Optoelectronic Properties of Graphene-Based van der Waals Hybrids [1st ed.] 9783030596262, 9783030596279

Table of contents :
Front Matter ....Pages i-xxii
Introduction (Kallol Roy)....Pages 1-11
Review: Electronic Band Structure and Interface Properties (Kallol Roy)....Pages 13-36
Review: Optoelectronic Response and van der Waals Materials (Kallol Roy)....Pages 37-77
Experimental Techniques, Instruments, and Cryostat (Kallol Roy)....Pages 79-121
Material and Heterostructure Interface Characterization (Kallol Roy)....Pages 123-139
Photoresponse in Graphene-on-MoS\(_2\) Heterostructures (Kallol Roy)....Pages 141-156
Switching Operation with Graphene-on-MoS\(_2\) Heterostructures (Kallol Roy)....Pages 157-170
Bilayer-Graphene-on-MoS\(_2\) Heterostructures: Channel Bandgap, Transconductance, and Noise (Kallol Roy)....Pages 171-189
Photoresponse and Photon Noise in Bilayer-Graphene-MoS\(_2\) Hybrids (Kallol Roy)....Pages 191-205
Number Resolved Single Photon Detection (Kallol Roy)....Pages 207-228
Various Graphene, MoS\(_{{2}}\) Devices and Room Temperature Operations (Kallol Roy)....Pages 229-236
Conclusion and Outlook (Kallol Roy)....Pages 237-245
Back Matter ....Pages 247-264

Citation preview

Springer Theses Recognizing Outstanding Ph.D. Research

Kallol Roy

Optoelectronic Properties of Graphene-Based van der Waals Hybrids

Springer Theses Recognizing Outstanding Ph.D. Research

Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists.

Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria • They must be written in good English. • The topic should fall within the confines of Chemistry, Physics, Earth Sciences, Engineering and related interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • If the thesis includes previously published material, permission to reproduce this must be gained from the respective copyright holder. • They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the significance of its content. • The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field.

More information about this series at http://www.springer.com/series/8790

Kallol Roy

Optoelectronic Properties of Graphene-Based van der Waals Hybrids Doctoral Thesis accepted by Indian Institute of Science, Bangalore, India

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Author Dr. Kallol Roy Department of Physics Indian Institute of Science Bangalore, India

Supervisor Prof. Arindam Ghosh Department of Physics Indian Institute of Science Bangalore, India

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-3-030-59626-2 ISBN 978-3-030-59627-9 (eBook) https://doi.org/10.1007/978-3-030-59627-9 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved 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 Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To Maa, Baba, Rituparna, Rimjhim, family and friends, Arindam da, and all teachers

Supervisor’s Foreword

Light-matter interaction in a solid is at the heart of optoelectronics where incident light causes the flow of electricity, or conversely, the charge carriers of opposite signs combine to produce light. Efficient conversion of light into electricity, and vice versa, are essential requirements for photovoltaic devices, light-emitting diodes and optical sensors, and even the emerging domain of quantum technologies through the realization of single photon emitters and detectors. While silicon and other bulk semiconductors are traditional backbones of optoelectronic devices and sensors, a quest for newer material aims to revolutionize our perception of functional optoelectronics. The discovery of graphene in 2004, and subsequently that of the atomically thin semiconductors from transition metal chalcogenides in 2009, triggered an unprecedented global activity in material science. Many of the chalcogenides possess an outstanding ability to absorb light even when the thickness is reduced to a single molecular layer. This led to excellent optoelectronic performance, and the foundation of flexible optoelectronics was laid. Yet, the true paradigm shift in device functionality came with the advent of van der Waals heterostructures, where atomically thin sheets of two or more dissimilar materials were brought within sub-nanometer distance. Although originally the van der Waals heterostructures were employed to enhance electronic transport in graphene transistors, it did not take long to realize that this unique bottom-up material synthesis protocol can yield a new genre of devices with unprecedented performance and control. The Ph.D. thesis of Dr. Kallol Roy, titled ‘Optoelectronic properties of graphene-based van der Waals hybrids’, is the one of the first demonstrations of the immense power of van der Waals heterostructures, where a binary hybrid of graphene and molybdenum di-sulphide (MoS2) is shown to be nearly ten orders of magnitude more efficient in converting light into electricity than typical bulk semiconductors. The crucial ingredient of the light-matter interaction in graphene/MoS2 hybrids is the inter-layer charge transfer across the interface when it is illuminated with visible light. The exceptional photo-responsivity arises as a result of massive optical gain because the transferred charge (electron) that contributes to current in graphene, circulates over a billion times in the circuit before it can recombine with the vii

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holes left behind in the MoS2 layer. The key novelty of the hybrid-based optoelectronic architecture outlined in this thesis lies in that it combines the graphene and the chalcogen layer to exploit the ‘best of both worlds’, namely, the high electronic mobility of graphene and the strong light absorption by the chalcogenide layer. The work also raises serious questions on the mechanism of charge transfer across van der Waals interfaces, which is relevant not just to optoelectronics, but to a plethora of other device concepts with van der Waals heterostructures. When Dr. Kallol Roy started research for the Ph.D. degree the technology to realize van der Waals heterostructure was at its infancy. It has thus been a rather steep learning process, for both him and me (the beneficiaries of which include subsequent generations of students and postdocs in my laboratory), motivated to create heterostructures with clean atomic interfaces. The initial part of the thesis provides a fascinating in-depth description of a purely homebuilt system, centered around an existing optical microscope, that performs this task with great control and versatility. The fruits of this versatility are apparent in the latter part of the thesis where Dr. Roy builds far more complex heterostructures with sequential overlaying of five or more separate layers. The purpose has been to extend the capability of his hybrid optoelectronic devices to the ultimate sensitivity limit and realize single photon detection with these. By using gapped bilayer graphene to capture the photo-generated electron transferred from MoS2, and thereby greatly reducing the dark current and noise, he demonstrates a photon counter with single-shot current measurements. The thesis explains how such devices function as a number-resolving single photon detector, which has been a precious goal for secured quantum information transfer protocols. Dr. Kallol Roy’s thesis is an exciting exposition of how novel material synthesis, innovative instrumentation and careful measurements can be combined to nucleate a new paradigm in on-chip material engineering. Configuring exotic device functionality and simulating fundamental concepts with van der Waals heterostructures have progressed in dramatic pace during the past few years. In that context, this thesis will provide an early perspective to the newcomers as well as experts in the field alike. Bangalore, India

Arindam Ghosh

Abstract

Light-matter interactions in atomically thin van der Waals materials have attracted significant attention in the recent days [1–8]. Although the thickness does not exceed few nanometers, such atomically thin materials alone or in combination with other nanostructures show exciting and unexpected photodetection properties [9– 18]. Fabrication of atomically sharp junctions can be achieved with 2D van der Waals heterostructures, which significantly enhances the scope to design a new type of physical systems, where novel phenomena can be studied [17, 19–23]. Heterostructures also combine properties of dissimilar materials resulting in improved device performances and hence, can be applied to multiple fields [24–26]. This thesis encompasses photoresponse study of various atomically thin heterostructures made of graphene, bilayer-graphene (BLG) and MoS2. A graphene-on-MoS2 heterostructure, made of monolayer graphene and few atomic layers of MoS2, combine superior electronic transport properties of graphene with the optical properties of MoS2. Such hybrids exhibit enormous photoresponsivity, with values as high as  1010 A W-1 at  130 K and  108 A W-1 at room temperature, which make these the most photoresponsive material available till date. The presence of tunable persistent photoresponse allows these to function as optoelectronic memory devices, where the persistent state shows a near perfect charge retention within the experimental time scale of operation (  12 hrs). Noise-free large-gain (109 1010 ) mechanism is one of the salient features of graphene-MoS2 hybrids. Devices made from BLG-on-MoS2 hybrids further help in improving the photoresponsive gain in these devices, and a large photoresponsivity (  109 A W-1) is maintained even when operating these devices at low channel bias (V DS \ 50 mV), or at a low range of channel current (I DS \ 10 nA). In an optimized operating condition, where circuit noise is lower than the signal from a single photoelectron, BLG-on-MoS2 devices function as a number resolved single photon detector. High specific detectivity and low noise equivalent power of these devices allow investigation of photon noise present in an optical source.

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Along with the optoelectronic property study, various optical and electrical characterizations are adapted that explain the interface properties of graphene-MoS2 heterostructures. For example, Raman spectroscopy and photoluminescence study at the interface suggest strong interlayer coupling and efficient dissociation of excitons, respectively, which play a key role in attaining large photoresponse. Interfacial barrier characteristics are also investigated in a vertical graphene-MoS2 geometry, which shows that the barrier height can be tuned by applying an electrostatic field. Various experimental techniques and instruments, such as heterostructure fabrication technique and setup, optical cryostat, etc., were developed in house to accomplish experimental investigation, which are discussed in details. The results of photoresponse study in van der Waals materials have opened up the possibility of designing a new class of photosensitive devices which can be utilized in various optoelectronic applications such as in biomedical sensing, astronomical sensing, optical communications, optical quantum information processing and in applications where low-intensity photodetection and number resolved single photon detection attracts tremendous interest.

References 1. Koppens FHL et al. (2014) Photodetectors based on graphene, other two-dimensional materials and hybrid systems. Nat Nanotechnol 9:780–793 2. Wang QH, Kalantar-Zadeh K, Kis A, Coleman JN, Strano MS (2012) Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat Nanotechnol 7:699– 712 3. Sun Z, Chang H (2014) Graphene and graphene-like two-dimensional materials in photodetection: mechanisms and methodology. ACS Nano 8:4133–4156 4. Li J, Niu L, Zheng Z, Yan F (2014) Photosensitive graphene transistors. Adv Mater 26:5239– 5273 5. Mak KF, Shan J (2016) Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat Photonics 10:216–226 6. Sun Z, Martinez A, Wang F (2016) Optical modulators with 2D layered materials. Nat Photonics 10:227–238 7. Long M, Wang P, Fang H, Hu W (2019) Progress, challenges, and opportunities for 2D material based photodetectors. Adv Funct Mater 29:1–28 8. Bertolazzi S et al. (2019) Nonvolatile memories based on graphene and related 2D materials. Adv Mater 31:1–35 9. Ci L et al. (2010) Atomic layers of hybridized boron nitride and graphene domains. Nat Mater 9:430–435 10. Lopez-Sanchez O, Lembke D, Kayci M, Radenovic A, Kis A (2013) Ultrasensitive photodetectors based on monolayer MoS2 . Nat Nanotechnol 8:497–501 11. Konstantatos G et al. Hybrid graphene-quantum dot phototransistors with ultrahigh gain. Nat Nanotechnol 7:363–368 12. Hong X et al. (2014) Ultrafast charge transfer in atomically thin MoS2 /WS2 heterostructures. Nat Nanotechnol 9:682–686 13. Xia F, Mueller T, Lin Y-M, Valdes-Garcia A, Avouris P (2009) Ultrafast graphene photodetector. Nat Nanotechnol 4:839–843

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14. Massicotte M et al. (2015) Picosecond photoresponse in van der Waals heterostructures. Nat Nanotechnol 11:42–46 15. Mueller T, Xia F, Avouris P (2010) Graphene photodetectors for high-speed optical communications. Nat Photonics 4:297–301 16. Yu WJ et al. (2013) Highly efficient gate-tunable photocurrent generation in vertical heterostructures of layered materials. Nat Nanotechnol 8:952–958 17. Britnell L, et al. (2013) Strong light-matter interactions in heterostructures of atomically thin films. Sci 340:1311–1314 18. Gabor NM et al. (2011) Hot carrier-assisted intrinsic photoresponse in graphene. Sci 334:648– 652 19. Gorbachev RV et al. (2012) Strong Coulomb drag and broken symmetry in double-layer graphene. Nat Phys 8:896–901 20. Kou L, et al. (2014) Robust 2D topological insulators in van der waals heterostructures. ACS Nano 8:10448–10454 21. Ubrig N et al. (2020) Design of van der Waals interfaces for broad-spectrum optoelectronics. Nat Mater 19:299–304 22. Cao Y, et al. (2018) Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nat 556:80–84 23. Cao Y, et al. (2018) Unconventional superconductivity in magic-angle graphene superlattices. Nat 556:43–50 24. Dean CR, et al. (2010) Boron nitride substrates for high-quality graphene electronics. Nat Nanotechnol 5:722–726 25. Levendorf MP, et al. (2012) Graphene and boron nitride lateral heterostructures for atomically thin circuitry. Nat 488:627–632 26. Geim aK, Grigorieva IV (2013) Van der Waals heterostructures. Nat 499:419–425

Publications Related to This Thesis 1. K. Roy, T. Ahmed, H. Dubey, T. P. Sai, R. Kashid, M. Shruti, K. Hsieh, S. Shamim, A. Ghosh. “Number-resolved single photon detection with ultra-low noise van der Waals hybrid.” Advanced Materials 30, 1704412 (2018). 2. K. Roy, M. Padmanabhan, S. Goswami, T. P. Sai, G. Ramalingam, S. Raghavan, and A. Ghosh. “Graphene-MoS2 hybrid structures for multifunctional photoresponsive memory devices.” Nature Nanotechnology 8, 826–830 (2013). 3. K. Roy, M. Padmanabhan, S. Goswami, T. P. Sai, S. Kaushal, and A. Ghosh. “Optically active heterostructures of graphene and ultrathin MoS2 .” Solid State Communications 175-176, 35–42 (2013). 4. M. Padmanabhan, K. Roy, G. Ramalingam, S. Raghavan, and A. Ghosh. “Electrochemical Integration of Graphene with Light-Absorbing Copper-Based Thin Films.” The Journal of Physical Chemistry C 116, 1200–1204 (2012). Conference Papers 1. M. Padmanabhan, K. Roy, S. Goswami, T. P. Sai, G. Ramalingam, S. Kaushal, S. Raghavan, and A. Ghosh. “Optoelectronic Properties of Graphene-MoS2 Hybrid.” MRS Proceedings 1505 (2013) (https://doi.org/10.1557/opl.2013.477). Book Chapter Contribution 1. M. A. Aamir, T. Ahmed, K. Hsieh, S. Islam, P. Karnatak, R. Kashid, P. S. Mahapatra, J. Mishra, T. Paul, A. Pradhan, K. Roy, A. Sahoo, A. Ghosh. “Chapter-5: 2D van der Waals Hybrid: Structures, Properties and Devices”, 2-D Inorganic Materials beyond Graphene. Edited by Prof. C. N. R. Rao, Prof. U. V. Waghmare, World Scientific (Europe), 169–238 (2017) https://doi. org/10.1142/9781786342706_0005.

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Acknowledgements

I express my sincere gratitude to my research supervisor Prof. Arindam Ghosh (AG) for his constant support and guidance throughout my term as an Integrated Ph.D. student in Indian Institute of Science (IISc), Bangalore, India. I am thankful to Prof. AG for giving me the opportunity to work in his Low-temperature Nano-electronics Group. All the works presented in my doctoral thesis were conceived and concluded in this lab itself. I am very much thankful to Dr. Medini Padmanabhan. I bagged an opportunity to work with her during the first 3 years as a research scholar. Strong collaboration with her has furnished results which have become primary building blocks of this thesis. My sincere thanks to all the lab members including Dr. T. Phanindra Sai, Dr. Srijit Goswami, Dr. Ranjit Kashid, Dr. Jayanta Kr. Mishra, Tanweer Ahmed, Avradip Pradhan, Subhamoy Ghatak, Saquib Shamim, Vidya Kochat, Paritosh Karnatk, Mohammed Ali Aamir, Anindita Sahoo, Kimberly Hsieh Sui Mee, Tathagata Paul, Phanibhusam Singha Mahapatra, Semonti Bhattacharyya, Saurav Islam, Harshit Dubey, Pranav Mundada, Dr. Mitali Banerjee, Dr. Amrita Singh, Dr. Atindra Nath Pal, Dr. Chandni U, Dr. Koushik R, Dr. Mohana Sundaram, Dr. Soumik Mukhopadhyay, Sneha Eashwer, Anupam Ghosh, Uma Maheswari, Reema Natu, Bhargava Thyagarajan, Ashwani Kumar, Priyamvada Bhaskar, Irfan Ansari, Dr. Bhupendra Kumar Sharma, Ojasvi Khare, Amogh Kinikar, Aditya Jayaraman, Saloni Kakkar, Bhaskar Ghawri for their support and collaboration. My earnest thanks to Prof. Ambarish Ghosh (CeNSE, Physics, IISc), Prof. Srinivasan Raghavan (CeNSE, ME, IISc), Debadrita Paria (CeNSE, IISc), Gopalakrishnan Ramalingam (ME, IISc) for multiple fruitful collaborations. My sincere thanks to the Department of Physics, Centre for Nano Science and Engineering (CeNSE), Centre for Cryogenic Technology (CCT) of IISc for facilitating research-friendly infrastructures and resources. I am thankful to the workshop engineer of Physics Department, Mr. Shariff, who assisted building many experimental setups which were needed for my doctoral research. My earnest gratitude to all the professors of Physics Department and other departments of IISc, who taught us various courses. I also thank all my professors, xv

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teachers, and tutors from my college and schools. Their guidance and motivation helped me shaping my academic carrier. I acknowledge the support provided by the office staffs of Physics, administration and finance departments of IISc. I am thankful to our lab secretaries for making our life easier by keeping track of ordered instruments, lab items, etc. My earnest thanks to all the IISc committees who are constantly working and maintaining a research-friendly livable campus. My sincere thanks to Prof. Chris Ford (Cambridge University) for CryoMeas. CryoMeas has been a very useful software (written in NI LabView platform) for interfacing instruments and collection of experimental data seamlessly. My sincere thanks to my research supervisor Prof. Arindam Ghosh for his suggestions which helped me improve the presentation style and layout of this thesis. My earnest thanks to the thesis reviewers for their comments. I also thank Saurav Islam, Saquib Shamim, Tanweer Ahmed, Phanibhusan Singha Mahapatra, Avradip Pradhan, Tathagata Paul, Saloni Kakkar, Bhaskar Ghawri, Rituparna Ghosh and Smt. Sunanda Vinayachandran (APC, IISc) for their useful comments. I acknowledge the fully funded Integrated Ph.D. program of Indian Institute of Science, Bangalore, India, for providing the opportunity to pursue an academic research carrier. I also acknowledge the GARP funding of Indian Institute of Science and travel grant from the Department of Science and Technology, India, for funding academic visit to an international conference during my Ph.D. tenure. Without the support from my family and friends, it would not have been possible to follow my dream of pursuing research! My deepest gratitude to all my family members for their unconditional love and support. Thanks to all my friends from my institute, college, school and native for their support and love.

