2 )7 with 1 oxygen vacancy

Fig. 22 Cluster Bi-(TiO2 )7 with 1 oxygen vacancy

= 4, 7 and 11) cluster on dielectric constant, refractive index, absorption coefficient and the conductivity has been simulated.

6 Summery Realizing rutile TiO2 as real engineering ceramics to contribute as substrate potential candidate in high-performance terahertz region that are having low dielectric loss, low cost, near-dispersion less broadband, high permittivity is of exceptional demand.

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Fig. 23 Cluster (TiO2 )11 with 1 oxygen vacancy

Fig. 24 Cluster Sb-(TiO2 )11 with 1 oxygen vacancy

It is very fast commandingly being deployed in several areas like integrated circuits and 3D structures into planar forms. This form of TiO2 has been extensively recognized as commercially reasonable candidate that encounters high demand for both low-loss and high permittivity applications at sub-Terahertz region. Here, the refractive index, dielectric constant, absorption coefficient and the conductivity of rutile TiO2 in the THz region have been discussed in correlation with band gap, density of states and band structure. Band gap of and band structure of doped and un-doped rutile (TiO2 )n nanoclusters (n = 4, 7, 11) shows excellent agreement with the available literature report that on Sb and Bi doping enhances refractive index loss in the terahertz region. Further, it also shows Bi doping has significant increase in refraction

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Fig. 25 Cluster Bi-(TiO2 )11 with 1 oxygen vacancy

Fig. 26 Cluster (TiO2 )4 with oxygen 1 vacancy

loss compared with Sb-doping. Creation of oxygen vacancy increases the band gap suggesting refractive index decreases with vacancy creation. HOMO-LUMO band gap for different cluster of doped and un-doped rutile also well supports the above results. The results indicate that, in the case of rutile TiO2 particles, the structure of the particle may have a more pronounced effect on the RI than the size of the particle. The refractive index loss of the material reflected here is not only highly promising over 0.2–0.8 terahertz range application, but also shows a path for doped rutile TiO2 to be an exceptionally impending material for the future generation terahertz applications. We anticipate the insight afforded by this study will support the growth of

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Fig. 27 Cluster Sb-(TiO2 )4 with oxygen 1 vacancy

Fig. 28 Cluster Bi-(TiO2 )4 with 1 oxygen vacancy

terahertz applications in several fields, planar integrated circuits, sub-wavelengthscale, slow-light devices, compact high Q-resonators, broadband and many more in future.

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Fig. 29 Cluster (TiO2 )7 with 1 oxygen vacancy

Fig. 30 Cluster Sb-(TiO2 )7 with 1 oxygen vacancy

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Fig. 31 Cluster Bi-(TiO2 )7 with 1 oxygen vacancy

Fig. 32 Positive and negative charge distribution in LUMO–LUMO 4 of Bi-(TiO2 )4

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Fig. 33 Positive and negative charge distribution in HOMO–HOMO 4 of Bi-(TiO2 )4

Fig. 34 Positive and negative charge distribution in LUMO–LUMO 4 of Bi-(TiO2 )8

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Fig. 35 Positive and negative charge distribution in HOMO–HOMO 4 of Bi-(TiO2 )8

Fig. 36 Positive and negative charge distribution in LUMO–LUMO 4 of Sb-(TiO2 )4

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Fig. 37 Positive and negative charge distribution in HOMO–HOMO 4 of Sb-(TiO2 )8

Fig. 38 Positive & negative charge distribution in LUMO – LUMO 4 of Sb-(TiO2 )8

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Fig. 39 Positive & negative charge distribution in HOMO – HOMO 4 of Sb-(TiO2 )8

References 1. M. Mumtaz et al., Investigation of the optical and conductive properties of antimony-doped titanium dioxide using terahertz time-domain spectroscopy. Laser Phys. Lett. 15, 105603 (2018) 2. M. Mumtaz et al., Investigation of the optical and conductive properties of antimony-doped titanium dioxide using terahertz time-domain spectroscopy. Opt. Mater. 96, 109357 (2019) 3. H. Matsuta, Measurement of Excited Argon Atom in Glow Discharge Plasma by Diode Laser Coherent Forward Scattering Spectrometry (DL-CFS), Spectrochimica Acta Part B: Atomic Spectroscopy, 105935 (2020) 4. A. El-Shaer, Towards low cost fabrication of inorganic white light emitting diode based on electrodeposited Cu2 O thin film/TiO2 nanorods heterojunction. Mater. Res. Bull. 116, 111–116 (2019) 5. H. Ferhati, Highly improved responsivity of self-powered UV–Visible photodetector based on TiO2 /Ag/TiO2 multilayer deposited by GLAD technique: Effects of oriented columns and nano-sculptured surface. Appl. Surf. Sci. 529, 147069 (2020) 6. P Bawuah, On the complex refractive index of N-doped TiO2 nanospheres and nanowires in the terahertz spectral region Vibrational Spectroscopy, 68, 241–245 (2013) 7. B.K. Nahak et al., An Investigation on Photocatalytic Dye Degradation of Rhodamine 6G Dye with Fe- and Ag-Doped TiO2 Thin Films. Part of the Lecture Notes in Electrical Engineering book series (LNEE) 673, 295–307 (2020) 8. N. Jhariya et al., Hydrothermal Synthesis of Surface Functionalized Semiconducting Nano Crystals and Study of their Photo induced Interaction with Natural Dye. Int. Res. Jnl. of Eng. & Tech. (IRJET) 5(5), 3892–3895 (2018) 9. D. S. Ginley D S et. al. Transparent Conducting Oxides, MRS Bull., 25, 15–8 (2000) 10. E. Fortunato et al., Transparent Conducting Oxides for Photovoltaics. MRS Bull. 32, 242–7 (2007) 11. A.K. Rana, Transparent Co3 O4 /ZnO photovoltaic broadband photodetector. Mater. Sci. Semicond. Process. 117, 105192 (2020) 12. E. Pulli, Transparent photovoltaic technologies: Current trends towards upscaling. Energy Convers. Manag. 219, 112982 (2020)

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Silicon Nanowires as a Potential Material for Terahertz Applications Shrabani Ghosh, Ankita Chandra, Sourav Sarkar, and K. K. Chattopadhyay