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 2D van der Waals Materials . . . . . . . . . 1.2 Van der Waals Heterostructures . . . . . . . 1.3 Scope of the Thesis . . . . . . . . . . . . . . . . 1.4 Thesis Layout . . . . . . . . . . . . . . . . . . . . 1.5 Device Types and Measurement Scheme References . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Review: Electronic Band Structure and Interface Properties . . . 2.1 Electronic Properties of Graphene, Bilayer Graphene, MoS2 , and BN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Bilayer Graphene . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Boron Nitride (BN) . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Molybdenum Disulfide (MoS2 ) . . . . . . . . . . . . . . . 2.2 Few Physical Phenomena Related to van der Waals Hybrid Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Mutual Interactions Between van der Waals Materials in Hybrids . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 2D Interface Characteristics and Schottky Barrier . . 2.2.3 Charge Transfer, Exciton Dynamics, and vdW-Interface . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review: Optoelectronic Response and van der Waals Materials . 3.1 Mechanism to Detect Light . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Photoconducting Effect . . . . . . . . . . . . . . . . . . . . . 3.1.2 Photovoltaic Effect . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Photothermoelectric Effect . . . . . . . . . . . . . . . . . . . 3.1.4 Bolometric Effect . . . . . . . . . . . . . . . . . . . . . . . . .

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3.1.5 Plasma Wave Assisted Photo Detection . . . . . . . . 3.1.6 Photogating Effect . . . . . . . . . . . . . . . . . . . . . . . 3.2 Photodetection Parameters . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Photoresponsivity . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Noise Equivalent Power . . . . . . . . . . . . . . . . . . . 3.2.3 Specific Detectivity . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Linear Dynamic Range . . . . . . . . . . . . . . . . . . . . 3.3 Noise Mechanisms in Photodetectors . . . . . . . . . . . . . . . . 3.3.1 Photon Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Photoelectron Noise . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Gain Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Receiver Circuit Noise . . . . . . . . . . . . . . . . . . . . 3.4 Physics of Persistent Photoresponse . . . . . . . . . . . . . . . . . 3.5 Photoresponse in Silicon and Non-silicon Materials . . . . . 3.5.1 Limitation and Scope with Group-IV Elements . . . 3.5.2 Extremely Low Intensity Optical Detection . . . . . 3.5.3 Non-silicon Photodetectors and Nanostructured Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Single Photon Detectors . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Single Photon Detector and Quantum Information Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Various Types of Single Photon Detectors . . . . . . 3.7 Photodetection with van der Waals Materials . . . . . . . . . . 3.7.1 Graphene Based Photodetectors . . . . . . . . . . . . . . 3.7.2 Photoresponse in Atomically Thin MoS2 . . . . . . . 3.7.3 Photoresponse in van der Waals Hybrids . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

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Experimental Techniques, Instruments, and Cryostat . . . . . . . . . 4.1 Van der Waals Heterostructure Fabrication Technique and Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Mechanical Cleaving, Substrate Roughness, and Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Optical Contrast and Layer Number Identification . 4.1.3 Heterostructure Fabrication Technique and Setup . . 4.2 Device Packaging Issue and Solution . . . . . . . . . . . . . . . . . 4.3 Optical Cryostat Design for Opto-Electronic Measurements . 4.3.1 Design-1: Optical Cryostat with Cold Finger . . . . . 4.3.2 Design-2: Optical Cryostat with Cold Finger and Radiation Shield . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Design-3: Flow Type Optical Cryostat . . . . . . . . . . 4.3.4 Optical Source and Light Coupling Units . . . . . . . . 4.3.5 Electrical Connection Layout and Control Units . . . 4.3.6 Calibration Unit . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.3.7 Spectral Response of LEDs . . . . . . . . . . . . . . . 4.3.8 Intensity Profile and Uniformity of Light Beam 4.3.9 Power Calibration . . . . . . . . . . . . . . . . . . . . . . 4.3.10 Achievable Low Temperature . . . . . . . . . . . . . 4.4 Instrument Interfacing, Data Acquisition and Analysis . . 4.4.1 Instrument Interfacing . . . . . . . . . . . . . . . . . . . 4.4.2 CryoMeas script to take data . . . . . . . . . . . . . . 4.4.3 Photocurrent at Different Top and Back Gate Voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 LabTalk script and data analysis . . . . . . . . . . . 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

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Material and Heterostructure Interface Characterization . . . . . 5.1 Raman Spectroscopy of Graphene and Bilayer Graphene . . 5.2 Raman Spectroscopy of MoS2 : Layer Number Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Interlayer Coupling and Exciton Dissociation at Graphene-MoS2 Interface . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Surface Topography of Graphene-MoS2 Hybrid . . . . . . . . 5.5 Tunable Barrier at Graphene-MoS2 Interface . . . . . . . . . . . 5.6 Tunable Electronic Properties of graphene and MoS2 . . . . 5.7 Graphene-on-MoS2 Substrate . . . . . . . . . . . . . . . . . . . . . . 5.8 Residual Doping and Barrier Formation in graphene-MoS2 Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Wavelength Dependent Photocurrent . . . . . . . . . . . . . . . . 5.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photoresponse in Graphene-on-MoS2 Heterostructures . . . . . 6.1 Controlled Photoresponse Study in Bare graphene and MoS2 Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Photoresponse in Graphene-on-MoS2 Hybrid . . . . . . . . 6.3 Charge Transfer and Photogating in Graphene-on-MoS2 Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Effect of Static Field (E) on Photocurrent (IP ) . . . . . . . . 6.5 Photoresponsivity (c) Estimation . . . . . . . . . . . . . . . . . 6.6 QE (g) and Gain (G) of Graphene-on-MoS2 Hybrids . . . 6.6.1 Quantum Efficiency (g) Estimation . . . . . . . . . 6.6.2 Photogain in Graphene-on-MoS2 Devices . . . . . 6.7 Photoresponse Versus Carrier Transit Time . . . . . . . . . 6.8 Photodoping Versus Charge Carrier Dynamics . . . . . . .

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125 128 129 131 133

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6.9

Excitation Bias and Illumination Power Dependent Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 6.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

7

Switching Operation with Graphene-on-MoS2 Heterostructures . 7.1 Basic Switching Operation . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Persistent Photoresponse and Reset Operation . . . . . . . . . . . 7.3 Optoelectronic Memory Operation . . . . . . . . . . . . . . . . . . . 7.3.1 Electrostatic field controlled switching . . . . . . . . . . 7.3.2 Intensity controlled switching . . . . . . . . . . . . . . . . 7.4 PPC Dynamics and Near Perfect Charge Retention . . . . . . . 7.5 Charge Carrier Dynamics and PPC . . . . . . . . . . . . . . . . . . 7.6 Scalability of Graphene-on-MoS2 FETs . . . . . . . . . . . . . . . 7.7 Room Temperature Operation and Long Time Cycles . . . . . 7.8 Theoretical Modelling of PPC . . . . . . . . . . . . . . . . . . . . . . 7.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

Bilayer-Graphene-on-MoS2 Heterostructures: Channel Bandgap, Transconductance, and Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Bandgap, Transfer Characteristics and Transconductance . . . 8.1.1 Photogating Effect, Transconductance and Dark Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 Bilayer Graphene and Channel Bandgap (Eg ) . . . . . 8.1.3 Dual Gated BLG-on-MoS2 Heterostructure . . . . . . 8.1.4 Transfer Characteristics of a Dual Gated BLG-on-MoS2 Device . . . . . . . . . . . . . . . . . . . . . 8.1.5 Transconductance, Mobility and Number Density . . 8.2 Gate Capacitance, Excitation Bias and Excitation Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Topgate Capacitance and Excitation Bias (VDS ) . . . 8.2.2 Excitation Frequency Versus Transfer Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.3 Channel Impedance and Phase . . . . . . . . . . . . . . . 8.3 Low Frequency Noise Characteristics . . . . . . . . . . . . . . . . . 8.3.1 Temporal Evolution of IDS and Power Spectral Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Evolution of Noise with Gate Voltage and Frequency Bandwidth . . . . . . . . . . . . . . . . . . . 8.3.3 Noise and Excitation Current . . . . . . . . . . . . . . . . . 8.3.4 Normalized Noise and Mobility Fluctuation . . . . . . 8.3.5 Dark Noise Versus Single Electron Signal . . . . . . .

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157 157 159 160 161 161 162 163 165 166 166 169 170

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xxi

8.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 9

Photoresponse and Photon Noise in Bilayer-Graphene-MoS2 Hybrids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Photoresponse Characteristics . . . . . . . . . . . . . . . . . . . . . . . 9.1.1 Photocurrent Evolution with Gate Electric Fields . . 9.1.2 Photoresponsivity in BLG-on-MoS2 Device . . . . . . 9.1.3 Illumination Power and Photoresponse . . . . . . . . . . 9.1.4 Excitation Bias and Non-linear Response . . . . . . . . 9.1.5 Quantum Efficiency (QE) of BLG-on-MoS2 . . . . . . 9.1.6 Thermal and Shot Noise Limited Noise Equivalent Power and Specific Detectivity . . . . . . . . . . . . . . . 9.2 Photon Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Photon Absorption and Receiver Circuit Noise . . . . 9.2.2 Illumination Power and Spectral Density of Noise . 9.2.3 Photon Noise, Dark Noise and Gate Electic Fields . 9.2.4 Photon Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.5 NEP and D from Photon Noise . . . . . . . . . . . . . . 9.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 Number Resolved Single Photon Detection . . . . . . . . . . . . . 10.1 Fundamentals of Graphene-on-MoS2 Detectors . . . . . . 10.2 Single Photon Detector Design . . . . . . . . . . . . . . . . . 10.3 Photon Counting Methods and Expectations . . . . . . . . 10.4 Light Pulse Calibration . . . . . . . . . . . . . . . . . . . . . . . 10.5 Performance Verification and Dark Noise . . . . . . . . . . 10.6 Finding Resetting Criteria . . . . . . . . . . . . . . . . . . . . . 10.7 Photon Counting Setup . . . . . . . . . . . . . . . . . . . . . . . 10.8 Number Resolved Detection of Photon . . . . . . . . . . . . 10.9 No-Count and Dark Count Events . . . . . . . . . . . . . . . 10.10 Comparison Between Various Single Photon Detectors 10.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . .

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. . . . . . . . . . . . .

11 Various Graphene, MoS2 Devices and Room Temperature Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Thickness Dependent Photoresponse in Thin MoS2 . . . . . . . 11.2 Large Area Graphene-MoS2 Detector and Room Temperature Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Vertical Phototransistor with Graphene-MoS2 -Graphene Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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xxii

Contents

12 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.1 Highlights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1.2 Photoresponse Characteristics and Key Results . . . . 12.1.3 Experimental Techniques and Interface Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.1 Exciton Dynamics at Graphene-MoS2 Interface . . . 12.2.2 Time Resolved Photocurrent and Detection Speed . 12.2.3 Absolute Absorption and Photoresponse in Atomically Thin Heterostructures . . . . . . . . . . . . . 12.2.4 Plasmonic Coupling of Light in Heterostructures . . 12.2.5 Photoelectron Noise Mechanism in Graphene-MoS2 Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2.6 Beyond MoS2 and Beyond Planar Structures . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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237 237 237 237

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240 241 241 242

. . 242 . . 242 . . 243 . . 244 . . 244

Appendix A: Instruments, Sample Noise, and Ground Mixing . . . . . . . . 247 Appendix B: Electrochemically Grown Photoactive Material on Large Area Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

Chapter 1

Introduction

1.1 2D van der Waals Materials Simple experimental demonstrations of the existence of atomically thin stable semimetal film [1] have led to the discovery of various 2D van der Waals (vdW) materials [2], which have attracted significant attention of scientific community in the past decade. Soon it was confirmed that such 2D systems can be used not only to study exotic physical properties of matter such as the relativistic physics of Dirac Fermions [3], quantum hall effect, neutral and charged exciton dynamics [4, 5], Polaritons [6], ultrafast electron cooling dynamics [7], Coulomb drag [8], anomalous Lattice vibrations [9], physics of massive chiral particle [10], Fermi edge singularity [11] etc., but also in various electronics and optoelectronics applications [12–18]. One of the important aspects of vdW materials is the possibility of high speed electronic application [19] with low power consumption rate [20–22]. Other possibilities include the use of these materials in making transparent and flexible devices [23–25]. The ever growing demand of electronic appliances with nominal power consumption rate require miniaturization of devices where the 3D technology (Silicon based) has already reached its limit [26, 27]. 2D van der Waals materials have shown significant potential in fulfilling such requirements [12, 17, 28, 29]. Various reports have shown that vdW devices can be embedded in silicon chips and multiple exciting device functionality such as ultrafast photodetector [30–32], mode-locked ultrafast Laser [33], optical mudulators [34] etc. can be realised. The discovery of 2D vdW metal (e.g. graphene), semiconductor (e.g. MoS2 ) and insulator (e.g. BN) support the idea of producing complete two dimensional electronic and optoelectronic devices [35]. However, the possibility of having a complete 2D-vdW based application is still a topic of research [12, 36, 37].

© Springer Nature Switzerland AG 2020 K. Roy, Optoelectronic Properties of Graphene-Based van der Waals Hybrids, Springer Theses, https://doi.org/10.1007/978-3-030-59627-9_1

1

2

1 Introduction

1.2 Van der Waals Heterostructures Conventional semiconductor heterostructures are of prime interest in many important fields such as in fabrication of LASER, high electron mobility transistors (HEMT), heterojunction bipolar transistors etc. Formation of a triangular quantum well at the interface of two dissimilar materials allow confining of electrons in two dimensions, leading to 2D-electron gas. The undoped semiconducting channels, unlike the MOSFETs, in such junctions help in reducing scattering of charge carriers because of the absence of impurities. Clean interface allows attaining large electron mobility, which is a key necessity to study various interesting quantum confinement phenomena in condensed matter physics, such as integer and fractional quantum hall effect [38], quantum spin hall effect [39, 40], Bloch oscillations of electrons [41, 42], excitonpolariton condensation [43, 44] etc. However, the cost of making such junctions is high because of the need of expensive fabrication techniques such as molecular bean epitaxy (MBE), or complex chemical vapour deposition (CVD) method etc. The success of conventional heterostructures has led to the idea of stacking various van der Waals materials in desired sequence to explore a new set of 2D hybrid materials [45]. Whereas the complex epitaxial growth techniques are necessary to fabricate a clean interface in a conventional heterostructure, the stability of atomically thin van der Waals materials can be exploited to make high quality interfaces by placing one atomic layer on top of the other by simple mechanical means [46, 47]. Typically, such a mechanical attachment process requires no lattice matching criteria. Thus, multiple layered materials, having different lattice constants, are also contacted with each other forming heterostructures. Similar attachment processes can be followed to stack multiple layers [45]. The obtained results from vdW heterostructures are remarkable, because not only it is easier to achieve an atomically smooth and clean interface, the interlayer hybridization can also be tuned, giving various interesting device functionality. For example, by placing graphene on boron nitride (BN), where the latter is a large bandgap insulator, extremely large electronic mobility can be achieved, since BN acts as an atomically smooth substrate devoid of traps [48]. A close matching of lattice parameters also allows the study of physics of 2D superlattice such as emergence of Moir´e pattern [49–52] etc. Various other interesting physical phenomena, such as resonant tunneling [53, 54], tunable metal-insulator transition [55], band offset and negative compressibility [56, 57], exciton dynamics [58–60], coulomb drag [8] etc., have also been explored using various van der Waals heterostructures. It should be mentioned here, although, the lattice matching criteria is not necessary for heterostructure fabrication, when two monolayers of same material are attached carefully, for example, by maintaining a appropriate twist angle between the crystallographic orientations of the two layers, completely new material-characteristics emerge [61–69]. Charge transfer across the interface of a vdW hybrid structure is one of the important features. Along with interlayer hybridization, charge transfer mechanism allows cooling of hot electrons, dissociation of excitons etc.; control on such physical pro-

1.2 Van der Waals Heterostructures

3

cess helps modifying the thermal and optical property of the material respectively. Thus, a vdW heterostructure gives the idea of tuning material properties. Weak van der Waals interactions between the layers allow keeping individual material properties unaltered. Results of various studies from multiple research groups are now available confirming such interesting properties involving van der Waals hybrids. Few of such examples relate to electron transfer study in graphene-Tungsten disulfide hybrids [70], tunability of exciton sates in graphene-MoS2 heterojunctions [71], ultrafast charge transfer mechanism in MoS2 -WS2 [72], confirmation of existence of long lived interlayer exciton in MoSe2 -WSe2 [58], valley-polarized exciton dynamics in monolayer WSe2 -MoSe2 [59, 73, 74] heterostructures etc. Various interesting device applications of vdW heterostructures have also been demonstrated, which include picosecond photoresponse in graphene-WSe2 -graphene hybrids [75], sub-thermionic tunnel transistor with extremely low sub threshold swing [76, 77] etc. Plenty of such results confirm the importance of 2D van der Waals heterostructures in discovering new phenomenon in solid state physics as well as realization of novel device architectures for multiple applications [17, 21].

1.3 Scope of the Thesis The scope of this thesis concerns the experimental investigations of the electronic and optoelectronic response of 2D van der Waals heterostructures (or hybrids) where the constituent materials are graphene, bilayer graphene (BLG), molybdenum disulfide (MoS2 ), and boron nitride (BN). Electronic and optoelectronic characterizations are carried out with the field effect transistor devices made from such hybrids. Hybrids are made by stacking the individual vdW materials in a desired sequence. The main objective has been to characterize and control the charge transfer mechanism across the graphene-MoS2 interface to achieve a new class of photoresponsive device, which combines superior electronic properties of graphene and the unique optical response of MoS2 . The control mechanism allow transferring photogenerated carriers from MoS2 to graphene. Owing to the high electronic mobility of graphene, the carrier transit time in the graphene channel appear small, which causes a high photogain resulting a large photoresponse. A quantitative study of the photoresponse characteristics and the respective physical mechanisms are presented. Multiple device architectures were investigated to confirm the tunability of the response by altering various physical parameters which control the photoresponse. Along with the high quality tunable interface characteristics, various other functionalities such as optoelectronic memory operation, number resolved single photon detection etc. are demonstrated. Chapter wise content of the thesis is illustrated in the following section.

4

1 Introduction

1.4 Thesis Layout An overview of the material properties is presented in Chap. 2. Keeping in mind that electronic band structure determines the electrical transport property of materials and the focus of this thesis is to study electrical transport characteristics of vdW-heterostructures under optical illumination; a description of basic electronic band structures of the relevant vdW materials is presented in this chapter. An understanding related to the interface characteristics of van der Waals heterostructures is also discussed. All the supporting informations is adapted from various existing literatures with appropriate citations. Chapter 3 gives an overview of various photodetection mechanisms and relevant parameters necessary for photoresponse characterization. This chapter also presents emerging photoresponse characteristics with vdW materials demonstrated by several research groups, outlining the state of the art in the study of optoelectronic phenomenon with these materials. Given the new field of vdW materials, there were not many known heterostructure fabrication techniques that could be used to stack multiple vdW materials (e.g. graphene, MoS2 , BN etc.) in any desired sequence. A ‘pick-and-attach’ technique has been developed in this thesis, which allows integration of multiple layers of different materials in a predetermined sequence. The dry attachment process followed in this technique allows maintaining clean interfaces between the materials. A customized micromanipulator has also been built, which was used to make the heterostructures using this technique. Details of the heterostructure fabrication process and micromanipulator are mentioned in Chap. 4. Although the report by Wang et al. [78] discusses a similar fabrication technique, our technique is the closer to the process described in Ref. [79]. Notably, the first heterostructure fabrication report by Dean et al. can only be applied to stack two vdW layers, which otherwise may contaminate the interfaces when followed to stack multiple layers [48]. A homemade optical cryostat was used to perform optoelectronic response study, and are presented in this thesis. Detail design schematics of multiple optical cryostats that were built and used is discussed in Chap. 4. Various other techniques such as semi-automatic process of data acquisition, analysis etc. are also discussed here. Chapter 5 covers details of optical and electrical characterizations that were carried out to confirm the material properties and heterostructure interface characteristics. For example, unique Raman-signature is used to identify the materials (e.g. graphene, bilayer graphene, MoS2 etc.), or quality of the crystal (such as defects or impurities etc.). Interlayer interaction mechanism in graphene-MoS2 heterostructures was studied from the evolution of Raman-vibrational modes of these materials. Photoluminescence studies were carried out to understand the contribution of charged and neutral excitons in MoS2 and graphene-MoS2 hybrids. Atomic force microscopic (AFM) study was performed to confirm the topography and thickness of the materials. Electrical transport characterization is employed to understand the tunable interface characteristics of graphene-MoS2 heterostructures.

1.4 Thesis Layout

5

Basic optoelectronic response study of a monolayer graphene-MoS2 hybrid is discussed in Chap. 6. A comparative study with graphene, MoS2 and grapheneMoS2 devices is presented to demonstrate the distinct nature of the response seen in hybrid devices. The response of the device under optical and electrical pulse is investigated. A theoretical model of photoresponse mechanism is also presented with a quantitative analysis with respect to various control parameters. Evolution of photoresponse with the variation of static electric field, excitation bias, illumination power etc. is also demonstrated. Chapter 7 describes the observation of persistent photoresponse in grapheneMoS2 heterostructures. Static electric field controlled erasability of persistent response allows remarkable optoelectronic memory operation. Here, monolayer graphene-MoS2 was utilized and operated with light and gate pulses to show switching-memory operation. A theoretical model is also discussed, supporting the nearly perfect charge retention characteristics of these devices. Zero band-gap of monolayer graphene leads to low channel resistance and transconductance, which play an important role in controlling photoresponse characteristics of these planar devices. Thus, a new type of device with dual gated structure was introduced, where a bilayer-graphene (BLG) was utilized as a channel material (receiver of photocarriers). Focus of Chap. 8 is to discuss detailed electrical characterisation of a dual gated BLG-on-MoS2 device. Further, a quantitative study of electrical-noise is presented. Static electrical field tunable nature of transconductance and electrical-noise characteristics are the highlights of this chapter. Such a study allowed quantitative comparison between measurable photosignal and dark noise present in these devices. Detailed photoresponse study of dual gated BLG-on-MoS2 device is presented in Chap. 9. Field controlled tunable nature of photoresponse and photon noise study are the focus of this chapter. Various photoresponse related parameters such as noise equivalent power and specific detectivity were estimated, and are presented here. Low gain-noise feature of these devices were utilized to detect photon noise. Detailed and quantitative analysis of photon noise characterisation is presented in this chapter. Extremely sensitive photoresponse and low gain noise are the salient features of graphene-MoS2 based planer hybrid devices. High detectivity and low noise ensure that the photosignal from even a single photon can also be resolved by employing these detectors. Chapter 10 shows an application of a dual gated BLG-onMoS2 device as a single photon detector. Fundamental difference in noise free gain mechanism, when comparing with a conventional avalanche photodetector, is also highlighted in this chapter. Various types of graphene-MoS2 devices, showing interesting photoresponse characteristics are chalked out in Chap. 11. Basic idea of this discussion is to elaborate other scheme of photoresponse study such as room temperature operation, fast scheme of operation in vertical structures, large scale device applications etc. A concluding remark, regarding the work presented in this thesis, is given in Chap. 12. The primary results are highlighted in this chapter. A discussion regarding the scope for future study is also presented.

6

1 Introduction

(a)

LED S

A

IDS

graphene | MoS2 | SiO2 | Si++

VDS

MoS2

Cr/Au

graphene graphene

MoS2

VBG

D

BG

SiO2

SiO2

Si++

Si ++

LED

(b) S

MoS2

Cr/Au

VTG

TG

A

IDS

VDS graphene

BN

BLG

BN graphene

D

BG

SiO2 Si ++

VBG

MoS2 SiO2 Si++

BLG

garphene | BN | BLG | MoS2 | SiO2 | Si++

Fig. 1.1 Device details and electrical connection layout. a Schematic representation of a graphene-on-MoS2 structure and electrical connection layout. (Left-panel) 3D-perspective of the device. (Middle-panel) Electrical connection layout when using backgate. (Right-panel) Sequence of the heterostructure stack. b 3D-perspective (left-panel), electrical connection (middle-panel), and stacking sequence (right-panel) of a dual gated BLG-on-MoS2 device

Two appendices have been added to include (a) detailed optimization of low frequency noise when using/connecting multiple instruments (Appendix A) and (b) photoresponse study with electrochemically grown large area graphene-CuX S hybrids (Appendix B). It has been found that the power connection layout, when powering multiple instruments, may lead to ground mixing, which adds noise in the measured electrical signal (Appendix A). Few possible schemes of ground mixing is demonstrated by quantitative analysis of low frequency power spectral density of electrical signal. Possible scheme of low/negligible ground mixing is also presented in Appendix A. The electrochemical growth of a photosensitive material on CVD-grown graphene is discussed in Appendix B. The motive of such a study was to integrate graphene with a photosensitive material in scalable method, resulting a large area hybrid device. Simple and low cost growth mechanism is an important aspect of this work.

1.5 Device Types and Measurement Scheme

7

1.5 Device Types and Measurement Scheme Mainly two types of graphene-MoS2 hybrid devices were utilized in this thesis. Schematic illustration of the device structures and electrical connection layout are presented in Fig. 1.1. One type of device was made by laying monolayer graphene on few layer MoS2 and referred to as graphene-on-MoS2 structure (Fig. 1.1a), the other type by stacking graphene, boron nitride (BN), bilayer-graphene and molybdenum disulfide (MoS2 ) sequentially, and is referred to as BLG-on-MoS2 structure (Fig. 1.1b). Graphene-on-MoS2 devices have single electrosatic gate control mechanism (backgate), whereas BLG-on-MoS2 devices have dual electrostatic gate control mechanisms (topgate and backgate). Typically, MoS2 in both type of devices are few layers thick (∼7–10 layers). BN thickness in BLG-on-MoS2 is ∼10–15 nm, so that the optical transparency for photoresponse experiments is high. All heterostructures are made on Si++ /SiO2 substrate having SiO2 oxide thickness of 285 nm. Heterostructures are fabricated following dry attachment technique, which is explained in Chap. 4. Electrical contacts on these devices are made following standard e-beam lithography and thermal evaporation of metals. Typically Cr and Au are used as contact metals. First a thin layer ( k B T , then the channel current remains limited by the saturation current (I0 ), hence, Eq. 2.11 simplifies to φB − ∗ α I = A A T e kB T . (2.13) Thus, determination of temperature dependent saturation current (I0 ) enables extraction of Schottky barrier height from the slope of ln(I /T α ) ver sus 1/T plot following Eq. 2.13 (also known as Arrhenius-type plot). 9 Discussions

of This Section Is Adapted from Ref. [10].

30

2 Review: Electronic Band Structure and Interface Properties

2.2.2.5

Barrier Height Estimation in FETs10

In case of a field effect transistors, when the device is being operated in the subthreshold regime, the total activation energy gets modified by the Fermi energy shift of the channel, and hence, the Eq. 2.13 is written as [82, 84] EA k I = AA T e BT , ∗

α

−

(2.14)

where E A indicates the total activation energy, written as E A = φ B + E C∞ − E C0 . Here, E C∞ and E C0 are conduction band minima in the bulk and at the interface respectively. E C∞ − E C0 is estimated following the flat band condition where E C∞ − E C0 = 0 (middle panel, Fig. 2.13). E C∞ − E C0 can be correlated with geometrical capacitance (Cox ) and interfacial capacitance (Cit ) of the device following the formula [10] E C∞ − E C0 = (VF B − VBG )/(1 + Cit /Cox )

(2.15)

Hence, E A is re-written as E A = φ B + (VF B − VBG )/(1 + Cit /Cox )

(2.16)

This formula is, however, valid in the VBG < VF B regime. VF B is the value of gate voltage (VBG ), where flatband condition satisfies. Higher value of VBG alters the barrier type such that the tunnelling phenomenon is accompanied by thermionic emission (Fig. 2.13a). It is evident from Eq. 2.16 [10] that E A varies linearly with VBG in the VBG < VF B regime. The value where it starts deviating from linearity gives

Fig. 2.14 Barrier height estimation. a Schematic illustration of flat condition. In V BG < VF B regime E A varies linearly with φ B . In flat band condition E A = φ B . b Extrapolation to remove VDS effect on φ B . True φ B is obtained at VDS = 0. Figures reprinted with permission [10]. Copyright (2015) Springer Nature 10 Discussions

of This Section Is Adapted from Ref. [10].

2.2 Few Physical Phenomena Related to van der Waals Hybrid Structures

31

the flat band condition where E A becomes equal to φ B . A scheme of this condition is presented in Fig. 2.14 [10, 66]. Experimentally saturation current of the device is estimated from the I DS − VDS curves. Multiple I DS − VDS treaces which are taken as a function of temperature (or gate voltage) gives a temperature (or gate voltage) dependent saturation current. In an experiment where I DS − VDS traces are recorded at various temperatures by keeping the gate voltage (VBG ) fixed, E A is estimated from the slope of the ln(I /T α ) ver sus 1/T plot (α = 3/2 for 2D) following Eq. 2.13. Similar procedure can be followed to obtain VBG dependent values of E A . The intersection between the linear and non-linear part of E A ver sus VBG plot gives the estimation of the barrier height (Fig. 2.14a) [10, 66].

2.2.2.6

Alternative Approach to Find φ B 11

An alternative method to find Schottky barrier is to consider the mathematical form, I = A A∗ T α e−(φ B −q VDS /n)/k B T .

(2.17)

This formula considers the fact that source-drain bias voltage (VDS ) can alter the barrier height [80, 83]. Here n is the ideality factor and considers the barrier lowering due to image charges. When using this method, activation energy is estimated for various VDS values and then a linear extrapolation gives proper barrier height for VDS =0 V (Fig. 2.14b).

2.2.3 Charge Transfer, Exciton Dynamics, and vdW-Interface Interlayer coupling and charge transfer mechanism across the interface are salient features of van der Waals (vdW) heterostructures. Controlling charge density in one material helps in modulating the property of the other while these remain separated by a van der Waals gap. Such characteristics were confirmed by studying the exciton dynamics. Excitons are the bound quasiparticles, which represent manybody interactions such as electron-electron, electron-hole interactions inside a physical systems. Ultrashort (∼ps) time resolved measurement, photoluminescence study etc. are the commonly used techniques to study exciton behaviours [44, 50, 85]. He et al. showed in their report that in graphene-WS2 heterostructures, the exciton resonance inside WS2 can be tuned by varying charge carrier density in graphene [44]. It is believed that the proximity of graphene, when forming heterostructures, suppresses the Coulomb interactions between electron and holes in WS2 . Reduced Coulomb interaction decreases exciton binding energy resulting in shorter lifetime, which is revealed in their time resolved differential reflection measurement. The 11 Discussions

of This Section Is Adapted from Ref. [10].

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2 Review: Electronic Band Structure and Interface Properties

free carrier density in graphene is considered to be the determinant factor of the screening mechanism. Various schemes of pump-probe study also reveal that nearly 100% of the photocarriers, generated inside WS2 , gets transferred to graphene within picoseconds time scale [44]. Tunable exciton states are also seen in graphene-MoS2 heterostructures [50]. In their experiment Li et al. used photoluminescence (PL) as the characterization tool to probe such effects under different gate bias conditions. It is shown that the PL intensity and peak-positions measured in graphene-MoS2 heterostructures are lower and blue-shifted respectively, compared to the values obtained from only MoS2 samples. Reduced intensity is attributed to the splitting of exciton because of the electric field present at heterostructure interface. The blue shift is explained following the contributions from specific excitions as oppose to the contributions from all three excitons (A, B, A− ) of MoS2 . Strong spin-orbit interactions in atomically thin MoS2 allow two stable neutral excitons ( A-excition, B-excition), and one charged exciton (A− -trion). The stability of any exciton depends on the screening by free charge carriers. Thus, modulation of free carrier density (e) alters the exciton contributions. Formation of A− also gets affected with the unavailability of the free electron density. External electric field (i.e. gate bias) can also split the excitions making these unstable. Thus, in graphene-MoS2 heterostructures, tunable nature of MoS2 carrier density and interfacial electric field allow altering specific-exciton contributions to the PL intensity. In the absence of excess negative carriers (at negative gate bias) trion formation reduces. At positive bias, the Schottky barrier splits excitons reducing PL intensities as the gate bias is increased [50]. More discussions on charge transfer and various types of exciton formation across different 2D interfaces can be found in the following references [86–91].