Abstract Terahertz is an important but underutilized frequency range which lies in between 0.3 and 10 THz in electromagnetic spectrum, occupying middle ground of both microwave and infrared region. It can carry few properties of both the wavelengths. As conventional electronic devices have failed to generate and detect the terahertz wave, there is a high demand to find alternatives. Silicon nanowire and its geometry are still under research as terahertz emitter. Here, two-stage metalassisted chemical etching (MaCE) process has been employed to synthesize the grass like silicon nanowires. The lengths and diameters of the nanowires are modified by varying different conditions. The silicon nanowires (SiNW) without HF treatment contain superficial silicon oxide layer which is different in properties compare to HF treated SiNW (SiNW-HF). It is evident that, HF/H2 O2 etching rate has been enhanced with the rise of the temperature, which results in highly dense, more fine nanowires in the same area (SiNW-HF-T). Additionally, by providing a carbon made conductive back, the etching rate of silicon wafer is enhanced in a particular orientation (SiNW-HF/C). SiNW, SiNW-HF, SiNW-HF-T, and SiNW-HF/C consist of silicon nanowires with average length of 1.6 µm, 3 µm, 7 µm, and 14.4 µm, respectively. Here, two important mechanisms are proposed for utilizing silicon nanowires as terahertz emitter. As terahertz detector, silicon nanowires have few shortcomings. To overcome such difficulties, silicon nanowire-reduced graphene oxide (SiNWHF-T/RGO(s) &SiNW-HF-T/RGO(h)) hybrid is synthesized in different methods. Deposition of RGO on silicon nanowires enhances the roughness to an extent that S. Ghosh · A. Chandra · S. Sarkar · K. K. Chattopadhyay School of Materials Science and Nanotechnology, Jadavpur University, Kolkata 700032, India e-mail: [email protected] A. Chandra e-mail: [email protected] S. Sarkar e-mail: [email protected] K. K. Chattopadhyay (B) Thin Film and Nano Science Laboratory, Department of Physics, Jadavpur University, Kolkata 700032, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Acharyya and P. Das (eds.), Advanced Materials for Future Terahertz Devices, Circuits and Systems, Lecture Notes in Electrical Engineering 727, https://doi.org/10.1007/978-981-33-4489-1_10

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hydrophilic nature of the nanowire is converted into hydrophobic for SiNW-HFT/RGO(s). This material can be utilized as broadband photodetector from visible to terahertz range. Keywords Terahertz · Silicon nanowires · Synthesis · RGO · Wettability

1 Introduction Progress in science and technology has inspired the researchers to utilize the terahertz (THz) frequency gap in electromagnetic (EM) spectrum, properly. It occupies 0.3–10 THz in electromagnetic spectrum [1, 2]. Like all other waves, it can also create pictures and transmit information [2]. As a part of EM wave, the properties of THz are calculated employing Maxwell equations[2, 3]. Generally, conventional electronic devices are inappropriate for generation and coherent detection of terahertz frequency with wavelength from 30 µm to 3 mm, though this wavelength has vast application in industry for product inspection, investigation of defects in tablet coating, spectroscopy, screening, etc., even detection of cancer can be done by this EM wave[1, 4, 5]. So, researchers are now paying their attention to the investigation of such materials which can show a path to the generation and detection of terahertz wave. In nanotechnology, one-dimensional nanostructures like nanowire and nanobelts are essential building blocks for electronic devices in present and future. Nanowire is quasi-1D nanostructure with diameter smaller than 300 nm; also, the length to diameter aspect ratio should be more than ten [6]. It has several advantages like enhanced strain relaxation [7], high surface area-to-volume ratio and efficient light trapping [8, 9], cheap with respect to cost as well as material consumption, etc. Such exclusive properties are responsible for its applications in solar cells [10], photodetector [11], single photon source [12], transistor [13], and nanoscale lasers [14]. Furthermore, this 1D structure can give new insight toward the shape and size effect on different properties [15]. As obtained from literature surveys, few structural parameters of nanowires highly influence the terahertz emission. Diameter, length, distribution of nanowires, vertical alignment, pitch, surface defects are important factors to consider before synthesization of an emitter for terahertz range [16]. To choose appropriate materials as terahertz emitter, different properties such as high absorption coefficient, high saturation velocity, short carrier lifetime and appropriate bandgap, etc., are required to prior analysis. Recently, several direct bandgap or doped semiconducting nanowires are considered as impressive terahertz (THz)radiator. It is primarily due to the combined oscillations of conductive electrons and confinement at the surface of nanostructures resulting in localized surface plasmon (LSP) effect [17–19]. As per previous report of Seletskiy et al., the enhanced emission of THz radiation was observed from free-standing long InAs nanowires (NWs) having length from 10 to 20 µm and diameter 60–450 nm [17]. The report gave the evidence that the low energy acoustic surface plasmon mode of nanowires

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caused the efficient terahertz emission. These modes were also particular for high aspect ratio geometries. There were many reports on InAs [20], InGaAs [16], GaAs [21, 22] nanowires which had been used as efficient terahertz emitter. Photo-Dember effect being one of the primary reasons influences the emission in terahertz range. Apart from this, excitation power, unique geometries with high aspect ratio and pitches, high absorption coefficients and surface plasmons were broadly discussed in those literatures for enhanced terahertz emission. For being indirect bandgap semiconductor, silicon is yet under research for behaving as terahertz emitter. There are few limitations such as small absorption coefficient, low dispersion, high refractive index at terahertz range and high resistivity than other direct bandgap semiconductors. Till now, there are only two reports on silicon nanowires as terahertz emitter [23]. Gyeong Bok Jung et al. had synthesized n-type silicon NWs by metal-assisted chemical etching and studied how the geometry of nanowires could influence the terahertz emission from it [24]. As per the discussion, the maximum emission could be obtained from the nanowires with length of 3 µm which had highest absorption property as in UV-VIS spectra. As the length was increased, the emission in terahertz range got saturated for failing to absorb more photons. This terahertz emission was attributed to photo-Dember mechanism though the effect of excitation pump intensity could not be ignored. Additionally, Hoyer et al. reported black silicon consisting of nanoneedles with diameter 300 nm and height 2 µm. It had behaved as terahertz emitter which was efficient enough as an indirect bandgap semiconductor. Here, the main focus was on the reduction of absorption length or the penetration depth of exciting wavelength in indirect band gap semiconductor by the formation of 1D structure which caused multiple reflections within the surface structure. It had high impact on anisotropy on photo excited charge carriers at the surface; it resulted in enhancement of terahertz emission compared to bulk. Now, two-dimensional sheets like structures (2D) are enriched by its own unique properties. Graphene is one of those rigorously studied materials in 2D [25]. Graphene is well known for its broadband photodetection property from visible to infrared range [26]. As obtained from theoretical explanation, the bandgap variation can extend working spectrum of graphene up to far infrared (FIR) region, even at terahertz range (THz) [27, 28]. From the previous studies, it is observed that reduced graphene oxide (RGO), extracted from graphite by chemical exfoliation, pursues a natural energy gap [29]. The narrow energy gap property of RGO is appropriate as photodetector from mid-infrared (MIR) (2.5–30 µm) to even THz (30–3000 µm) range. As per previous reports of Chitara et al., the NIR (1.55 µm) photodetectors can be achieved by utilizing extensively reduced RGO [30]. There are few limitations of RGO to behave as broadband photo detector, and they are limited by optical absorbance, energy gap of tens of meV. These are not suitable for VIS and NIR photodetection. However, apart from the emission of THz frequency from Si nanowire (SiNW) arrays, they have few advantages as photodetector which can compensate the deficits present in RGO. Si has bandgap of ~1.12 eV which is appropriate for photodetection from VIS to NIR range. Additionally, the vertically grown nanowire array can