References 1. Castro Neto, A (2009) Pauling’s dreams for graphene. Phys (College Park Md) 2, 30 2. Greber, T (2009) Graphene and boron nitride single layers 1–54. http://arxiv.org/abs/0904. 1520 3. Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK (2009) The electronic properties of graphene. Rev Mod Phys 81, 109–162 4. McCann E (2012) Electronic properties of monolayer and Bilayer Graphene. Nanosci Technol 57:237–275 5. Mak KF, Lee C, Hone J, Shan J, Heinz TF (2010) Atomically thin MoS2 : a new direct-gap semiconductor. Phys Rev Lett 105:136805 6. Wang QH, Kalantar-Zadeh K, Kis A, Coleman JN, Strano MS (2012) Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat Nanotechnol 7:699–712 7. Kuc A, Zibouche N, Heine T (2011) Influence of quantum confinement on the electronic structure of the transition metal sulfide TS2 . Phys Rev B 83:245213 8. Splendiani A et al (2010) Emerging photoluminescence in monolayer MoS2 . Nano Lett 10:1271–1275 9. Wang ZM (2014) MoS2 , Lecture notes in nanoscale science and technology, vol 21. Springer International Publishing, Cham

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10. Allain A, Kang J, Banerjee K, Kis A (2015) Electrical contacts to two-dimensional semiconductors. Nat Mater 14:1195–1205 11. Novoselov KS et al (2005) Two-dimensional gas of massless dirac fermions in graphene. Nature 438:197–200 12. Pauling L (1960) The nature of the chemical bond and the structure of molecules and crystals: an introduction to modern structural chemistry, 3rd edn. Cornell University Press 13. Drut JE, Lähde TA (2009) Is graphene in vacuum an insulator? Phys Rev Lett 102:1–4 14. Drut JE, Lähde TA (2009) Lattice field theory simulations of graphene. Phys Rev B - Condens Matter Mater Phys 79, 1–14 15. Meyer JC et al (2007) The structure of suspended graphene sheets. Nature 446:60–63 16. Wallace PR (1947) The band theory of graphite. Phys Rev 71:622–634 17. Saito R, Dresselhaus G, Dresselhaus MS (1998) Physical properties of carbon nanotubes, 1st edn. World Scientific Publishing Company 18. Katsnelson MI, Novoselov KS, Geim AK (2006) Chiral tunnelling and the Klein paradox in graphene. Nat Phys 2, 620–625 19. Zhang Y et al (2009) Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459:820–823 20. Yu WJ, Liao L, Chae SH, Lee YH, Duan X (2011) Toward tunable band gap and tunable dirac point in bilayer graphene with molecular doping. Nano Lett 11:4759–4763 21. Ding Y et al (2011) First principles study of structural, vibrational and electronic properties of graphene-like MX2 (M=Mo, Nb, W, Ta; X=S, Se, Te) monolayers. Phys B Condens Matter 406:2254–2260 22. Wilson J, Yoffe A (1969) The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties. Adv Phys 18:193–335 23. Ahmed T, et al (2019) Thermodynamically stable octahedral MoS2 in van der Waals heterobilayers. 2D Mater 6, 041002 24. Enyashin A, Gemming S, Seifert G (2007) Nanosized allotropes of molybdenum disulfide. Eur Phys J Spec Top 149:103–125 25. Botello-Méndez AR, López-Urías F, Terrones M, Terrones H (2009) Metallic and ferromagnetic edges in molybdenum disulfide nanoribbons. Nanotechnology 20, 325703 26. He J, Wu K, Sa R, Li Q, Wei Y (2010) Magnetic properties of nonmetal atoms absorbed MoS2 monolayers. Appl Phys Lett 96 27. Ramakrishna Matte HSS, et al, (2010) MoS2 and WS2 analogues of graphene. Angew Chemie - Int Ed 49, 4059–4062 28. Jiang H (2012) Electronic band structures of molybdenum and tungsten dichalcogenides by the GW approach. J Phys Chem C 116:7664–7671 29. Kadantsev ES, Hawrylak P (2012) Electronic structure of a single MoS2 monolayer. Solid State Commun 152:909–913 30. Kumara A, Ahluwalia PK (2012) Electronic structure of transition metal dichalcogenides monolayers 1H-MX2 (M = Mo, W; X = S, Se, Te) from ab-initio theory: new direct band gap semiconductors. Eur Phys J B 85:18–22 31. Ping Y, Rocca D, Galli G (2013) Electronic excitations in light absorbers for photoelectrochemical energy conversion: first principles calculations based on many body perturbation theory. Chem Soc Rev 42:2437–2469 32. Ramasubramaniam A, Naveh D, Towe E (2011) Tunable band gaps in bilayer transition-metal dichalcogenides. Phys Rev B - Condens Matter Mater Phys 84, 1–10 33. Conley HJ et al (2013) Bandgap engineering of strained monolayer and bilayer MoS2 . Nano Lett 13:3626–3630 34. Chu T, Ilatikhameneh H, Klimeck G, Rahman R, Chen Z (2015) Electrically tunable bandgaps in bilayer MoS2 . Nano Lett 15:8000–8007 35. Komsa HP, Krasheninnikov AV (2012) Effects of confinement and environment on the electronic structure and exciton binding energy of MoS2 from first principles. Phys Rev B - Condens Matter Mater Phys 86, 1–6

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36. Cheiwchanchamnangij T, Lambrecht WRL (2012) Quasiparticle band structure calculation of monolayer, bilayer, and bulk MoS2 . Phys Rev B - Condens Matter Mater Phys 85, 205302 37. Ugeda MM et al (2014) Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor. Nat Mater 13:1091–1095 38. Coehoorn R, Haas C, de Groot, RA (1987) Electronic structure of MoSe2 , MoS2 , and WSe2 . II: the nature of the optical band gaps. Phys Rev B 35, 6203–6206 39. Beal AR, Liang WY, Hughes HP (1976) Kramers-Kronig analysis of the reflectivity spectra of 3R-WS2 and 2H-WSe2 . J Phys C Solid State Phys 9, 2449–2457 40. Beal AR, Hughes HP (1979) Kramers-Kronig analysis of the reflectivity spectra of 2H-MoS2 , 2H-MoSe2 and 2H-MoTe2 . J Phys C Solid State Phys 12:881–890 41. Coy Diaz H, et al (2015) Direct observation of interlayer hybridization and dirac relativistic carriers in graphene/MoS2 van der waals heterostructures. Nano Lett 15, 1135–1140 42. Komsa HP, Krasheninnikov AV (2013) Electronic structures and optical properties of realistic transition metal dichalcogenide heterostructures from first principles. Phys Rev B - Condens Matter Mater Phys 88, 085318 43. Tongay S et al (2014) Tuning interlayer coupling in large-area heterostructures with CVDgrown MoS2 and WS2 monolayers. Nano Lett 14:3185–3190 44. He J et al (2014) Electron transfer and coupling in graphene-tungsten disulfide van der Waals heterostructures. Nat Commun 5:5622 45. Tongay S et al (2012) Thermally driven crossover from indirect toward direct bandgap in 2D semiconductors: MoSe2 versus MoS2 . Nano Lett 12:5576–5580 46. Kang J, Li J, Li S-S, Xia J-B, Wang L-W (2013) Electronic structural moiré pattern effects on MoS2 /MoSe2 2D heterostructures. Nano Lett 13:5485–5490 47. Tongay S et al (2014) Monolayer behaviour in bulk ReS2 due to electronic and vibrational decoupling. Nat Commun 5:3252 48. Tongay S et al (2013) Broad-range modulation of light emission in two-dimensional semiconductors by molecular physisorption gating. Nano Lett 13:2831–2836 49. Yu Y et al (2015) Equally efficient interlayer exciton relaxation and improved absorption in epitaxial and nonepitaxial MoS2 /WS2 heterostructures. Nano Lett 15:486–491 50. Li Y et al (2016) Tuning the excitonic states in MoS2 /Graphene van der Waals heterostructures via electrochemical gating. Adv Funct Mater 26:293–302 51. Cui X et al (2015) Multi-terminal transport measurements of MoS2 using a van der Waals heterostructure device platform. Nat Nanotechnol 10:534–540 52. Liu Y et al (2015) Toward barrier free contact to molybdenum disulfide using graphene electrodes. Nano Lett 15:3030–3034 53. Ubrig N et al (2020) Design of van der Waals interfaces for broad-spectrum optoelectronics. Nat Mater 19:299–304 54. Bernardi M, Palummo M, Grossman JC (2013) Extraordinary sunlight absorption and one nanometer thick photovoltaics using two-dimensional monolayer materials. Nano Lett 13:3664–3670 55. Chuang H-J et al (2014) High mobility WSe2 p -and n - type field-effect transistors contacted by highly doped graphene for low-resistance contacts. Nano Lett 14:3594–3601 56. Larson J, Snyder J (2006) Overview and status of metal S/D Schottky-barrier MOSFET technology. IEEE Trans Electron Devices 53:1048–1058 57. Liu J et al (2008) Carrier density and schottky barrier on the performance of DC nanogenerator. Nano Lett 8:328–332 58. Anwar A, Nabet B, Culp J, Castro F (1999) Effects of electron confinement on thermionic emission current in a modulation doped heterostructure. J Appl Phys 85:2663–2666 59. Dubois E, Larrieu G (2004) Measurement of low Schottky barrier heights applied to metallic source/drain metal-oxide-semiconductor field effect transistors. J Appl Phys 96:729–737 60. Çankaya G, Uçar N (2004) Schottky barrier height dependence on the metal work function for p-type Si schottky diodes. Zeitschrift fur Naturforsch - Sect A J Phys Sci 59, 795–798 61. Tung RT, Ng KK, Gibson JM, Levi AFJ (1986) Schottky-barrier heights of single-crystal NiSi2 on Si(111): the effect of a surface P-N junction. Phys Rev B 33:7077–7090

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62. Schulman DS, Arnold AJ, Das S (2018) Contact engineering for 2D materials and devices. Chem Soc Rev 47:3037–3058 63. Wang Y et al (2019) Van der Waals contacts between three-dimensional metals and twodimensional semiconductors. Nature 568:70–74 64. Wang L et al (2013) One-dimensional electrical contact to a two-dimensional material. Science 342:614–617 65. Kappera R et al (2014) Phase-engineered low-resistance contacts for ultrathin MoS2 transistors. Nat Mater 13:1128–1134 66. Das S, Chen H-Y, Penumatcha AV, Appenzeller J (2013) High performance multilayer MoS2 transistors with scandium contacts. Nano Lett 13:100–105 67. Yang Z et al (2019) A fermi-level-pinning-free 1D electrical contact at the intrinsic 2D MoS2 metal junction. Adv Mater 31:1808231 68. Léonard F, Talin AA (2011) Electrical contacts to one- and two-dimensional nanomaterials. Nat Nanotechnol 6, 773–783 69. Muller RS, Kamins TI, Chan M (2003) Device electronics for integrated circuits. Wiley 70. Banerjee K, Amerasekera A, Dixit G, Chenming, H (1997) Temperature and current effects on small-geometry-contact resistance. In International electron devices meeting. IEDM technical digest, vol 00. IEEE, pp 115–118 71. Stokbro K, Engelund M, Blom A (2012) Atomic-scale model for the contact resistance of the nickel-graphene interface. Phys Rev B 85:165442 72. Xia F, Perebeinos V, Lin Y-M, Wu Y, Avouris P (2011) The origins and limits of metal-graphene junction resistance. Nat Nanotechnol 6:179–184 73. Kang J, Sarkar D, Liu W, Jena D, Banerjee K (2012) A computational study of metal-contacts to beyond-graphene 2D semiconductor materials. IEEE Int Electron Devices Meet 407–410 74. Popov I, Seifert G, Tománek D (2012) Designing electrical contacts to MoS2 monolayers: a computational study. Phys Rev Lett 108:156802 75. Kang J, Liu W, Sarkar D, Jena D, Banerjee K (2014) Computational study of metal contacts to monolayer transition-metal dichalcogenide semiconductors. Phys Rev X 4:1–14 76. Kang J, Liu W, Banerjee K (2014) High-performance MoS2 transistors with low-resistance molybdenum contacts. Appl Phys Lett 104:2–7 77. Gan LY, Zhao YJ, Huang D, Schwingenschlögl U (2013) First-principles analysis of MoS2 /Ti2 C and MoS2 /Ti2 CY2 (Y=F and OH) all-2D semiconductor/metal contacts. Phys Rev B - Condens Matter Mater Phys 87, 1–7 78. Yuasa S, Nagahama T, Fukushima A, Suzuki Y, Ando K (2004) Giant room-temperature magnetoresistance in single-crystal Fe/MgO/Fe magnetic tunnel junctions. Nat Mater 3:868–871 79. Parkin SSP et al (2004) Giant tunnelling magnetoresistance at room temperature with MgO (100) tunnel barriers. Nat Mater 3:862–867 80. Chen JR et al (2013) Control of Schottky barriers in single layer MoS2 transistors with ferromagnetic contacts. Nano Lett 13:3106–3110 81. Sze S, Ng KK (2006) Physics of semiconductor devices. Wiley, Hoboken, NJ, USA 82. Muller RS, Kamins TI, Chan M (2002) Device electronics for integrated circuits, 3rd edn. Wiley 83. Lin Y-F et al (2014) Barrier inhomogeneities at vertically stacked graphene-based heterostructures. Nanoscale 6:795–799 84. Mott NF (1976) Impurity band conduction: experiment and theory: the metal-insulator transition in an impurity band. J Phys Colloq 37, C4–301–C4–306 85. Massicotte M et al (2015) Picosecond photoresponse in van der Waals heterostructures. Nat Nanotechnol 11:42–46 86. Sulas-Kern DB, Miller EM, Blackburn JL (2020) Photoinduced charge transfer in transition metal dichalcogenide heterojunctions - towards next generation energy technologies. Energy Environ Sci 87. Vialla F, et al (2019) Tuning of impurity-bound interlayer complexes in a van der Waals heterobilayer. 2D Mater 6

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88. Ahmed T, et al (2020) A generic method to control hysteresis and memory effect in Van der Waals hybrids. Mater Res Express 7 89. Lukman S, et al (2020) High oscillator strength interlayer excitons in two-dimensional heterostructures for mid-infrared photodetection. Nat Nanotechnol 90. Brotons-Gisbert M et al (2020) Spin-layer locking of interlayer excitons trapped in moiré potentials. Nat Mater 19:630–636 91. Calman EV et al (2020) Indirect excitons and trions in MoSe2 /WSe2 van der Waals heterostructures. Nano Lett 20:1869–1875

Chapter 3

Review: Optoelectronic Response and van der Waals Materials

3.1 Mechanism to Detect Light1 Conventional photodetectors act as light sensors that generate electrical signal upon receiving light. There are various physical mechanisms by which an optical signal can be converted into electrical signals. Some of these are photoconducting effect, photovoltaic effect, photothermoelectric effect, bolometric effect, plasma wave assisted photo detection, photogating effect [1] etc. (Fig. 3.1). It is the design scheme and choice of materials that determine the governing detection mechanism. Underlying physical mechanism of photodetection is the determining factor for detection ability and speed of detection. A brief description of various photodetection mechanisms is illustrated in the following sections.

3.1.1 Photoconducting Effect2 Conventional semiconductors show a change in electrical conductance when it absorbs photons. In the presence of light, carrier densities reach a steady state value because of the equilibrium between electron-hole (e − h) generation and recombination. Invoking quasi-Fermi levels for electron and holes is often customary to explain photoconductivity phenomenon (see Sect. 5.6.4 in Ref. [2]). Difference in quasi-Fermi levels (in the presence of light) from the Fermi level (in dark) changes the electrical conductivity of the material. This change in conductivity is probed by using a voltage (current) bias where a change in current (voltage) is noted as a signal of photoexcitation. The conductivity change is directly related to the photocarrier densities that take part in the electrical transport, hence, this phenomenon is known 1 Discussions 2 This

of this section is inspired from Ref. [1]. section is inspired from Ref. [2].

© Springer Nature Switzerland AG 2020 K. Roy, Optoelectronic Properties of Graphene-Based van der Waals Hybrids, Springer Theses, https://doi.org/10.1007/978-3-030-59627-9_3

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Fig. 3.1 Mechanisms to detect light. a–d Schematic presentation of various types of photosignal detection. Figures reprinted with permission [1]. Copyright (2014) Springer Nature

as the photoconductivity effect. Various semiconductor based photodetectors such as Silicon, Germanium, CdS etc. rely on this photoconductivity effect for photodetection. Considering one type of carrier (n-type) in a photoconductor, the temporal response of the detector is obtained following the dynamic equation (Sect. 11.3.3 of Ref. [2]), d(n − n P ) (n − n P ) = η(t) − . (3.1) dt τ Here n is the carrier density in absence of light, n P and  P are carrier densities and photocarrier generation rate respectively, at time t, τ is the recombination lifetime of the photocarriers, and η is the quantum efficiency. The physical origin of Eq. 3.1 arises from the fact that, at any time (t) the net rate of carrier density change (d(n − n P )/dt) is equal to the sum of effective generation rate (η P ) and recombination rate (−(n − n P )/τ ). The negative sign in the recombination rate accounts for the decrease in carrier density. Here generation rate  P assumes intrinsic absorption property (absorption coefficient) of the material, the effect of diffusion of photocarrier is yet to be included. Physically it is understood that only a certain fraction (η) of the total generated photocarriers contribute to the net charge density because of diffusion. Thus, the effective generation rate is obtained by multiplying  P with η. Temporal response of a photoconducting detector can be derived from Eq. 3.1 for different photoexcitation functions ( P (t)). Figure 3.2 depicts three such scenarios where excitation functions are (a) short square pulse type (Fig. 3.2a), (b) long square pulse (Fig. 3.2b), and (c) Sinusoidal (Fig. 3.2c). The respective mathematical expressions are written as (Sect. 11.3.3 in Ref. [2]), n − n P = η P T e−t/τ n − n P = η P τ (1 − e−t/τ ) η P τ n − nP = √ sin(ωτ + θ). 1 + ω2 τ 2

(3.2) (3.3) (3.4)

Here ω is the angular frequency of the sinusoidal excitation and θ is a constant phase. It is clear from the above expressions (Eqs. 3.2–3.4) that the characteristic time scale

3.1 Mechanism to Detect Light (a) Photoexcitations

39

(b) ΓP

(c) ΓP

ΓP sin(ωt)

T >1/τ ), the photon number (n p ) received within a fixed interval (τ ) at any time is never certain (unique). For an ideal light source, the received photon number n p always assumes a value around the mean value n p  following the Poisson distribution function (Sect. 17.5 in Ref. [12]; Sect. 11.A in Ref. [2]), P(n p ) =

e−n p  n p n p n p!

(3.13)

Thus, when examining multiple events, even in an ideal scenario, where all input excitations are same and the expected photon number output is n p  within a time τ , different events will show different values, and the probability of occurrence of n p is given by P(n p ) (Fig. 3.3a). The noise in photon number n p is extracted by estimating the variance n 2p , which is essentially equal to the mean of n p (n p ). Thus, the photon noise magnitude can be estimated following the formula 

n 2p  =



n p .

(3.14)

3.3 Noise Mechanisms in Photodetectors

45

The above discussions show that the arrival of random number of photons adds noise in the photodetection.

3.3.2 Photoelectron Noise Photoelectron noise appears since the absorption of photons within the photosensitive material do not occur at 100% efficiency. An additional uncertainty appears because of the finite recombination lifetime of the generated electron-hole pairs. The second case suggests that a successful generation of photocarrier, following absorption process, may not contribute to photocurrent because of the carrier recombination. The randomness of photoelectron generation thus, manifests as noise in the photocurrent signal (Fig. 3.3b). The combined noise arising from these two processes is estimated by considering the internal quantum efficiency (η) of the detector. Photoelectrons follow similar statistics as that of photons. When using an ideal photon source, if n e is the number of photoelectrons generated from n p number of photons at any time, within an interval τ , then the variance of n e can be written as (Eq. 17.5-2, Ref. [12]), n 2e  = n e  = ηn p .

(3.15) (3.16)

The noise in photoelectron number is estimated following the expression, 

n 2e  =

 ηn p .

(3.17)

Photoelectron number being the determinant factor of photosignal strength, noise in photoelectron number adds to the total noise in the signal.

3.3.3 Gain Noise The internal complex gain mechanism of a photodetector often adds noise because of the uncertainty in the carrier multiplication process. For example, in an avalanche photo diode (APD), the secondary carrier generation is a statistical process (probabilistic) and depends on the electron and hole ionization coefficients (αe , αh ). The probabilistic nature allows a wide range of outcome rather than a specific value. Hence, the gain G remains distributed around a mean G in a given detection scenario, such as under a fixed bias condition of an APD (Fig. 3.3c) etc. The effect of random carrier multiplication (random value of G) appears as noise in photocurrent (I P ); the variance of photocurrent is estimated following the expression (Eq. 17.5-20, Ref. [12]),

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I P2  = 2eFG I P  f, = 2e η FG  f. 2

(3.18)

2

(3.19)

I P  = eηG

(3.20)

where mean of I P is given by,

Here  f and F are the bandwidth and excess noise factor of the detector respectively.  is the photon flux impinging onto the detector. Excess noise factor of a photodetector is estimated following the expression, G 2  G2 G 2  = 1+ G2

F=

(3.21) (3.22)

3.3.4 Receiver Circuit Noise Thermal fluctuations in a resistive path adds noise to the current (I D ) flowing through the resistor (thermal noise). Typically, a receiver circuit has a finite resistance that produces additional current noise. If the effective resistance (R) of the receiver circuit is low, then significant noise contribution gets added to the actual signal. Quantum nature of electron also adds noise (shot noise). Various other mechanisms such as number density fluctuations, mobility fluctuations etc., also couple noise to the receiver circuit (flicker noise). Depending on the material property and device architecture, such a noise may have significant contributions so as to reduce the signal to noise ratio. Power spectral density of thermal noise or shot noise remains constant for all frequencies (Eqs. 3.8 and 3.9); because of such uniform distributions these are also termed as white noise. The power spectral density of flicker noise is inversely proportional to the frequency ( f ), hence known as 1/ f noise. Being 1/ f in nature, contribution of flicker noise is one of the dominant sources of noise in receiver circuit when working within small frequency ranges, i.e. f < 100 Hz [13, 14]. Following few sections discuss the origin of such noise. Often, these types of noises are called ‘phantom’ noise or ‘dark’ noise.

3.3.4.1

Flicker Noise3

Flicker noise is one of the dominant sources of noise when working at low frequencies, and is also known as 1/ f noise. Various system dependent models are adapted 3 Discussions

of this section is adapted from Ref. [15].

3.3 Noise Mechanisms in Photodetectors

47

to explain the origin of flicker noise [13, 16–18]. For example, in homogeneous metals and semiconductors electron-phonon scattering leads to mobility fluctuations, resulting 1/ f noise [17–19]. An empirical formula (Eq. 3.23) presented by Hooge is used to quantify this noise, and hence, known as Hooge model [19]. The voltage (V ) or current (I ) normalised noise is inversely proportional to the total number of electrons (N ) present in the conductor. Here γ H is known as Hooge parameter, and α = 1 when the noise source is purely 1/ f in nature. SI ( f ) γH = I2 Nfα

(3.23)

1/ f noise can also originate because of trapping-detrapping mechanism of charge carriers, and commonly seen in metal oxide semiconductor filed effect transistors (MOSFET) [20]. Trap states present in the oxide can add or remove carriers from the channel leading to carrier density (n) fluctuations. Random fluctuations in carrier density leads to conductivity fluctuation causing 1/ f noise. A quantitative analysis of the normalized noise power distribution is obtained following the McWhorter model, and is written as [20, 21], q 2nt k B T 1 SI ( f ) = × 2 2 2 I 8wle n f

(3.24)

Here q is electronic charge, n t the trap state density per unit energy, k B the Boltzmann constant, T the temperature, n the number density of carriers, w the width, and l is the length of the channel. McWhorther model assumes that trapping-detrapping process only changes the number density of charge carriers, while the effective potential landscape remains the same leading to absence of mobility fluctuations. The trap states that are nearby Fermi energy E F only contribute to the noise. Often slow relaxation of defects or disorders can cause 1/ f noise. Such noise characteristics is commonly seen in case of metal films, and estimated following the Dutta-Horn model [14]. Typically the noise power is Lorentzian (Si ( f ) ∼ τ /(1 + (2π f τ )2 )) if the system has a single relaxation time (τ ), however, the noise characteristics is 1/ f type if the system has multiple relaxation time. For example in case of defects that are distributed over a wide band of energy scales, the relaxation time varies along with the variation of activation energy following τ = τ0 ex p(E/k B T ). Here τ0 is inversely proportional to the Debye frequency (ω). A more detailed discussion can be found in Refs. [14, 15]. Quantum mechanical interference phenomenon in high mobility samples can also lead to 1/ f noise. If phase coherence length is larger than the elastic mean free path of the system, then backscattering of electronic wave functions takes place due to the presence of impurities. Any change in the configuration of such impurities can alter the effective transmission coefficient of electrons, leading a quantized fluctuation (∼ e2 / h) in conductance. At sufficiently low temperatures such conductance-fluctuation follow 1/ f characteristics. Such a quantum phenomenon is also known as universal conductance fluctuation [22–25].

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Another source of 1/ f noise may originate from the local interference between the electronic wavefunction and the defect centres. In this model structural defects act as independent scattering centres. The overall scattering phenomenon becomes strongly dependent on the separation between the defects when the separation becomes comparable to the electronic Fermi wavelength. The origin of 1/ f noise is due to the movement or rotation of these defect states. The noise contribution can be estimated following the Pelz and Clarke model, which is discussed in Refs. [15, 26]. This type of noise is typically seen at higher temperature values [15, 27, 28].

3.3.4.2

Thermal Noise

Thermal motion of the charge carriers cause a small but measurable change (noise) in electrical current flowing through any conventional electrical conductor. Johnson and Nyquist in their respective experimental and theoretical results quantified this noise value considering electrical analogue of gas pressure [29, 30]. It was assumed that the thermal motion of charge carriers cause agitation to the electrical modes of oscillation. A conductor of resistance R is simplified as a loss-less transmission line with each end terminated by a resistance of value R. The electrical normal modes are now considered to exist along this line. Electrical analogue of gas pressure allow considering equipartition law of thermodynamics and gives the energy per mode of oscillation to be k B T , where T is the temperature of the conductor. Total noise is estimated by adding the energy values of all such normal modes [31–33]. Following Nyquist’s derivation, the total current noise, due to thermal agitation, in a conductor of resistance value R is estimated as, IJ =

 4k B T /R

(3.25)

In an ideal resistor, this value of noise is frequency independent, i.e. power spectral density is equal at all frequencies, hence known as white noise. It can also be realized from the formula that the noise value (I J ) only depends on the resistance value (R) of the conductor, and does not depend upon the shape or material constituting the conductor. Following the name of the inventors, thermal noise is also referred to as Johnson noise or Nyquist noise [29, 30].

3.3.4.3

Shot Noise

Shot noise in electrical circuits arise because of the fact that current is carried by discrete number of charges (electrons). Idea of shot noise was first introduced by Walter Schottky in 1918 when studying the current-fluctuations in vacuum tube due to photoelectric effect. In an electronic device, typically electron injection process through the contact can be considered to be an independent event. Thus, shot noise is described by Poisson distribution. The shot noise (I S ) contribution in a device which is carrying an average current I is estimated from the following formula,

3.3 Noise Mechanisms in Photodetectors

IS =

49

√ 2eI .

(3.26)

Typically, I S is much lower than the other source of noise such as thermal noise or flicker noise values. For low current values, where the number of charge carriers, which are taking part into the conduction, becomes comparable with the uncertainty in the number of electron injection events, across the current-probes, then shot noise should be taken into account. Such noise typically follow Poisson distribution. Shot noise is also white, i.e. the noise spectral power does not depend on frequency.

3.4 Physics of Persistent Photoresponse Persistent photoresponse is a commonly seen phenomenon in photodetection study. There are various known intrinsic and extrinsic mechanisms that cause persistent photoresponse (PPC) in semiconducting materials. Intrinsic PPC mechanism relates to the disorders/defects present in the material [34–36]. Persistent photoresponse has been used consistently in the past as a characterization tool to understand the physical properties of doped semiconductors and conventional heterojunctions [37]. Thus, in material science and device physics, persistent photoresponse study bears significant importance. Extrinsic mechanism such as molecular absorption/disruption can cause PPC. For example, oxygen disruption in WO3 nanowire [38] or in ZnO nanowire [39] creates vacancies that act as electron trapping centers causing PPC. Using this same idea, it was shown that giant persistent photoconductivity can exist in SrTiO3 /LaAlO3 heterostructures. Substrate induced PPC in atomically thin MoS2 is another example of extrinsic source of PPC. Traps in the substrate lead to a random potential landscape, which induces localized electronic states resulting in PPC [40]. However, the trap-center assisted mechanism fails to explain the origin of PPC in compound semiconductors [34]. It was found that the capture cross-section of photoexcited carriers in compound semiconductors is extremely small ( E F ) for a longer time (∼100 ps) because of weak electron-phonon coupling in graphene [172]. Longer lifetime allows diffusion of hot electrons to relatively colder region and generates a thermoelectric voltage. Presence of p-n junction increases the thermoelectrically generated photovoltage (Fig. 3.5). Such mechanism of photovoltage generation is alternatively known as Photothermoelectric effect (see Sect. 3.1.3). This demonstrates the utilization of electron-phonon interaction, one of its fundamental property, of graphene in a photodetector.

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Fig. 3.5 Hot carrier assisted photoresponse in graphene. a Optical image of the device. Current (I ) is measured under fixed source-drain bias condition (VS D ). Thin yellow are the source drain contacts. Thick yellow region indicate topgate where VT G is applied. Boron-nitride is used as top gate dielectric. MLG indicate monolayer graphene. Outline of graphene is indicated by the white dashed lines. b Transfer characteristics in the operational range of V BG and VT G . Doping types in the bottom-and-top gate region is indicated by p and n signs. c Scheme of experiment in the p-n doped junction (top panel). Bottom panel show respective electronic band structure of monolayer graphene. E F indicate Fermi energy. d Spatial dependence of photocurrent. e Back gate voltage dependence of thermovoltage and resistance at VT G = 2.0 V, VS D = 0 V, and 40 K temperature. Here 1 mW optical power is used at the triangular spot shown in (d). Figures reprinted with permission [172]. Copyright (2011) The American Association for the Advancement of Science

3.7.1.3

Asymmetric Contacts, Plasmonic Structures, and Photoresponse

Efficient separation of photocarriers is essential in generation of large photocurrent (photovoltage). Radiative or non radiative recombinations reduce the photosignal [2]. Echtermeyer et al. showed in their report [174] that photocarriers in graphene can be efficiently separated utilizing the electric field at metal-graphene interfaces. Small metal structures are made on graphene to get such interfaces. Plasmonic modes of the metallic structures further help in concentrating the oscillating electric field of light and enhance light matter interactions at the metal-graphene interface. Combined effect of junction and plasmonic coupling of light gives large photovoltage generation (Fig. 3.6e–g). When finger like plasmonic structures are used, the photovoltage becomes sensitive to the polarization of incident light (Fig. 3.6e, f). Higher photovoltage is achieved in TR polarization compared to the L polarized directions. A 110 nm finger width gives better enhancement factor (∼20) compared to the 130 nm wide fingers, which gives an enhancement factor of ∼4 (Fig. 3.6h, i). Maximum photocurrent of 10 mA W−1 is achieved in these devices. This is an example where efficient recovery of photocurrent has been achieved by utilizing metal-graphene interface and plasmonic coupling of light in graphene transistors.

3.7 Photodetection with van der Waals Materials

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Fig. 3.6 Asymmetric contacts, plasmonic structures, and photoresponse. a A monolayer graphene (blue) on SiO2 substrate (purple) with plasmonic structures (yellow coloured small extended rectangles from the bigger rectangles made of Ti/Au. Scale bar 20 µm). b–d various plasmonic structures. Here Longitudinal and transverse polarization directions are indicated by L and TR respectively (scale bar 1 µm). e–g Photovoltage at different parts of the device. e, f Phototexcitation with 514 nm having polarization along L and TR directions respectively. g Photovoltage generation in nanodot array shown in figure (d). Here 633 nm wavelength is used in TR polarized direction. Colour scales are indicated by −4 mV = blue, and 12 mV = red. h, i Enhancement coefficient and normalized photocurrent for finger like structures having pitch of 110 nm, 130 nm respectively (inset). Figures reprinted with permission [174]. Copyright (2011) Springer Nature

3.7.1.4

Band Engineering and Photoresponse Tuning in Graphene

Band structure engineering is a feature achievable using nanostructures. It can help in extending device response over a wide range of wavelengths. It can also be utilized to control photocarrier generation-recombination mechanism which determines photosignal strength. The idea of band structure engineering was adopted by Zhang et al. to achieve improved photoresponse in graphene [106]. A bandgap is introduced into the electronic bands by patterning graphene quantum dots (GQDs) on monolayer graphene sheet (Fig. 3.7a); energy band diagram of GQDs is illustrated in Fig. 3.7b. The red shaded region indicates midgap band (MGB) in the graphene channel arising from defects along the edges, and on the surface of GQDs. Quantum confinement in the electronic states of GQDs result in bandgap E g . High photoresponsivity of these devices is attributed to the trapping of photo-electrons in MGB (middle panel, Fig. 3.7b), as the hole circulates in the conduction channel. Long lifetime of e − h pairs allow a large photoconducting gain, and results in large photoresponse

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(a)

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Fig. 3.7 Band engineering and photoresponse tuning in graphene. a Device scheme of monolayer graphene quantum dot array (GQDs). b Schematics of optical excitation (left panel), trapping of photo-electrons (black solid circles, middle panel), and carrier recombination mechanism (right panel). c Generation of photocurrent under the illumination of visible (532 nm, left panel), nearinfrared (1.47 µm, middle panel), and mid-infrared (∼10 µm, right panel) wavelengths. Figures reprinted with permission [106]. Copyright (2013) Springer Nature

(Sect. 3.1.1). Such GQDs based devices show photoresponsivity of >8 A W−1 , which is nearly three orders of magnitude higher than the other graphene based devices presented previously [174]. Small bandgap leads to broadband photoresponse in such devices over a wavelength range of 0.5–10 µm (Fig. 3.7c).

3.7.1.5

High Speed Graphene Photodetectors

Back-scattering free charge transport is one of the salient features that promote high speed applications of graphene transistors. Fast carrier responses also help in achieving high speed photodetection in graphene. Photodetection speed (GHz range) is an important parameter in multiple applications including in optical communications. Mueller et al. showed that a metal-graphene-metal contacted graphene detector can be operated at GHz speed [175]. Such high speed is tested with the 1550 nm wavelength used in optical communications. Use of different metal contacts (Ti and Pd) allow developing an asymmetric electric field between the contacts. Such asymmetry leads to efficient photocurrent generation. In conventional graphene transistors

3.7 Photodetection with van der Waals Materials

(b)

(a)

(c)

61

(d)

Fig. 3.8 High speed graphene photodetectors. a Schematic of metal-graphene-metal (MGM) device. (Inset) Scaning electron microscope image of device with false color (scale bar 5 µm). b Photocurrent tunability at various gate voltages. c Photocurrent variation by varying the optical power. d Relative photoresponse at GHz modulation frequency. The 3 dB bandwidth is obtained at 16 GHz frequency. Figures reprinted with permission [175]. Copyright (2010) Springer Nature

use of similar metals lead to symmetric electric field. Thus, effective photocurrent from one contact gets cancelled by the other, when both contacts are illuminated uniformly. Figure 3.8a shows the device architecture used by Mueller et al. Application of gate voltage tunes the electric field in Ti-graphene-Pd region by modulating the carrier density in graphene. Thus, a prominent modulation in photocurrent is observed as a function of gate voltage (Fig. 3.8b). The responsivity of the device is estimated to be 1.5 A W−1 (Fig. 3.8c). The 3-dB bandwidth of these devices remain as high as 16 GHz (Fig. 3.8d).