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decrease the light reflection intensively over a wide spectral range from VIS to NIR. As a result, light harvesting property of SiNW array is significantly improved. Thus, the hybrid composed of SiNW arrays and RGO can enhance the light harvesting property of device as well as an efficient, broadband photo-response property should be witnessed from THz to VIS, even at NIR range [31]. Cao et al. had introduced RGO and n-type silicon nanowires arrays into a single photodetector heterojunction which had broad photo-response from visible to terahertz region in room temperature [32]. There are various reports on different elongated nanowires which show that nanowires with high length and desired diameter can act as most efficient terahertz emitter than bulk depending on the excitation pump power. In this field, silicon is still under research for its indirect bandgap. Nanostructuring is the only solution to establish silicon in terahertz region. Keeping all these properties in mind, here, silicon nanowires are synthesized utilizing MaCE [33] with the variation of different synthesis parameters to obtain different lengths and diameter which can have high impact on terahertz emission. RGO and silicon nanowire hybrid system which can be employed as broadband photodetector with different efficiencies are also synthesized in two different mechanisms. Important properties are analyzed. Change in wettability with synthesis parameters is an important factor to discuss with surface roughness.

2 Experimental Section 2.1 Synthesis 2.1.1

Synthesis of Silicon Nanowires

Silicon nanowires were synthesized by conventional two-step metal assisted chemical etching (MACE) process employing commercially available p-type silicon wafers (100). Few parameters were optimized to synthesis wire like silicon in nano-range. In the first step, silicon wafers were cleaned by sonication in ethanol and acetone. After that, wafers were immersed in piranha solution to remove organic residues. A layer of oxygen was produced by piranha solution which was removed by 5% HF solution. After every step, wafers were rinsed by de-ionized water (DI). The cleaned wafers were transferred into HF/AgNO3 solution for one minute to deposit silver nanoparticles on the surface. After rinsing, the Si wafers were etched by HF/H2 O2 solution for 60 min. Thereafter, the wafers were dipped into HNO3 to dissolve excess Ag nanoparticles. Thus, silicon nanowires were produced but a thin oxide layer was also generated by HNO3 which was removed by HF solution. In this paper, different parameters were varied during this synthesis process. Two different sets of silicon nanowires were produced with and without the last HF treatment which were termed as SiNW-HF and SiNW, respectively. To investigate the effect of temperature on

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synthesis, one set of sample was etched at 60 °C naming SiNW-HF-T. Additionally, another set of nanowires was generated utilizing carbon tape as catalyst called as SiNW-HF/C.

2.1.2

Synthesis of Silicon Nanowires-Reduced Grapheme Oxide (RGO) Composite

Graphene oxide (GO) was synthesized from graphite powder by modified Hummer’s method. Half part of synthesized GO was reduced hydrothermally (12 h).

2.1.3

SiNW-HF-T/RGO(S)

The hydrothermally produced RGO was sonicated in ethanol and spin coated on SiNW-HF-T forming SiNW-HF-T/RGO(s).

2.1.4

SiNW-HF-T/RGO(H)

Here, the remaining half of synthesized GO was sonicated in DI water for quick dispersion and the solution was transferred into a stainless steel Teflon line autoclave. The SiNW-HF-T was tied in a glass slide keeping etched side bare and front faced. After that, the glass slide was placed inside the autoclave in an inclined manner keeping upside downward. The whole system was kept at 180 °C for 12 h. Thus, the RGO was deposited on SiNW-HF-T successfully which formed SiNW-HF-T/RGO(h).

2.2 Characterizations Morphological study as-synthesized samples was conducted by field emission scanning electron microscopy (FESEM, Hitachi, S-4800). Raman analysis was conducted with the excitation of a 532 nm laser source (WITECH) which could assure the RGO layer formation. To investigate the surface property of nanowires and composites, wettability study was performed using Dataphysics OCA 15EC.

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3 Results and Discussions 3.1 Morphological Analysis To examine the morphologies of as-synthesized silicon nanowires, FESEM is conducted. Figure 1a represents the FESEM image of SiNW confirming the formation of nanowires which are little agglomerated. As the last HF treatment is not performed, SiO2 is not removed from the surface of SiNW. In addition, the distinct nanowires are observed in SiNW-HF as shown in Fig. 1b. Here, the oxide layer originated from nitric acid is washed out by HF acid. To investigate the effect of temperature during etching process, SiNW-HF-T is synthesized. Figure 1c is the top-view FESEM of SiNW-HF-T assuring the perfect realization of nanowires even at high temperature. Carbon catalyst has been used in SiNW-HF/C where carbon tape is fixed at the back side of silicon wafer to examine the activity of carbon as etching catalyst. The proper formation of silicon nanowires is observed in SiNW-HF/C as shown in Fig. 1d. Figure 2 is the cross-sectional FESEM image of silicon nanowires varying different synthesis parameters. SiNW has the length of 500 nm to 2 µm as shown in Fig. 2a, whereas SiNW-HF consists of distinct nanowires with the length of 2–3 µm with more sharpness. Here, HF treatment plays an important role to consider for the changing morphology. Figure 2c is the cross-sectional view of SiNW-HF-T which

Fig. 1 FESEM image (top view) of a SiNW, b SiNW-HF, c SiNW-HF-T, d SiNW-HF/C

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Fig. 2 FESEM image (cross section) of a SiNW, b SiNW-HF, c SiNW-HF-T, d, e SiNW-HF/C

contains longer nanowires than previous two methods with the length of 7–10 µm. Such enlargement of nanowire is the outcome of high-temperature etching process. Temperature eases the oxidation below the silver nanoparticles during synthesis which results in higher rate of etching by HF at 60 °C. As the HF/H2 O2 etching rate rises, wafer can be etched deeper inside with respect to room temperature synthesis. Furthermore, SiNW-HF/C is displayed in Fig. 2d, e in different magnifications which depict the most perfect and homogeneous formation of nanowires with the length of almost 14–14.5 µm. Another synthesis parameter, carbon catalyst is important here to speed up the HF/H2 O2 etching in a more directional way in room temperature without changing itself. It results in most directionally vertical and systematic formation of nanowires with highest length among all the as-synthesized nanowires. Now, another parameter which can be analyzed from FESEM is diameter of the nanowires in different conditions. For high-temperature etching process, SiNW-HF-T has narrower diameter than other samples. The diameter of nanowire for SiNW-HF/C is quite wider than previously synthesized samples. In addition, the diameter is almost constant as we progress from tip to base, i.e., lengthwise. SiNW, SiNW-HF, and SiNW-HF-T have narrow tip and wide base of nanowires. In SiNWHF/C, carbon tape catalyzes the etching reaction in a most directive way which causes the straight formation of homogenous nanowires like physical method.

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Fig. 3 FESEM image of a hydrothermally synthesized RGO (12 h), b SiNW-HF-T/RGO(s), c RGO on hydrothermally (6 h) synthesized SiNW-HF-T/RGO(h), d SiNW-HF-T/RGO(h) hybrid

In the second step, RGO is deposited on HF-treated silicon nanowires etched at high temperature. Here, two different synthesis processes have been followed. Figure 3a is the FESEM image of hydrothermally synthesized RGO which is thin and very fine in nature. This RGO is spin coated on SiNW-HF-T which is shown in Fig. 3b. A successful deposition of fine RGO sheet just above the distinct nanowires is observed. In another synthesis process, GO is reduced hydrothermally (6 h) in the presence of silicon nanowires so that reduction and deposition can occur, simultaneously. Figure 3c depicts the FESEM image of RGO deposited on SiNW-HFTin hydrothermal method. Here, RGO sheet is thicker than previous process. The top-view FESEM of SiNW-HF-T/RGO(h) is represented in Fig. 3d. It shows that RGO sheet wraps the silicon nanowires lengthwise. The nanowires are fully covered by thick layer of RGO sheet; thus, distinct nature of nanowires are modified by amalgamation of each other through the 2D dense sheet.

3.2 Raman Analysis Primarily, Raman spectroscopy is conducted to confirm the formation of RGO in the hybrid system. The Raman spectra of SiNW-HF-T/RGO(s) and SiNW-HF-T/RGO(h) are presented in Fig. 4a, b, respectively. There are Raman active peak at 526 and

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Fig. 4 Raman spectra of a SiNW-HF-T/RGO(s), b SiNW-HF-T/RGO(h)

528 cm−1 for both the hybrid system, and they are mainly first-order transverse optical (TO) phonon mode of the silicon nanowires [34]. Thus, the presence of silicon nanowires can be reassured from the Raman spectroscopy. Besides, the Raman peak situated at 1361 and 1353 cm−1 for both the hybrid correspond to D band (ID ) of graphene which arises due to the presence of defects like corrugation, twisting and edges. Another intense peak at 1602 and 1603 cm−1 of both figures in Fig. 4 is associated to G band (I G ) of graphene which are the contribution of doubly degenerate E 2g phonon modes at the Brillouin zone of the sp2 hybridized carbon network of graphite. The ratio of the intensity of ID and IG (ID /IG ) denotes the average size of sp2 domain. For smaller size of sp2 domain, higher ratio is achieved [35]. This property is observed in RGO for its enhanced aromaticity and delocalization of network. During chemical reduction, sp3 gets diminished while the conjugated graphene network of sp2 carbon atoms is reestablished. Generally, the size of the reestablished network is smaller than the graphite layer which causes the increment of ratio ID /IG . For SiNW-HF-T/RGO(s), the ratio is 1.1, whereas for SiNW-HF-T/RGO(h), it is 1.2. This indicates more number of defects in the hydrothermally synthesized hybrid system. Two small and broad peaks are observed within 2680–2940 cm−1 which are assigned to the D peak and defect activated D + D peak, respectively. The number and coupling between the layers of graphene are correlated with the position and the shape of 2D band [36]. Here, the intensity of 2D peak is weak for both types of chemical synthesis processes though the peak position is consistent with the mechanically exfoliated graphene.

3.3 Wettability Study To study the surface properties, wettability study of sample surface is performed using DI. As observed from Fig. 5a, Si wafer pursues DI contact angle (CA) of 76.1° which depicts that the wafer is hydrophilic in nature. Figure 5b is DI CA on SiNW when the drop touches the surface and it is 40° which also denotes hydrophilic surface

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Fig. 5 DI contact angle on a Si wafer; b, c SiNW; d, e SiNW-HF, f, g SiNW-HF-T, h, i SiNW-HF/C, j SiNW-HF-T/RGO(s), k SiNW-HF-T/RGO(h)

property. Henceforth, the droplet starts to spread out and the CA becomes 12° after ten minutes (after stability). It can be assumed that as the surface is not treated by HF, and the presence of oxide layer is prominent which increases the surface energy of the substrate resulting in highly hydrophilic nature. Surface roughness is also an important property to discuss in wettability study. Wenzel model can be applied for SiNW which transforms the surface of Si more hydrophilic than smooth wafer. It correlates with the high surface roughness property of SiNW [37]. After that, wettability is conducted for SiNW-HF which is presented in Fig. 5d, e. It describes the opposite surface property of SiNW. The initial CA is 130.5° denoting the hydrophobicity, and even after stability, it maintains the angle to be 123.3° which indicates quite stability. After the removal of oxide layer by HF treatment, there is a drastic change in surface property. The surface energy is reduced here. Additionally, air is trapped within nanowires and it prohibits the water spreading. However, the surface roughness can be described by Cassie–Baxter model which is associated with the enhancement of roughness by HF-treated nanowires [38]. The DI CAs on SiNW-HF-T are presented in Fig. 5f, g. The initial CA is 92.17°, and after stability test, it becomes 5°. The water droplet diminishes after certain time describing super hydrophilic property. However, initial CA is hydrophobic in nature but due to the high length and lowest diameter of nanowires, pining effect on DI droplet becomes prominent which eases the spread of water. Thus, morphology is an important factor for fluctuating surface property. Here, surface roughness can be illustrated using Wenzel model [39]. The CAs on SiNW-HF/C are represented in Fig. 5h, i which describe that the surface is hydrophobic in nature with CA of 110° but after certain time (ten minutes), the angle transforms to 71.73° which denotes hydrophilic surface. Thus, a typical surface roughness property is observed where a transformation from Cassie–Baxter

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model to Wenzel model is exhibited. Generally, HF-treated nanowires pursue high CA with hydrophobic property as observed from SiNW-HF. Here, the extremely high length becomes the obstacle to hold the water droplet. Furthermore, the CA is higher for SiNW-HF/C than SiNW-HF-T due to its wide diameter, the surface pinning of nanowire is lower with respect to SiNW-HF-T [37–39]. Figure 5j, k describes the wettability property of SiNW-HF-T/RGO(s) and SiNWHF-T/RGO(h), respectively. Highest water CA of 140.5° is observed for SiNW-HFT/RGO(s), and it symbolizes highly hydrophobic surface with high stability. Thus, the pinning effect of SiNW-HF-T is overcome using the spin-coated RGO sheet. The surface roughness property can be explained by Cassie–Baxter model in this case. For SiNW-HF-T/RGO(h), the CA is 92° which is just hydrophobic. Here, due to the hydrothermal reduction of GO, the surface becomes so uneven that the CA cannot be improved though the stability is achieved.