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3.7.2 Photoresponse in Atomically Thin MoS2 Recent findings on layered transition metal dichalcogenides (TMDCs) have revealed multiple interesting optoelectronic properties of these materials [1, 176]. Presence of Van Hove singularities in the electronic density of states of TMDCs dramatically enhance light-matter interactions [177]. Enhanced light-matter interactions lead to outstanding optoelectronic response in the devices made of TMDCs. For example, a monolayer MoS2 , which is less than a nanometer thick [178], shows photoresponsivity as high as 880 A W−1 [179]. Other features such as tunability of bandgap with layer numbers [180], electrical tunability of bandgap of bilayer MoS2 [181], valley and band structure engineering of twisted bilayer MoS2 [182], presence of tightly bound trions [183] (which has no analogue in conventional semiconductors) in monolayer MoS2 , large excitonic binding energy in monolayer WS2 [184] make these useful for optoelectronic and valleytronic applications. Following sections highlight basic photoresponse mechanism in TMDC materials, and use of these to improve various aspects of photodetectors. This study is to stress on the fact that these materials can be used in developing new generation photodetectors with ultra-high detection sensitivity and fast response time.

Fig. 3.9 Strong light matter interactions in TMDCs. a Electronic density of states (DoS) in monolayer MoS2 , WS2 , and WSe2 . High density of states available at different energy values allow strong light matter interactions. b Joint density of states (JDoS) of monolayer MoS2 , WS2 , and WSe2 . Van Hove singularities associated strong peaks in JDoS is observed in the visible energy range, allowing strong light matter interactions. Figures reprinted with permission [177]. Copyright (2013) The American Association for the Advancement of Science

3.7 Photodetection with van der Waals Materials

3.7.2.1

63

Strong Light Matter Interactions in Transition Metal Dichalcogenides (TMDCs)

Transition metal dichalcogenide (TMDCs) are bound to show strong light matter interactions because of the presence of Van Hove singularities in electronic density of states. Strong peaks in the joint density of states (JDoS [177]) appear associated with Van Hove singularities (VHs) in the visible energy range (Fig. 3.9). Effect of VHs on photoresponse is directly measured by JDoS. High JDoS associated with any energy value allow electronic transitions around the energy in a large region in momentum space (E − k space). Thus, high transition probability is achieved, resulting in large photoresponse.

Fig. 3.10 Electric field controlled photoresponse in MoS2 . a Optical image of a monolayer MoS2 . b Optical image of the field effect transistor (FET) device configuration of the monolayer MoS2 . c Transistor like output characteristics of MoS2 at different optical illumination power. d Scheme of energy band diagram at open circuit condition and at different gate bias conditions. The bending in the bands are considered by considering the conduction energy (E c ) at 4.5 eV, valance band energy (E v ) at 6.3 eV (E g = 1.8 eV). The Fermi energy (E F ) of MoS2 and Au are considered to be located at 4.7 eV and 5.1 eV respectively. Figures reprinted with permission [185]. Copyright (2012) American Chemical Society

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3 Review: Optoelectronic Response and van der Waals Materials

Electric Field Controlled Photoresponse in MoS2

Optical illumination can be utilised to tune the quasi-Fermi levels of a direct band gap semiconductor [2]. Such tunable property can lead to interesting device applications. Such an example is presented by Yin et al. A field effect transistor is prepared with monolayer MoS2 on a Si++ /SiO2 substrate (Fig. 3.10a, b). Illumination of different optical power allow demonstration of transistor like action of the device (Fig. 3.10c). Figure 3.10d illustrates the mechanism of phototransistor action for various gate and source bias conditions.

3.7.2.3

High Photoresponsivity in Monolayer MoS2

In their work, Lopez-Sanchez et al. has showed that a monolayer MoS2 (107 A W−1 , Fig. 3.13b). These devices, photogenerated carriers (holes) gets transferred from PbS to graphene due to the influence of the interfacial electric field. Interfacial electric field develops because of the initial Fermi energy difference between graphene and PbS. A net charge transfer allows a change in conductivity of

3.7 Photodetection with van der Waals Materials

67

graphene channel. Trapping of one type of charge inside PbS results in a long lifetime of the photo carriers, allowing an extremely high responsivity (>107 A W−1 ). This phenomenon is also alternatively known as photogating effect, as the charged PbS acts as local gate, which alters the conductivity by changing effective carrier concentration into the graphene channel. High carrier mobility of graphene allows low carrier transit time between the source-drain channel, and the long lifetime of the photogenerated e − h pairs lead to a large gain in photoconductivity, resulting in a large photoresponsivity. Such devices also show large detectivity of ∼1013 cm Hz1/2 W−1 . A change in the response band is made by choosing QDs of different sizes. Smaller QDs have large excitonic gap compared to the bigger QDs, hence, the peak response appears at smaller wavelengths (950 nm) compared to the value ∼1450 nm for larger QDs (Fig. 3.13b). This also establishes the tunable nature of photoconductivity by selecting the size of QDs. Zhang et al. also presented high quality photoresponse characteristics of similar graphene-PbS hybrid structures [194]. From these studies it is clear that photocarriers from one material (PbS) can be transferred to another material (graphene) where electronic mobility is large. Physical proximity between the materials and interfacial electric field helps in transferring one type of charge carriers. When transferred onto the highly mobile region, charge carriers move fast showing low carrier transit time and long carrier lifetime lead-

Fig. 3.14 High quantum efficiency in vertical heterostructures. a Scheme of vertically stacked graphene-MoS2 graphene photodetector on Si/SiO2 substrate. b current-voltage (I DS -VDS ) characteristics in dark (blue line) and in presence of light (red line). 80 µW illumination power was used with 524 nm illumination wavelength. c Tunable external quantum efficiency (EQE) by the selection of backgate voltage (VBG ). (inset) EQE at different illumination power. d Device scheme of a graphene-MoS2 -metal vertical transistor. e EQE variation with illumination power at various wavelengths. f wavelength dependent EQE at fixed illumination power of 5 µW. Figures reprinted with permission [195]. Copyright (2013) Springer Nature

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ing superior photoresponse. Such a mechanism leads to the idea of external field controlled photoresponse characteristics in graphene-MoS2 structures, which is the main topic of discussion of this thesis.

3.7.3.2

High Quantum Efficiency in Vertical Heterostructures

Vertically stacked heterostructures can harvest light efficiently. Yu et al. presented graphene-MoS2 -graphene and graphene-MoS2 -metal type of transistors where the photoresponse is tuned using an external electric field (Fig. 3.14). A highest external quantum efficiency is achieved in graphene-MoS2 -metal type of devices reaching a value of 55%, and shows a maximum internal quantum efficiency of 85% [195].

Fig. 3.15 Picosecond photoresponse in graphene-WSe2 -graphene heterostructures. a Schematic of charge transfer mechanism in graphene-MoS2 -graphene heterostructures. b Schematic of device cross-section with time resolved photocurrent measurement setup. V B indicates the bias voltage between the top and bottom graphene layers. c Photocurrent as a function of time delay (t) between the two pulses. Photocurrent value is normalised with respect to the different t values. (inset) Band diagram and charge transfer scheme under optical illumination. Red curved arrows indicate incoming photons, blue circle indicate photogenerated holes, blue filled circles indicate photogenerated electrons. d Responsivity of the device at different energy values. Respective excitonic peaks (A, B, A ) of WSe2 are labelled following the Wilson and Yoffe convention. Figures reprinted with permission [189]. Copyright (2015) Springer Nature

3.7 Photodetection with van der Waals Materials

3.7.3.3

69

Picosecond Photoresponse in Graphene-WSe2 -Graphene Heterostructures

Massicotte et al. showed that picosecond photoresponse can be achieved in a graphene-WSe2 -graphene photodetector (Fig. 3.15). A shorter than 5.5 ps response time is reported, which is estimated from time-resolved photocurrent spectroscopy measurement. Such ultrafast charge transfer leads to the idea of utilization of van der Waals heterostructures to make high speed photodetectors.

(a)

(c)

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Fig. 3.16 Atomically thin p-n junction and photovoltage. a (left panel) Schematic of heterostructure made of monolayers of MoS2 , and WSe2 . (right panel) optical image of the device. (inset) scheme of stacking sequence in the overlapped region. b Rectification characteristics at various gate voltages. (Inset) evolution of source-drain current (Ids ) with respect to the gate voltage (Vg ). Two curves for MoS2 , and WSe2 separately. c Energy band scheme in vertical (right panel), and lateral (left panel) directions. d source-drain bias (Vds ) dependent photoresponse for different gate voltage settings Vg . (Inset) colour presentation of photocurrent density in the operational range of Vds , Vg . Figures reprinted with permission [196]. Copyright (2014) Springer Nature

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3 Review: Optoelectronic Response and van der Waals Materials

Atomically Thin p-n Junction and Photovoltage

The remarkable stability of van der Waals materials can be utilized for making sharp interface/junctions. Such a feature was exploited by Lee et al. to make atomically thin p-n junctions. An n-type monolayer MoS2 is assembled with another p-type monolayer WSe2 to make the atomically thin p-n junction (Fig. 3.16a). Figure 3.16b shows the rectifying current voltage characteristics (I DS − VDS ). I DS − VDS is tuned by applying an external gate electric field, which controls the tunnelling assisted recombination of majority carriers in the layers. Inset of Fig. 3.16b represents transfer characteristics of individual layers (blue indicate MoS2 , red indicate WSe2 ), which establishes n and p type nature of the respective materials. Electronic band diagram of the p-n junction is presented schematically in Fig. 3.16c. Lateral and vertical directions are depicted in the left and right panels respectively. Electrons (e−) and holes (h+) recombine with each other in forward bias condition following either Langevin processes or Shockley-Read-Hall; such recombination scheme is indicated by blue and red arrow respectively (right panel). Band offset for electrons (E C ) and holes (E V ) appears because of realignment of Fermi energies (left panel). Photovoltage generation is a direct consequence of the p-n junction under optical illumination (Fig. 3.16d). Choice of different back gate voltage alters the junction potential allowing tunable photoresponse. Inset of Fig. 3.16d shows color representation of the photocurrent density in the operational range of Vds and Vg .

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43. Tebano A, Fabbri E, Pergolesi D, Balestrino G, Traversa E (2012) Room-temperature giant persistent photoconductivity in SrTiO3 /LaAlO3 heterostructures. ACS Nano 6:1278–1283 44. Dutta S, Narayan KS (2004) Gate-voltage control of optically-induced charges and memory effects in polymer field-effect transistors. Adv Mater 16:2151–2155 45. Jeon S et al (2012) Gated three-terminal device architecture to eliminate persistent photoconductivity in oxide semiconductor photosensor arrays. Nat Mater 11:301–305 46. Editorial (2010) Simply silicon. Nat Photonics 4:491–491 47. Chen X, Li C, Tsang HK (2011) Device engineering for silicon photonics. NPG Asia Mater 3:34–40 48. Paniccia M, Photonics N (2010) Integrating silicon photonics. Nat Photonics 4:498–499 49. Hochberg M, Baehr-Jones T (2010) Towards fabless silicon photonics. Nat Photonics 4:492– 494 50. Jackson WB, Amer NM (1982) Direct measurement of gap-state absorption in hydrogenated amorphous silicon by photothermal deflection spectroscopy. Phys Rev B 25:5559–5562 51. Reed GT, Jason Png C (2005) Silicon optical modulators. Mater Today 8:40–50 52. Soref R (2010) Mid-infrared photonics in silicon and germanium. Nat Photonics 4:495–497 53. Paul B, Singh B, Ghosh S, Roy A (2016) A comparative study on electrical and optical properties of group III (Al, Ga, In) doped ZnO. Thin Solid Films 603:21–28 54. Das K, Mukherjee S, Manna S, Ray SK, Raychaudhuri AK (2014) Single Si nanowire (diameter  100 nm) based polarization sensitive near-infrared photodetector with ultra-high responsivity. Nanoscale 6:11232–11239 55. Akinwande D et al (2019) Graphene and two-dimensional materials for silicon technology. Nature 573:507–518 56. Hayden O, Agarwal R, Lieber CM (2006) Nanoscale avalanche photodiodes for highly sensitive and spatially resolved photon detection. Nat Mater 5:352–356 57. McDonagh C, Burke CS, MacCraith BD (2008) Optical chemical sensors. Chem Rev 108:400–422 58. Wolfbeis OS (2005) Materials for fluorescence-based optical chemical sensors. J Mater Chem 15:2657 59. Qazi H, Mohammad A, Akram M (2012) Recent progress in optical chemical sensors. Sensors 12:16522–16556 60. Rodrigo D et al (2015) Mid-infrared plasmonic biosensing with graphene. Science 349:165– 168 61. Howes PD, Chandrawati R, Stevens MM (2014) Colloidal nanoparticles as advanced biological sensors. Science 346:1247390–1247390 62. Pumera M (2011) Graphene in biosensing. Mater Today 14:308–315 63. Martin CR, Siwy ZS (2007) Learning nature’s way: biosensing with synthetic nanopores. Science 317:331–332 64. Tarkhov M et al (2006) Single Photon counting detector for THz radioastronomy. In: Seventeenth international symposium space terahertz technology, pp 119–122 65. Bobin J, Starck J-L, Ottensamer R (2008) Compressed sensing in astronomy. IEEE J Sel Top Signal Process 2:718–726 66. Starck J-L, Murtagh F, Pirenne B, Albrecht M (1996) Astronomical image compression based on noise suppression. Publ Astron Soc Pacific 108:446 67. Zappa F, Tisa S, Tosi A, Cova S (2007) Principles and features of single-photon avalanche diode arrays. Sens Actuators A Phys 140:103–112 68. Hadfield RH (2009) Single-photon detectors for optical quantum information applications. Nat Photonics 3:696–705 69. Divochiy A et al (2008) Superconducting nanowire photon-number-resolving detector at telecommunication wavelengths. Nat Photonics 2:302–306 70. Verevkin A et al (2004) Ultrafast superconducting single-photon detectors for near-infraredwavelength quantum communications. J Mod Opt 51:1447–1458 71. Zappa F, Tisa S, Tosi A, Cova S (2007) Principles and features of single-photon avalanche diode arrays. Sens Actuators A Phys 140:103–112

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Chapter 4

Experimental Techniques, Instruments, and Cryostat

Photoresponse study of van der Waals heterostructures, discussed in this thesis, has been accomplished following (a) sample fabrication, (b) optoelectronic measurements, and (c) analyses of recorded data. Various experimental techniques, instruments, and software codes are independently developed in order to complete these. Fabrication techniques and setup have been developed to prepare samples, optical cryostat was developed to perform optoelectronic experiments, and software codes are written on various platforms (e.g. LabView, CryoMeas, Origin) to record and analyse experimental data etc. Detail informations related to all such developments are mentioned in following sections.

4.1 Van der Waals Heterostructure Fabrication Technique and Setup One of challenging task of sample fabrication is to find and attach atomically thin (or only few nm thick) flakes that have lateral microscopic dimensions (few μm to few mm). Small flake dimension is a natural consequence of mechanical cleaving process from bulk crystal [1–4]. Emerging field of van der Waals (vdW) materials do not offer any low-cost commercial setup to attach such small flakes leading heterostructure formation. Also, during our first few set of experiments we were not aware of the availability of any commercial setup which we could use for heterostructure preparation. Thus, sample fabrication of van der Waals heterostructures led to the development of various techniques such as pick-orient-attach (or pick-and-attache) technique, fast confirmation of layer number finding of atomically thin materials etc. Heterostructure fabrication setup was also built, use of which allows attaching small vdW flakes (here ∼few μm) with high translational and rotational precision. Detail of fabrication techniques and the developed instrument are discussed in following sections. © Springer Nature Switzerland AG 2020 K. Roy, Optoelectronic Properties of Graphene-Based van der Waals Hybrids, Springer Theses, https://doi.org/10.1007/978-3-030-59627-9_4

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MLG

SiO2 10 μm

SiO2 BLG

SiO2 10 μm

10 μm MoS2

10 μm SiO2

MoS2

Fig. 4.1 Atomically van der Waals materials. Optical images of a monolayer graphene (MLG), b Bilayer-graphene (BLG), c Monolayer MoS2 and d multilayers MoS2 on Si++ /SiO2 substrate with SiO2 thickness of 285 nm

4.1.1 Mechanical Cleaving, Substrate Roughness, and Yield The flakes are obtained from bulk materials following mechanical cleaving (exfoliation) with sticky tape (e.g. Scotch tape). The commonly used substrate for exfoliation process is Si++ /SiO2 . To cleave, the bulk material is brought in physical contact of SiO2 . Van der Waals attraction between SiO2 and the respective materials allows attaching some part of bulk-material in the form of small flakes onto SiO2 (Fig. 4.1). Typical size of these flakes vary from few micrometers to few tens of micrometers, and differ significantly depending on substrate roughness, material etc. For example, highly polished SiO2 shows less yield in obtaining single to few layers of materials than rough SiO2 . Often, polished SiO2 is treated with RCA1 solution (NH4 OH:H2 O2 :H2 O = 1:1:5) to increase the surface roughness to achieve better/bigger flakes. Oxygen plasma treatment and heating the substrate before exfoliation can also be beneficial to improve the yield [5]. Different materials can also show different exfoliation yield. Such as mechanical exfoliation of graphene gives much better yield than MoS2 while similar substrates are used; this can be attributed to either low van der Waals force between MoS2 –SiO2 or strong interlayer coupling force between MoS2 layers. After exfoliation these small flakes are located using high resolution optical microscope (typical magnification factor 500x, 1000x). Si++ /SiO2 having SiO2 thickness of ∼100 or ∼300 nm is the preferable substrate for sample fabrication. Such thickness of SiO2 gives best optical contrast for graphene like atomically thin structures and ease the finding of these small flakes [6]. Use of sticky tape always leave polymer residues in many parts of SiO2 , and appear from the parts wherever it is not covered with the material. Tape residue can cause various low performance related issues such as high contact resistance, low mobility, residual doping of the channel etc. It is noticed that a continuous/unbroken bulk does not give good exfoliation yield, rather the presence of broken edges increase the yield of thinner flakes. However, multiple broken edges allow the glue to come in contact with SiO2 , leaving residues. Practically, it is a trade-off between the two that gives a reasonable exfoliation with less polymer residue.