3.4 Application in Terahertz Frequency Range Emission in terahertz frequency (THz) is dependent on the geometries and aspect ratio of the 1D structure. By increasing the length of silicon nanowires, highly intense THz emission can be achieved. By this nano-structuring process, surface-to-volume ratio is increased which causes improved emission. As obtained from previous literature, ntype silicon nanowires can behave as efficient THz emitter which is length dependent and the length of 3 µm can give the highest emission due to its maximum absorption of photons [24]. Considering the length and diameter of nanowire as important factors, several synthesis parameters are varied to obtain different lengths of nanowires with the maximum of 14.5 µm in this paper. They can be utilized in THz radiation system according to its suitable applications. To analysis the THz emission from silicon nanowires, two basic mechanisms are proposed. They are charge separation by builtin electric field and photo-Dember effect. Charge separation by built-in electric field: GaAs is established as THz emitter by a built-in electric field for its large bandgap and high surface fields. Polarity of the THz wave can also be altered by n- or p-type doping. Silicon has a disadvantage of long penetration depth with low absorption coefficient. By long nanowires, the light absorption property is improved by multiple reflections within the surface structures as shown in Fig. 6a [23]. It eliminates the drawback of large absorption length of photons in the surface. Intentionally, the penetration depth of photon is reduced for this indirect bandgap semiconductor. Thus, the space charge layer and penetration depth both are modified in the same range and photo-induced carrier separation is faster in the space charge layer (l < w) (cf. Fig. 6b). By the irradiation of laser, the photo-excited carriers are accelerated by existing built-in electric field. These carriers can overcome the surface field by hole drift into the bulk and the electron drift toward the surface. Even, dipole oscillations happen among the carriers while waiting for a new balance in which radiation can occur as THz wave.

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Fig. 6 a Multi-reflection within silicon nanowires, as a result, b reduction of penetration depth (l < w) causes overlapping of space charge region and photoexcited carriers, c photo-Dember effect

Photo-Dember Effect: In the base substrate and 1D wires, the anisotropy in the diffusion velocities of the photo-excited electron and hole causes terahertz emission [23]. It is also called photo-Dember effect. The proposed mechanism in silicon nanowires is presented in Fig. 6c. Higher carrier combination and mobility are also important factors for the efficient terahertz emission. In addition, the large change in local potential should be grown for the confinement in the electron–hole pairs in the long and sharp nanowires with high absorption which has high impact on the radiation. InAs is suitable for photo-Dember induced THz emission due to its high electron mobility. Doping does not affect the polarity of emission in this case. Choice of excitation wavelength by suitable pump beam power is very important here. For flawless emission, the penetration depth of the pump beam should be less than the diameter of the nanowires. By analyzing previous literatures and concepts, extended silicon nanowires can be introduced as an efficient terahertz emitter. Either of the mechanisms will be followed for the efficient terahertz emission from the silicon nanowires. Additionally, silicon nanowire MOSFET (SNFET) has a great future in THz integrated circuit application[13, 40]. SiNW-HF-T/RGO hybrid can be employed as broadband photodetector from visible to even THz frequency by varying the bandgap of RGO deposited on nanowire as presented in the diagram of Fig. 7. Fig. 7 Proposed broadband photo-detection by SiNW-HF-T/RGO hybrid

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4 Conclusion It can be concluded that silicon nanowires are successfully synthesized by MACE process varying different conditions. Long nanowires are obtained at hightemperature etching process with sharpest tip. Using carbon tape as catalyst, long nanowires are achieved with wider and constant diameter with respect to other nanowires. Furthermore, HF treatment on nanowires is also an important parameter to discuss. It influences the surface energy and roughness properties which have high impact on wettability. However, long nanowires have adverse effect in holding water droplet on tip which transforms the surface to superhydrophilic in nature. However, the longest nanowires with wide diameter as observed in SiNW-HF/C have both types of wetting properties with time. Using two different synthesis methods, RGO is deposited on silicon nanowires successfully. Important properties have been analyzed. SiNW-HF-T/RGO(s) has highly hydrophobic surface whereas SiNW-HFT/RGO(h) is just hydrophobic in nature with high stability with time. These short to long nanowires can be proposed as efficient terahertz emitter according to its usage due to its special geometry with high absorption property. By proper excitation, the long Si nanowires may compete with the terahertz emitter made of direct bandgap semiconductor nanowires. Here, two important mechanisms are proposed for terahertz emission from silicon nanowires. In future, the emission activity will be experimentally verified. Additionally, silicon nanowires-RGO hybrid can be accomplished as an efficient visible to terahertz broadband photodetector. It has huge application in imaging, remote sensing, photometer, and analytical measurement. Acknowledgements One of us (SG) wishes to thank the Council for Scientific and Industrial Research (CSIR), the Government of India, for providing her a senior research fellowship through “CSIR-SRF” (File no: 09/096(0926)/2018-EMR-I) while other (AC) wants to thank Technical Education Quality Improvement Programme (TEQIP phase III scheme, Jadavpur University) for providing fellowship during the work. The authors wish to acknowledge the University Grants Commission (UGC), the Government of India for the support under the “University with Potential for Excellence (UPE-II)” scheme.

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Analysis of Optical Performance of Dual-Order RAMAN Amplifier Beyond 100 THz Spectrum Rajarshi Dhar, Arpan Deyasi, and Angsuman Sarkar

Abstract Optical performance of dual-order embedded RAMAN amplifier is analyzed for 200–km-long communication system beyond 100 THz spectrum. From the analysis, BER, input and output OSNR, Q-factor are obtained for practical ranges of bit rate under simultaneous applications of co- and counter-propagating pumping lasers. Comparative analysis is carried out with the published data for single-order system, and significance improvement is observed in terms of higher BER, Q-factor and OSNR. For 10 Gbps system, the improvement is maximum; whereas for system with 2.5 Gbps data rate, insignificant development is notified. For all the systems, peak value of Q-factor as well as constancy of gain profile is notified which is critical for implementing the system without incorporation of external amplifier. Keywords Dual-band RAMAN amplifier · Eye diagram · Q-factor · Bit error rate · Input and output OSNR · Bit rate · Fiber length

1 Introduction Like any communication system, optical communication systems also need the requirement of amplification for the faithful transmission and reception of signals. Optical signals and systems mainly deal with the intensity of the waves unlike voltage and current in case of electrical signals. Some optical systems are architecture in such

R. Dhar Department of Electronics and Telecommunication Engineering, IIEST Shibpur, Howrah, India e-mail: [email protected] A. Deyasi (B) Department of Electronics and Communication Engineering, RCC Institute of Information Technology, Kolkata, India e-mail: [email protected] A. Sarkar Department of Electronics and Communication Engineering, Kalyani Govt Engineering College, Kalyani, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Acharyya and P. Das (eds.), Advanced Materials for Future Terahertz Devices, Circuits and Systems, Lecture Notes in Electrical Engineering 727, https://doi.org/10.1007/978-981-33-4489-1_11

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a way that the signals are released with high amplitude at the start of the communication channel so that they are immune to the noises and other signal degradations in the circuit, while other architectures deal with systems where dynamic or distributed amplifications are used so that at regular intervals the signal is amplified. In recent times, extensive research has led to new solutions to achieve nice, significant and stable amplifications in optical technology. Different types of amplifiers starting from basic ones like the semiconductor laser amplifiers or SLAs which are also known as doped amplifiers which are in-line amplifiers to complex ones like the Raman amplifiers [1]. SOAs are mainly classified into two groups—Fabry-Perot amplifiers (FPA) and traveling wave amplifiers (TWA) both of which has their advantages and disadvantages with respect to working principle, operation frequency but find extensive application in the optical industry [2]. With advancements in amplifications, the different components of an optical channel also have gone extensive research like photodiodes, wavelength selective switches, and chromatic dispersion fibers [3]. The different types of optical amplifiers and their explanations are given henceforth.

1.1 Semiconductor Optical Amplifiers (SOA) The structure of an SOA is similar to that of a semiconductor laser. It follows the same principle by which a LASER achieves amplification that is by population inversion between the valence and the conduction bands. It consists of an active medium (a p-n junction) in the form of a waveguide, with a structure much like the stripe geometry laser (Fig. 1). Due to population inversion, the stimulated emission causes the photons to be emitted with greater energy and hence provide amplification to the signal. This in this way an incoming photon can be amplified with the injection of right amount of current into the LASER cavity and achieving the gain [4, 5]. As much as the SOA has significant gain but they are also very noisy devices due to the fact that they are spontaneous emission devices and they also have low gain saturation. They are designed to work both at 1300 and 1550 nm optical windows. The gain factor and the noise figure of the SOAs are given by the following expressions [5] g = Γ gm − aint ,

(1)

where G is the optical confinement factor (the fraction of the propagating signal power confined to the SOA waveguide), gm the material gain, and aint the optical loss coefficient. gm is a function of the injected carrier (electron) density and wavelength, N F = 2 pinv K ,

(2)

where pinv is the effective population inversion parameter and K is the excess noise factor.

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Fig. 1 Schematic structure of semiconductor amplifier

The various nonlinearities of SOAs like cross-phase modulation, cross-talks, fourwave mixing and their applications in optical communications like in designing of optical gates have been discussed in work [6]. Several improvements in SOAs like optical mode profile, low polarization dependence, increased output power, and implementing them in circuits are discussed in other literature [7, 8]. SOAs have proved to be very useful devices in the optical industry and mainly implemented for the amplification of ultra short pulses [5] but with time more robust and faithful amplification systems have been developed like the all-optical EDFA and Raman amplifiers which are now used for long distant optical amplifications.

1.2 Doped Fiber Amplifiers (DFA) DFA or doped fiber amplifiers are the mostly used fiber amplification methods. As the name suggests, the main playing factor here is the doping material which are mainly rare earth metals, among which the most dominant is the erbium (Er3+) along with ytterbium and neodymium. The erbium-doped fiber amplifiers or EDFAs are incorporated with the original communication channel to provide the gain, and thus, they are also one type of in-line amplifiers. The DFAs function accordingly the SOAs, i.e., by the way of amplified spontaneous emission or ASE. Thus, an external pump is required for the amplification by DFAs. The pump provides the necessary

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Fig. 2 Schematic communication diagram with EDFA

power needed for the population inversion. The theoretical explanation of EDFAs is presented in work [9, 10]. There the author has given the basic fundamentals about the erbium ion which is the most crucial part behind the amplification process. The specific quantum numbering of the atom and energy labeling using the Russell– Saunders theory has been described there along with the theoretical energy-level explanation. The different energy emission rates along with their expressions are given. Modeling of EDFA using the propagation and rate equations of a homogeneous, two-level laser medium [11, 12]. The authors have done extensive work starting from the properties of erbium in glass medium and measuring the loss spectrum to the spatial modeling of the same. The spectral properties are also calculated using the numerical method approach for the analysis of cross-talk and other interferences. One of the main drawbacks of EDFAs is that they can only work in the 1550 and 980 nm windows. EDFAs have proved to be extremely effective in the modeling of WDM networks with even more than 100 channels. But for those purposes, the correct pumping schemes and wavelengths are necessary to be known along with the gain and noise profiles of the amplifiers so that noises do not interfere with the signals and all these are done through the numerical approach techniques. Other than this, there are several architectures of the amplifier which provide different gain and noise spectrums; thus, different implementations require different architectures to get good and stable gains. The gain and noise spectrum has been studied in the literature [13] while different architectures like dual-stage quadruple technique to have high gain and low noise figure [10] and the two-stage EDFA for high gain [11] are also reported here. The other rare earth metals like ytterbium, neodymium, and terbium are used along with erbium as another added dopant for the better effectiveness of the amplifiers (Fig. 2).