4.1 Van der Waals Heterostructure Fabrication Technique and Setup After green filter 1 1 2

1000 1 (SiO2)

Pixel number

800

400

1

2 (MLG) 3 (TLG)

-1

Intensity 180

FWHM 4.8

2

150.2

4.8

3

170.1

4.8

After green filter

1000

2 3

600

(b)

Pixel number

(a)

81

2 (BLG)

1 (SiO2)

1

800

2

600 -- Intensity FWHM 1 180 4.8 2 159.7 4.8

400 200

200

0

0 140

160

180

Intensity (0-255)

200

140

160

180

200

Intensity (0-255)

Fig. 4.2 Graphene layers and unique optical contrast. a Histogram of a 100 × 100 pixel image (inset) with monolayer (MLG) and triple layers (TLG) of graphene on 285 nm SiO2 . b Histogram of a 100 × 100 pixel image (inset) with bilayer graphene (BLG) on 285 nm SiO2

4.1.2 Optical Contrast and Layer Number Identification Confirmation of layer number comes from Raman spectroscopy [7–9]. Raman spectroscopy is preferred to characterize monolayer or few layer samples because of the unique and highly sensitive spectral response of these layered structures. Often atomic force microscopy (AFM) is used to find the thickness of thicker flakes. However, thickness confirmation of monlayer materials ( 90 K QUIT loop ]#Diff Vbg loop #**********Reset source values before END d0 r0,1200,-107 r0,120,441 #Set all gate sources to zero at END

4.4.4 LabTalk script and data analysis Often multiple parameters, in addition to the main/targeted parameters, are recorded to answer critical questions that may arise to justify the device performance. Such addition increases the volume of acquired dataset in a significant way. For example, when performing a top gate voltage dependent experiment, the gate leakage current (Ileakage ) is also recorded, along with the gate voltage (VTG ) and source-drain current (IDS ). Typically when the leakage current is low then it has no role in actual data analysis, however recording of expected low values give additional confidence in justifying the field effect response of the device. Thus, three columns (VTG , IDS , Ileakage ) are recorded here. When repeating this experiment for a range of back gate voltages (VTG ) the collection of columns become large and mixed (often a set of 300–1000 columns). It is useful to use programming script to extract desired sub-set of data from the big-set. LabTalk is the programming environment of Origin, which is used not only to extract a desired sub-set of data but also to do other tasks such as perform mathematical calculations, curve fitting, organizing data etc. Following is an example where script is used to estimate photocurrent (I P ) from a large set of data. The elementary LabTalk operators are used here. Description of the elementary operators can be found in LabTalk programming manual of OriginLab.

4.4.4.1

Photocurrent (I P ) Analysis Using LabTalk script

//**********Input Parameters //Step-01 parameters: Copy data int l1=4; //1st X-column of light off data int l2=10; //1st X-column of light on data int l3=12; //on off cycle repating after these columns

//Step-02,03,04 parameters: Interpolation, Ids, Ip tg1=-3.2; //top gate minimum value

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tg2=+3.2; //top gate maximun value dtg=0.01; //step size

//Step-04 parameters: Label Vbg, XYZ format Vbg=70; dVbg=-5;

//**********Step-01 copy data //Data 141_I-Vtg at diff Vbg @609nm //Copy proper set of columns to "Sheet1" including labels. int jj=1, kk=wks.ncols, kk=kk-l3; for(int ii=0;ii 0 E F stays inside the conduction band, hence, the negatively charged carriers (electrons) control the channel conductance. However, for VBG < 0, E F stays at the lower part of the conical shape (valance band, topleft panel, Fig. 5.8a), and as a result, positively charged carriers (holes) now control the channel conductance. Zero bandgap between the conduction and valence bands allows a smooth transition in channel resistance when changing from hole ( p) type carrier to electron (n) type (left to right). The highest resistance point is referred to as charge neutrality point (CNP) because at this value of gate voltage E F lies in the middle of conduction and valence band. Available density of states at CNP is minimum, hence, the effective channel conductance attains a minimum value. In a pristine graphene transistor, CNP is expected to appear at VBG = 0 V. However, residual doping effect can alter the CNP position. Different substrates, or fabrication related contamination may cause residual doping. In the given R − VBG characteristics (Fig. 5.8a) a small shift of the CNP to the right is observed, indicating residual p-type doping, and is attributed to the polymer residues that remain with the graphene layer after the metal-lead fabrication process. The ease of tunability of ambipolar channel characteristics is a natural consequence of the gap less band structure of graphene. The mobility value of graphene is estimated to be ∼7000 cm2 V−1 s−1 . Figure 5.8b shows the transfer characteristics of a few-layer MoS2 FET prepared on Si++ /SiO2 substrate. To fabricate electrical leads only Au is used as contact metal. The measurements are carried out in two probe configuration (see Sect. 1.5). Presence of a bandgap in MoS2 allows varying the channel conductance (g = I DS /VDS , where

132

5 Material and Heterostructure Interface Characterization

(a)

MoS2

(b)

graphene

DOS

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EF

EF x

g ( x 10 -7 Ω -1)

R (kΩ)

2 μm

4

2

0

x

localized states

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6

Ec

EF

60

30 VTH

0 -30

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15

30

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0 VBG (V)

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60

Fig. 5.8 Tunable electronic properties of graphene and MoS2 . a (Bottom panel) Electrostatic tunability of source drain channel resistance of a graphene field effect transistor (FET) on a Si++ /SiO2 substrate. (Inset) Scanning electron micrograph of a device. (Top panels) Variation of Fermi energy E F when changing gate voltages (V BG ). b (Bottom panel) Source-drain conductance characteristics of a few-layer MoS2 FET. (Top panels) Variation in E F when accessing different density of states responsible for channel conduction

I DS = source-drain current and VDS = source-drain voltage) over a wide range of values. Here VDS is kept fixed at 0.1 V and gate voltage (VBG ) is varied. At negative gate voltages (VBG < VT H ) E F stays deep inside the energy gap, allowing access to only few electronic states in the band tail (top-left panel Fig. 5.8b) [17]. Due to presence of few electronic states in this range of VBG , the channel conductance is consequently also low. As VBG is increased above a threshold value (VT H ), E F moves near the conduction band allowing access to large number of electronic states, which result in increasing channel conduction. A detailed study with thin MoS2 flakes indicate that the electrical transport is mainly dominated by the localized states originating from the disordered potential landscape of the underlying SiO2 substrate [17]. It should be mentioned here that nitride based dielectric substrates help improving the mobility of MoS2 [18]. Further, tuning of E F into the valence band cannot be achieved on application of larger negative gate voltages, thus forbidding electrical conduction because of holes. Often Fermi level pinning is considered to be the reason for unavailability of hole conduction in MoS2 FET [19–21]. From the presented characteristics the mobility value of MoS2 is estimated to be ∼10 cm2 V−1 s−1 .

5.7 Graphene–on–MoS2 Substrate

133

5.7 Graphene–on–MoS2 Substrate A two probe measurement with graphene-on-MoS2 hybrid is carried out choosing a pair of contacts as source and drain (Fig. 1.1a). A Keithly-2400 source-measure unit (SMU) is used as a DC sourcing and measuring unit to monitor the source-drain characteristics. Another SMU is used to control the gate voltage (VBG ) supply to the device. The black line in Fig. 5.9 (top panel) shows the source-drain current (I DS ) versus gate voltage (VBG ) characteristics of the graphene-on-MoS2 device. This data was taken at 130 K temperature with 0.1 V source-drain bias (VDS ). The MoS2 used in this particular device consists of ≈5 layers. Unlike bare graphene characteristics (Fig. 5.8a), a clear asymmetry in the transfer characteristics arise because of the VBG dependent conducting property of MoS2 . Naturally n-doped MoS2 becomes conducting when VBG is increased beyond the threshold voltage value (cyan line, VT H ≈ −23 V). Availability of a large number of electronic states in MoS2 prevents further modulation of the E F position of graphene-on-MoS2 structure (bottom-right panel). Hence, changes in carrier density in graphene appear insignificant with respect to the increment of backgate voltage. Insignificant modulation in E F , which controls the carrier density, leads to an almost fixed value of channel conductivity, hence, a saturation in the I DS is observed for VBG  VT H regime. This effect is also alternatively considered as the screening of gate voltage (VBG ) to graphene by MoS2 . However, on the negative side of the gate voltages (VBG  VT H ) E F lies deep down the band-tail (bottom-left panel) where available electronic states are very low inside MoS2 . Hence, MoS2 acts almost as an insulator, allowing graphene to see the complete effect of gate voltage. This observation is clear from the modulation of graphene channel current for VBG  VT H regime. It needs to be noted here that, at any VBG , the conductance values of graphene channel are always large (atleast by two orders of magnitude; see Sect. 5.6) compared to the values of MoS2 channel. Hence, the possibility of forming a parallel current path in the MoS2 channel is neglected. Substrate induced control on the electrical response of graphene, for example hysterias or anti-hysteresis in graphene transistor, is discussed in the following Refs. [22, 23].

5.8 Residual Doping and Barrier Formation in graphene-MoS2 Interface Residual doping in graphene can be considered as an indication of barrier formation at graphene-MoS2 interface. A barrier is formed to prevent the spontaneous charge transfer across the interface when these come in contact. Inset of Fig. 5.10a depicts simplified band diagram of graphene and MoS2 . Fermi energy of MoS2 (E Fm ) stay g above the Fermi energy of pristine graphene (E F ). Thus, electrons (blue circles) from MoS2 starts moving to graphene through the van der Waals gap. In equilibrium Fermi energy (E F ) stays at an intermediate position leaving graphene electron doped (Inset,

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180

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GMoS (μS) 2

Ids (μA)

420

V

TH

0 -20

-50

10

Vg (V) graphene MoS 2 DOS

graphene MoS 2 DOS Ec

Ec

EF

EF x

x

Fig. 5.9 Transfer characteristics of graphene-on-MoS2 FET. (Top panel) black line indicates source drain current (I DS ) versus gate voltage (VBG ) characteristics of graphene-on-MoS2 device. Transfer characteristics of a MoS2 FET of similar thickness is represented by the cyan curve. (Inset) Schematic of a hybrid device. (Bottom panel) Schematic presentation of electrostatic doping for VBG < VT H (left panel) and VBG > VT H (right panel)

Fig. 5.10b). Effect of electron doping shows a left-shift in charge neutrality point in the gate dependent transfer characteristics study. Because of this charge transfer, MoS2 gets depleted of charges (red-shedding) and alters the exciton dynamics (see Sect. 5.3). A systematic gate controlled evolution of I DS is presented in Fig. 5.10 for both BLG-on-MoS2 and only MoS2 channels. Orange traces indicate I DS − VBG and I DS − VT G characteristics of BLG-on-MoS2 -channel when VT G and VBG are kept fixed at zero voltages respectively (Fig. 5.10a, b). Both the orange traces show that the charge neutrality point (CNP, lowest I DS ) is shifted towards the negative side in respective gate voltage axes. The small left-shift from zero value is an indication of residual electron doping of the BLG channel, and can be attributed to the charge transfer due to realignment of Fermi energy of BLG and MoS2 owing to the physical proximity of these layers [24]. The work function of MoS2 is smaller than the work function of graphene [24–29], hence, as a result of the physical proximity, electrons get transferred to graphene to equilibrate the Fermi energy (inset, Fig. 5.10a). The effect of charge exchange creates an inbuilt electric field leading to a Schottky barrier

5.8 Residual Doping and Barrier Formation in graphene-MoS2 Interface (a) 9 Ec EFm

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vdW gap

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135

vdW gap MoS2 φΒ DOS

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x

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0

1

2

VTG (V)

Fig. 5.10 Transfer characteristics of a BLG and MoS2 channel. a VBG dependence of I DS of BLG-on-MoS2 FET for VT G = 0 V (orange line) and of only MoS2 (cyan line) on Si++ /SiO2 substrate. b Topgate dependent evolution of I DS of BLG-on-MoS2 channel at VBG = 0 V. Insets in a, b illustrate the residual doping mechanism

formation (φ B , inset, Fig. 5.10b). Owing to the dry fabrication process, where BLG always remains protected between MoS2 and BN, the possibility of doping from polymer used in the device fabrication process can be eliminated. The cyan trace in Fig. 5.10a illustrates the transfer characteristics of only MoS2 FET. It is apparent that MoS2 remains non-conducting till ∼20 V (threshold voltage, VT H ∼ 20 V), and hence, presence of it under BLG does not screen VBG , giving a symmetric I DS − VBG curve around CNP till this range (orange trace, Fig. 5.10a). Although bilayer graphene on MoS2 (BLG-MoS2 ) type devices (Fig. 1.1b) were used for this study, use of BLG or monolayer-graphene does not bare any significance, rather, both types of materials are expected to reveal similar dopingmechanism across the interface. However, there are two reasons why BLG-MoS2 type devices (Fig. 1.1b) were used instead of monolayer graphene-on-MoS2 type devices (Fig. 1.1a); (a) top surface of BLG-MoS2 type devices remain protected with BNlayer and does not come in contact with the polymer which is used in the device fabrication process. Thus, possibility of doping the BLG-channel by the presence of polymer-residues can be eliminated. This helps asserting the fact that the electronic doping in BLG has occurred because of the charge transfer between BLG and MoS2 only. (b) The top-gated structure in BLG-MoS2 type deices helps probing the BLG-channel without applying any vertical electric field inside MoS2 . Otherwise, presence of a vertical filed inside MoS2 can induce additional charge transfer to the BLG channel. A separate dual gated device (like Fig. 1.1b) with monolayergraphene in place of BLG is also expected to show similar residual doping mechanism across graphene-MoS2 interface. Such analogy assumes the work function of pristine monolayer-graphene and bilayer-graphene to have similar values. More discussions on graphene-MoS2 interface can be obtained in the following Refs. [25, 30, 31].

136

VTG 1.44V

25 20

IP (%)

Fig. 5.11 Wavelength dependent photocurrent. Percentage change in photocurrent at various wavelength values. VDS , VBG , VT G , and PL E D are kept fixed at 50 mV, −40 V, 1.44 V, and 36 fW µm−2 respectively

5 Material and Heterostructure Interface Characterization

15 10 5 0 400

500

600

700

λ (nm)

800

900

1000

5.9 Wavelength Dependent Photocurrent Owing to the presence of the excitonic states in MoS2 it is important to understand the wavelength dependent photoresponse characteristics in graphene-MoS2 devices. Use of improper wavelength often fails to excite the respective exciton states [4, 32], hence a reduced photoresponsivity arises [33, 34]. Figure 5.11 shows wavelength dependent photocurrent response of a BLG-onMoS2 device, where MoS2 is few layers (≈8–10 layers) thick. The vertical-axis represents percentage change in photo current which is estimated using the relation I P = 100 × (I L − I D )/I D %. Here I L , I D are source-drain current in presence and absence of light respectively. Different set of LEDs are used to get different wavelengths. The optical power is kept fixed at PL E D = 36 fW µm−2 throughout the experiment. Relatively large photo response near 600 nm (highest at 609 nm) is understood from the optical absorption characteristics of MoS2 , and also relates to the A, B and A−1 excitons of MoS2 (Sect. 5.3). For example, peak near 600 nm wavelength resembles the efficient absorption near A− , A and B excitonic peaks (peaks not resolved here). Peak near 500 nm resembles the high-energy exciton of MoS2 [7, 35]. At shorter wavelengths, the overall decay in I P happens because of the reduced photon flux and expected to remain constant when the I P is normalized with the excitation wavelength (λ) [36].