1.3 Raman Amplifiers Raman amplifiers are the most modern and effective method for optical communication. They work on the principle of stimulated Raman scattering which is one of the nonlinear properties of optics. Work on Raman amplifiers began in the 1970s [14], before the EDFAs, but they did not get enough interest due to the lack of good pumping schemes. Then in the mid-90s the development of good and stable pumping schemes led to renewed interest in Raman amplifiers. The same author, Stolen in one of his later papers have presented his study in the development of

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stimulated Raman scattering in silica single-mode fibers [15]. The theory of Raman amplification includes the development of stokes and anti-stokes signals. The basic energy-level diagram of Raman amplification is given below, The frequencies depicted by ‘f p ’, ‘f s ’, and ‘f a ’ represent pump frequency, stoke frequency, and anti-stokes frequency, respectively. The two energy levels or states that are shown here are the intermediate and ground states. The stokes and the antistokes are equi-distant from the pumping frequency as shown in the following figure. When electrons are energized by the pump, they get excited to the virtual state or the meta-states, then after completion of their life-times in those states, get down to the lower energy states at two different frequencies other than the pumping frequency. They are, respectively, called the stokes frequency and the anti-stokes frequency [16]. The frequency at which the electrons are energized from ground levels to virtual levels, they release their energies to jump back to vibrational states is called the stoke frequency or stokes. The other frequency at which the electrons release their energy to get down to the ground levels after being energized to virtual levels from intermediate states is called the anti-stoke frequency or the anti-stokes. Amplification is achieved when the signal wavelength is equal to the stokes wavelength. Raman amplifiers have found extensive interests in the optical domain because of their flexibility and their equal functioning capabilities in all the three optical domains. Moreover, the flat-gain nature gives them an extra edge over SOAs and EDFAs. Thus, Raman amplifiers are greatly used for WDM and DWDM networks [17]. With proper fiber lengths and pumping architectures, Raman amplifiers can be very effective in optical communication systems.

2 Raman Amplifiers in Details As explained in the previous section, the Raman amplifiers have proven to be extremely effective in all-optical windows. Moreover in the 1550 nm window, the Raman amplifiers can be incorporated with EDFAs for achieving more gain. The study of Raman gain profiles has shown that the gain from Raman amplification is spread over a frequency shift of nearly 40 THz with a peak at around 13 THz. The 13 THz mark in wavelength corresponds to 100 nm [18]. Thus, it is necessary to have a wavelength difference of 100 nm or frequency difference of 13 THz between the signal and pump to achieve good gain from the pump. However, the gain profile in the 1310 nm window shows that the difference must be around 70 nm for effective [19]. The Raman gain profile is shown in the following figure [20]. Raman amplifiers are mainly implemented with the distributed amplification system. The distributed amplification system, as the name suggests, is distributed along the full channel of the optical channel. With the optical losses like fiber loss, nonlinearity loss, the signal is bound to lose power after propagation of some distance; hence, distributed amplification helps in that case to provide an uniform gain to the whole communication channel.

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There are mainly three pumping architecture for the distributed Raman amplifiers—forward pumped or co-pumped, backward-pumped or counter-pumped and bidirectional-pumped or co and counter-pumped. The forward pump architecture causes the signal and the pump to flow in the same direction hence is also called the co-propagating architecture. The backward-pumped architecture has the signal and pump flowing in opposite directions and hence is also called the counter-propagating structure. The bidirectional architecture is the combination of these two architectures. The bidirectional architecture is the most effective method to have maximum flatgain, and hence, this architecture finds great applications in long-haul WDM and DWDM networks [21].

2.1 Higher-Order Pumping One of the major drawbacks in single-order pumping of Raman amplifiers is the signal-pump of the pump-signal cross-talk. This results in additional noise in the channel. Now this drawback can be overcome by the use of bidirectional pumping scheme but in recent methods second- or higher-order pumping schemes are used [22, 23]. This results in greater gain as well as lesser noise and thus improved OSNR [24]. The second-order pumping scheme helps in the improvement of SNR and also reduces double Rayleigh scattering. It helps in pushing the Raman gain further into the channel, and hence, they can be highly beneficial for long-haul networks. The second-order pumping scheme requires the use of another pump in conjunction with the first-order pump but with a frequency difference of about 13.2 THz. The second-order pump can be co-propagated with the first-order pump or can be counter-propagated which depends on the amplification. New schemes of higherorder pumping with multiple pumping seeds in both co- and counter-propagating architectures for the 1550 nm window have been given in the literature [24]. As stated earlier multiple pumping schemes can hugely improve the gain and can be used for long-haul networks which are presented in several works [25–27]. The use of second- and higher-order pumping has been also effective for WDM long-haul networks as has been described the [28–31]. In all these literatures, experimental results have been achieved which are in great agreement with the theoretical ones. The mathematical and the quantitative analyses of the higher-order pumping have been solved extensively along with their advantages in improvement of noise tile in WDM networks [32] and other applications in several domains of optics are reported in works [33–36].

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2.2 Novelty of the Present Work As stated above, the second-order pumping provides a lot of advantages over singleorder pumping in terms of higher and more distributed gain over the whole length of the channel and improved OSNR. The novelty of this work is in the new architecture which has been used for the second-order pumping. We have used second-order pumps in both co- and counter-propagating directions which have provided much higher gains, better OSNR, better Q-factors and low BER as analyzed from the eye diagrams. Another aspect about the novelty of our work lies in the optical window which we have used. All the above literatures have explored the pumping schemes in the 1550 nm window while we have used the 1310 nm window.

3 Results The whole study has been done in the Opti-System Software environment. The simultaneous co- and counter-propagating dual-order structure has been used for the present work. It has been simulated and the said results have been obtained.

3.1 Results Obtained for Second-Order Pumping The following results are obtained at 1310 nm bandwidth. The information signal was kept at a power of 0 dBm and the first-order pump was kept at 1240 nm with a power of 26.02 dBm or 400 mW. The second order was kept at 1170 nm with the same power as the first-order pump. Results include the gain and eye height evolution curves for distance of 200 km for the bit rates of 2.5, 5, 7.5, and 10 Gbps followed by the Q-factor and eye height curves, the eye diagrams taken at distances of 70 and 150 km, respectively, for four aforesaid bit rates. Figure 3 represents gain characteristics of the system simulated over a fiber length of 200 km. From the plot, it can be seen that the nature of the curves are same but differ in values which is very obvious because the gain of the system depends on the bit rate of the system. The values for the 2.5 Gbps system are the maximum among all and decreases when we increase the bit rate because more power is required to send data at more data rates. All the curves show a peak at a distance of about 50–70 km which is the optimum distance of the channel. Above that length, though the gain is significant enough, but the noise figure gradually increases and above 200 km, it completely engulfs the gain. The fall of gain with distance is validated with the fact that more power is required for sending the same data over long distances. Hence, it will be beneficial for the system to be designed for 150 km and then attach distributed amplification after that and again continue for 150 km. Figure 4 shows the evolution of the eye height over the whole span of 200 km.

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Fig. 3 Comparative study of gain characteristics for the dual pump RAMAN amplifier system

Fig. 4 Comparative study of eye heights for different bit rate

Same as the gain curves the shape is the same but the values near the peak point are maximum for the lowest-order bit system with value near to 6 arbitrary units (a.u.). The value of eye height helps on determining the sensitivity of the system, the more the eye height; more easily will be the determination of 1 and 0. Also bigger eye height means that the effect of noise is less; hence, signal has high SNR. With the increase of bit rates, the system becomes more loaded, and hence, the determination of bits becomes difficult with increasing bit rates, which thus gets reflected by decreasing eye height. Figures 5, 6, 7, 8, 9, and 10 show the Q-factor, eye height, and the eye diagram for the 2.5 Gbps system at two distances of 70 and 150 km, respectively. From the Q-factor curves, we can observe that the values remain somewhat same for both the distances, the reason being that the gain is so high that even with great distances the power dissipation is very low. Hence even with the distances being doubled, the Q values are still the same. Both the eye height curve and eye diagrams give

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Fig. 5 Variation of Q-factor with time for 2.5 Gbps data rate for 70 km length

knowledge about the sensitivity of the system. The value decreases when the distance is increased concluding the fact that transmission of signals with increasing distance at same power causes the determination of bits a difficult job for the system hence causes the eye height to decrease. The same is repeated for 7.5 Gbps data rate, and corresponding profiles are shown in Figs. 11, 12, 13, 14, 15, and 16, respectively. From the Q-factor curves, we can observe that the values remain somewhat same for both the distances, the reason being the same as explained above. Both the eye height curve and eye diagrams give knowledge about the sensitivity of the system. The change in values can be validated using the same explanation given before. The other thing that can be observed here is the decreasing eye height as compared to the previous systems. It has been explained before that increase in bit rates causes the eye height to decrease as it increases the load on the channel. On the overall analysis of the Q-factor variations for all the bit rates, it can be seen that as the curve is more spread in case of 2.5 Gbps system while it becomes extremely narrower in case of 10 Gbps system. The reason can be explained as follows. At lower data rates, the storage of energy starts at lower bit period that it does for larger data rates; hence, the Q-factor starts to increase at lower bit periods and is able to maintain it for longer length of the bit period.

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Fig. 6 Variation of Q-factor with time for 2.5 Gbps data rate for 150 km length

Fig. 7 Variation of eye height with time for 2.5 Gbps data rate over 70 km length

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Fig. 8 Variation of eye height with time for 2.5 Gbps data rate over 150 km length

Fig. 9 Eye diagram for 70 m distance with four different data rates

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Fig. 10 Eye diagram for 150 m distance with four different data rates

Fig. 11 Variation of Q-factor with time for 7.5 Gbps data rate for 70 km length

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Fig. 12 Variation of Q-factor with time for 7.5 Gbps data rate for 150 km length

Fig. 13 Variation of eye height with time for 7.5 Gbps data rate for 70 km length

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Fig. 14 Variation of eye height with time for 7.5 Gbps data rate for 150 km length

Fig. 15 Variation of eye diagram with time for 7.5 Gbps data rate for 70 km length

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Fig. 16 Variation of eye diagram with time for 7.5 Gbps data rate for 150 km length

4 Conclusions Simulated findings thus show that dual-order systems can be really beneficial in terms of higher gain and higher Q-factor. Higher gains can lead to the designs of long haul effective systems both for single channel and WDM or DWDM systems. Moreover, the dual-order systems can have better noise figure and hence the effect of noise is significantly reduced. If in place of dual-order systems, higher-order pumping is used with two or three higher-order pumps, the gain is even greater than this system. But such high-order system leads to cost problems as more number of high power pumps lead to higher design and installation cost.

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A Novel Approach Dual Material Double Gate Germanium-Based TFET Jayabrata Goswami, Anuva Ganguly, Aniruddha Ghosal, and J. P. Banerjee

Abstract Modeling and design are carried out of an n-type dual material double gate Tunnel Field Effect Transistor (DMDGTFET) using Ge as a channel material for optimization of the low power device performance parameters like subthershold swing, total gate delay, power dissipation and (On–Off) current ratio, respectively. The energy band diagram, surface potential, and electric field are obtained for on state and off state of the device by the solution of 2D Poisson’s equation utilizing indigenously developed software. The results show that both on current, and (On– Off) current ratio are higher in TFET with Ge than Si as a channel material. In this paper, authors analytically and numerically solved 2D Poisson’s equation for the optimization of low power device performance parameters by changing the channel length from 20 to 30 nm and gate oxide thickness from 2 to 5 nm, respectively. The device performance parameters such as subthershold swing, (On–Off) current ratio, total gate delay, and power dissipation are found 15 mV/decade, 2.190 × 106 , 7.8 ps and 2.44 fW at channel length 20 nm and gate oxide thickness 2 nm, respectively. Thus, dual material double gate germanium-based TFETs are promising next generation devices for ultra large scale integration as well as low power digital system. Keywords DMDGTFET · (on–off) current ratio · Total gate delay · Power dissipation

J. Goswami (B) · A. Ganguly · A. Ghosal · J. P. Banerjee Institute of Radio Physics and Electronics, University of Calcutta, 92, APC Road, Kolkata 700009, India e-mail: [email protected] A. Ganguly e-mail: [email protected] A. Ghosal e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 A. Acharyya and P. Das (eds.), Advanced Materials for Future Terahertz Devices, Circuits and Systems, Lecture Notes in Electrical Engineering 727, https://doi.org/10.1007/978-981-33-4489-1_12

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1 Introduction The ordinary MOSFETs are coming to its restrictions, so researchers and engineers are trying to find modern concepts to replacement the ordinary Metal–Oxide– Semiconductor Field Effect Transistor (MOSFET).The main driving force of present research work is to overcome the restriction of MOSFET in ultra large scale integration (ULSI) circuit through the use of novel transistors like TFET [1–3]. The channel length of TFETs can be reduced as low as 20 nm to fulfill the latest standard of international technology roadmap of semiconductors (ITRS) [4]. The research is pointed to improve the performance potential of this transistor, where the carriers are produced by the method of interband tunneling. These scaled down tunnel transistors serves the reason of ULSI integration with very high speed and memory [5]. The prerequisites of modern device technology are difficult for digital switching. The switching device should be recognize between the logical “0” and “1” of the device, i.e., off state and on current should vary by a few orders of magnitudes. Moreover, the speed of digital switching ought to be high which depends on a few factors. In this respect, the researchers are constrained to replace CMOS by tunnel field–effect transistors (TFETs) [6].The TFETs have received much consideration recently since of its (a) much better control of gate over the channel, (b) less susceptibility to short channel effect (SCE), (c) superior performance as regards (On–Off) current ratio and sub-threshold slope. The optimization of structural parameters of TFET is needed to achieve the higher (On–Off) current ratio and lower subthershold slope with minimum leakage current. The performances of TFET over CMOS transistors are: (a) On state current within the extend of hundreds of milliamperes, (b) subthershold slope distant underneath 60 mV per decade, (c) (On–Off) current ratio >105 and (d) drain voltage