5.10 Summary • Unique Raman signatures of graphene and MoS2 are utilized as a tool to identify layer numbers. Because of mode stiffening due to van der Waals coupling force between the layers, a monotonic blue shift of A1g peak of MoS2 is observed as 1 shows a red shift, which is attributed the layer number increases. However, E 2g

5.10 Summary

•

•

•

• •

•

137

to the structural property change, and long range Coulomb interactions as layer number is increased. Peak-position difference is utilized as a characteristic tool in identification of layer numbers. In Raman characteristics of graphene-MoS2 devices, the A1g peak shows blue shift compared to the position of pristine MoS2 . Such shift shows a close match with the value of 2-layer crystalline MoS2 . This indicates a similar strength of interlayer coupling in graphene-MoS2 hybrids via van der Waals interactions. Negligible shift 1 indicates less structural effect on MoS2 , due to the presence of graphene in in E 2g the hybrid structure. Photoluminescence study reveals the charge transfer and exciton splitting at the graphene-MoS2 interface. Charge transfer reduces electron carrier density in MoS2 , thus, charge-exciton (A− ) formation reduces significantly. Charge transfer also induces an interfacial electric field, which splits A and B excitons in MoS2 . Study with atomic force microscope (AFM) shows that nearly perfect interface can be produced via mechanical attachment technique. However, the appearance of residues is common, leading to the formation of bubbles that prevent smooth interface formation. Static electric field tunability of the barrier at graphene-MoS2 interface has also been demonstrated. It is seen that the interfacial barrier can be tuned from few hundreds of meV to close to zero value. Gate voltage dependent electrical characteristics of dual gated BLG-on-MoS2 devices show residual electron doping in graphene. Residual doping follows electron transfer from MoS2 leading Schottky barrier formation at the interface. Depletion of electron density in MoS2 also supports the evolution of exciton dynamics obtained from photoluminescence study at graphene-MoS2 interface. Wavelength dependent photoresponse in graphene-MoS2 devices appear because of the limited absorption efficiency of MoS2 in selective range of wavelength values.

References 1. Ferrari AC et al (2006) Raman spectrum of graphene and graphene layers. Phys Rev Lett 97(4):187401 2. Malard LM, Pimenta MA, Dresselhaus G, Dresselhaus MS (2009) Raman spectroscopy in graphene. Phys Rep 473:51–87 3. Li H et al (2012) From bulk to monolayer MoS2 : evolution of Raman scattering. Adv Funct Mater 22:1385–1390 4. Mak KF et al (2012) Tightly bound trions in monolayer MoS2 . Nat Mater 12:207–211 5. Li Y et al (2016) Tuning the excitonic states in MoS2 /graphene van der Waals heterostructures via electrochemical gating. Adv Funct Mater 26:293–302 6. Buscema M, Steele GA, van der Zant HSJ, Castellanos-Gomez A (2014) The effect of the substrate on the Raman and photoluminescence emission of single-layer MoS2 . Nano Res 7:561–571

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7. Castellanos-Gomez A, Quereda J, van der Meulen HP, Agraït N, Rubio-Bollinger G (2016) Spatially resolved optical absorption spectroscopy of single- and few-layer MoS2 by hyperspectral imaging. Nanotechnology 27:115705 8. Yadav P, Srivastava PK, Ghosh S (2015) Dielectric screening of excitons in monolayer graphene. Nanoscale 7:18015–18019 9. Hong X et al (2014) Ultrafast charge transfer in atomically thin MoS2 /WS2 heterostructures. Nat Nanotechnol 9:1–5 10. He J et al (2014) Electron transfer and coupling in graphene-tungsten disulfide van der Waals heterostructures. Nat Commun 5:5622 11. Ross JS et al (2017) Interlayer exciton optoelectronics in a 2D heterostructure p-n junction. Nano Lett 17:638–643 12. Chen H et al (2016) Ultrafast formation of interlayer hot excitons in atomically thin MoS2 /WS2 heterostructures. Nat Commun 7:12512 13. Joo M-K et al (2017) Electron-hole pair condensation in graphene/MoS2 heterointerface. arXiv:1711.00606 14. Haigh SJ et al (2012) Cross-sectional imaging of individual layers and buried interfaces of graphene-based heterostructures and superlattices. Nat Mater 11:764–767 15. Khestanova E, Guinea F, Fumagalli L, Geim AK, Grigorieva IV (2016) Graphene bubbles on a substrate: universal shape and van der Waals pressure. Nat Commun 7:1–10 16. Jain SK, Juriˇci´c V, Barkema GT (2017) Probing the shape of a graphene nanobubble. Phys Chem Chem Phys 7465–7470 17. Ghatak S, Pal AN, Ghosh A (2011) Nature of electronic states in atomically thin MoS2 fieldeffect transistors. ACS Nano 5:7707–7712 18. Bhattacharjee S, Ganapathi KL, Mohan S, Bhat N (2017) A sub-thermionic MoS2 FET with tunable transport. Appl Phys Lett 111:163501 19. Bampoulis P et al (2017) Defect dominated charge transport and Fermi level pinning in MoS2 /metal contacts. ACS Appl Mater Interfaces 9:19278–19286 20. Gong C, Colombo L, Wallace RM, Cho K (2014) The unusual mechanism of partial Fermi level pinning at metal-MoS2 interfaces. Nano Lett 14:1714–1720 21. Yang Z et al (2019) A Fermi-level-pinning-free 1D electrical contact at the intrinsic 2D MoS2 metal junction. Adv Mater 31:1808231 22. Sahoo A et al (2018) Out-of-plane interface dipoles and anti-hysteresis in graphene-strontium titanate hybrid transistor. npj 2D Mater Appl 2:9 23. Ahmed T et al (2020) A generic method to control hysteresis and memory effect in Van der Waals hybrids. Mater Res Exp 7 24. Sachs B et al (2013) Doping mechanisms in graphene-MoS2 hybrids. Appl Phys Lett 103:251607 25. Kwak JY et al (2014) Electrical characteristics of multilayer MoS2 FET’s with MoS2 /graphene heterojunction contacts. Nano Lett 14:4511–4516 26. Kim S et al (2012) High-mobility and low-power thin-film transistors based on multilayer MoS2 crystals. Nat Commun 3:1011 27. Yu YJ et al (2009) Tuning the graphene work function by electric field effect. Nano Lett 9:3430–3434 28. Kim JH et al (2013) Work function engineering of single layer graphene by irradiation-induced defects. Appl Phys Lett 103 29. Yun JM et al (2013) Efficient work-function engineering of solution-processed MoS2 thin-films for novel hole and electron transport layers leading to high-performance polymer solar cells. J Mater Chem C 1:3777–3783 30. Rathi S et al (2015) Tunable electrical and optical characteristics in monolayer graphene and few-layer MoS2 heterostructure devices. Nano Lett 15:5017–5024 31. Lee I et al (2020) Photoinduced tuning of Schottky barrier height in graphene/MoS2 heterojunction for ultrahigh performance short channel phototransistor. ACS nano 14:7574–7580 32. Mak KF, Lee C, Hone J, Shan J, Heinz TF (2010) Atomically thin MoS2 : a new direct-gap semiconductor. Phys Rev Lett 105:136805

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33. Lui CH et al (2014) Trion-induced negative photoconductivity in monolayer MoS2 . Phys Rev Lett 113:166801 34. Saigal N, Ghosh S (2015) Phonon induced luminescence decay in monolayer MoS2 on SiO2/Si substrates. Appl Phys Lett 107:242103 35. Dhakal KP et al (2014) Confocal absorption spectral imaging of MoS2 : optical transitions depending on the atomic thickness of intrinsic and chemically doped MoS2 . Nanoscale 6:13028–13035 36. Wu CC et al (2013) Elucidating the photoresponse of ultrathin MoS2 field-effect transistors by scanning photocurrent microscopy. J Phys Chem Lett 4:2508–2513

Chapter 6

Photoresponse in Graphene-on-MoS2 Heterostructures

Basic optoelectronic response study of graphene-on-MoS2 heterostructures is discussed in this chapter. It is shown that the optical response of MoS2 can be combined with the high quality electronic transport property of graphene leading to ultrasensitive photoresponse. In the back gated field effect devices, the photogenerated carriers are separated because of the presence of gate induced electric field, which prevents photogenerated electron-hole pairs to recombine. Presence of a gate electric field (E) allows electrons to move to graphene from MoS2 , allowing a controlled doping, and is termed as photodoping (or photogating). Photodoping effect is measured by measuring the change in electrical conductivity in the graphene channel. A comparative photoresponse study between graphene-on-MoS2 , bare graphene, and bare MoS2 , is demonstrated to highlight the superior response of graphene-on-MoS2 structures. Electrostatic control of the photodoping mechanism is illustrated with supporting experimental data. A charge carrier dynamics model has been adapted to explain the high photogain mechanism, and also to explain the high photoresponsivity achieved in these devices. Charge carrier dynamics model allows us to connect the high quality electronic mobility of graphene to the large photogain mechanism. Further, experimental evidence has been presented in this chapter to support the carrier dynamics model. Interested readers may look into the review report by Long et al., for an elaborated discussion on the progress and challenges for graphene and other 2D materials based photodetectors [1].

6.1 Controlled Photoresponse Study in Bare graphene and MoS2 Devices Light and gate pulse dependent experiments are performed to understand the photoresponse of graphene and MoS2 field effect transistors (FET) separately (Fig. 6.1). Both experiments are performed keeping VDS and VBG fixed, and monitoring the channel resistance as a function of time. A sequence of light pulses (indicated by the © Springer Nature Switzerland AG 2020 K. Roy, Optoelectronic Properties of Graphene-Based van der Waals Hybrids, Springer Theses, https://doi.org/10.1007/978-3-030-59627-9_6

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6 Photoresponse in Graphene-on-MoS2 Heterostructures graphene

Light pulse

Gate pulse

MoS2

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VBG (V)

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0.25

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0.92 0.90

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1.80 0.149 0.145 0.132

20

0.129

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1.89 18

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2.00

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R (M)

R (k)

0.36

6.40 5.60

24

30

t (minutes)

0.119

40

50

t (s)

100

Fig. 6.1 Controlled photoresponse study in bare graphene and MoS2 devices. (Left-panel) Photoresponse test of a graphene field effect transistor (FET) on Si++ /SiO2 substrate. (Right-panel) Photoresponse test of few layer MoS2 device. Light and gate pulses are used to excite and reset the devices respectively. Appearance of light and gate pulses are indicated by vertical red (dashed) and cyan (dotted) lines respectively. Different gate voltage values are used to find electrostatic tunablity of photoresponse if present

red dashed lines) is applied to capture the photoresponse of the devices; each light pulse is accompanied by a gate pulse as a routine reset operation that is needed if significant persistent photoresponse is present (see Fig. 4b in Ref. [2]). Similar experiments are performed for several VBG values to understand the electrostatic tunability of photoresponse under such pulsing operations. Operational range for graphene and MoS2 are chosen considering the presence of charge neutrality point (CNP), and threshold voltage (VT H ) of graphene and MoS2 respectively (see Sect. 5.6, 5.7, 5.8). Left panel in Fig. 6.1 shows the result obtained with graphene FET. No measurable change in the channel resistance is observed when light pulse is applied. This null result is understood from the ultrafast charge recombination mechanism [3, 4] of photo generated electron hole pairs (e − h). Fast recombination of e − h pairs results in a short lifetime of these carriers, leading to a negligible change in the effective carrier concentration which determine the electrical conductance. To keep clarity in the presentation, the transient spikes in the resistance values have been removed at the places of gate pulses. Right panel in Fig. 6.1 indicates results obtained with bare MoS2 FET. At higher VBG values, lowering of resistance is observed at the places where light pulses are

6.1 Controlled Photoresponse Study in Bare graphene and MoS2 Devices

143

applied. Because of finite band gap of few layer MoS2 (∼1.3 eV Ref. [5]), a rise in quasi-Fermi level of electron occurs in presence of light pulses, causing a decrease in channel resistance (see photoconducting effect, Sect. 3.1.1). However, towards negative side of VBG no significant photoresponse is observed. Availability of negligible number of accessible states in the band tail along with the strongly localized nature of these electronic states [6] leads to negligible photoresponse in this regime (VBG VT H . A scheme of charge transfer mechanism is presented in the inset of Fig. 7.1a (also see Sect. 6.3). VBG dependent switching operation is further illustrated in Fig. 7.1b. In this experiment resistance of the device is monitored as a function of time by turning the light on and off in alternative sequence. Different panel indicate similar set of experiments performed with different VBG settings while source-drain bias (VDS ) is kept fixed. Shaded regions indicate the duration of illumination pulses. The vertical-axes indicate the percentage change of resistance, defined as R/R = 2(Rl − R p )/(Rl + R p ), caused by the light (see Fig. 7.2a). Appreciable switching magnitude is observed only for VBG < VT H , where MoS2 acts like a dielectric allowing sufficient amount of electric field (E) inside MoS2 . Strong E efficiently separate electron hole pairs (e − h) causing prominent switching magnitude in presence of light. For VBG > VT H , E is low to show significant switching magnitude.

(b)

(a) light dark

R / R (%)

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0V

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0

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18

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Fig. 7.1 Basic switching operation. a Transfer characteristics (R − V BG ) of a monolayer graphene-on-MoS2 device in presence and absence of light. (Inset) The band diagram of the respective materials at different gate voltages (V BG ). b VBG dependent switching operation of the device under the illumination of white light. The shaded region indicate presence of light

7.2 Persistent Photoresponse and Reset Operation

159

7.2 Persistent Photoresponse and Reset Operation It needs to be mentioned that the operations presented in Fig. 7.1b does not illustrate the response of the device when light is illuminated for very first time. Such an example is presented in Fig. 7.2a. The initial resistance of the device at dark is marked by Rd . After the first illumination cycle, the device does not return to its original dark state. It rather stays in an intermediate state (R p ), referred to as the state of persistent photoresponse (PPC). In subsequent light on and off cycles, the device switches between Rl and R p as shown in Fig. 7.2a. PPC in graphene-on-MoS2 samples is observed for a wide range of gate voltages (VBG ) and is found to be extremely stable, because of electric field (E) meditated (partial) trapping of one type of photogenerated carriers (here holes (h)) in the MoS2 -SiO2 interface. A strong negative VBG helps in holding more number of holes showing larger PPC. Tunability of PPC with application of proper VBG allow these device to be used as an optoelectronic memory devices. More details of such memory/switching operations along with the theoretical model with quantitative explanation of PPC is discussed in subsequent sections. Recovering PPC is an important aspect of the switching operation. A full recovery in PPC allows switching operation to hold over any number of cycles without any significant change in the original state of the device. Trapping of photogenerated holes in MoS2 -SiO2 interface happens because of the VBG generated electric field (E), alternatively suggests that lowering of E may allow release of these trapped charges. Lowering of E values are done by applying a positive gate voltage pulse for a short duration. A test experiment with gate voltage pulse of different height (VBG ) is presented in Fig. 7.2b. When the device is operating at −40 V, a gate pulse with 20 V height completely recovers the persistent state. Further use of increased pulse height, (a)

(b)

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Rl

Rp

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20 V

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Fig. 7.2 Persistent photoresponse and reset operation. a Demonstration of persistent state. Device resistance does not comeback to the original dark state (Rd ), rather stay in an intermediate state (R P ) termed as persistent state. After first light on-off cycle it keeps on switching between Rl and R P . b Testing of recovery operation (RESET) of PPC using different values of V BG pulse magnitude

160

7 Switching Operation with Graphene-on-MoS2 Heterostructures

such as 30 V, does not alter the recovered state. The duration of the pulse width is restricted by charge carrier dynamics, and response speed of the measurement setup used in these experiments. Similar light pulses are used in all cycles when performing SET operation. VDS is also kept fixed while monitoring the sample resistance.

7.3 Optoelectronic Memory Operation It is observed that PPC in graphene-on-MoS2 devices depend strongly on VBG . Application of a positive gate pulse can release the trapped charges, resetting the device resistance to its original dark value. This idea of resetting the device allows demonstration of the switching operation possible with the application of light and gate pulses respectively. A basic switching operation is presented in Fig. 7.3a. VBG of the device is kept fixed at a particular value (−17 V) and resistance is monitored as a function of time (cyan line). An application of a light pulse (vertical red line) takes the device to the persistent state (R p ). This operation is termed as ‘SET’. The device remains in R p state unless a positive gate voltage pulse is applied (vertical green line). A suitable gate voltage pulse (VBG = 20 V) brings the device to its original state (Rd ), and is termed as ‘RESET’ operation. However, choice of improper VBG can cause null result in switching operation as illustrated by the orange line. Here VBG is set at +5 V where photogating effect is negligible because of the increased conductivity of MoS2 (Sect. 6.8).

(a)

SET pulse sequence

RESET

(b)

VBG (V) -20

1.59

light pulse

1.57

gate voltage pulse

-25

1.13

0.92

1.69

VBG= -17.5 V

R 

VBG = 5 V

Rd

0.87

0

200

t (s)

400

1.64 600

R (k)

R (k)

Rp

R (k)

1.11 0.83

-30

0.81 -35

0.64 0.62

-40

0.52 0.50

10

20

30

40

50

t (minute)

Fig. 7.3 Optoelectronic memory operation. a SET and RESET operation at a suitable gate voltage (cyan line). Vertical red (dashed), and cyan (dotted) lines indicate appearance of light and gate pulses respectively. V BG can be set to get no memory effect as indicated by orange line. b Switching operation at various VBG values. Light and gate pulse magnitudes are kept similar for all panels

7.3 Optoelectronic Memory Operation

161

7.3.1 Electrostatic field controlled switching A detail evolution of switching action at different VBG is illustrated in Fig. 7.3b. Here light and gate pulse heights are kept similar for all cycles in all panels. Different panel indicate switching operations performed at different gate voltages. Multiple cycle in any panel illustrate repeatability of the device operation. Application of higher negative gate voltage (bottom panels) allows holding of more trapped charges, hence a more prominent switching action is achieved. However, as VBG increases towards positive value, capability to hold the trapped charges reduces because of the reduced electric filed (E) present in the bulk of MoS2 , hence, a less prominent switching effect is observed (upper panels).

7.3.2 Intensity controlled switching A control in switching amplitude (PPC effect) can be achieved by changing the light pulse intensity. Effect of variable light pulse intensity is presented in Fig. 7.4a. Here VBG is kept fixed at −40 V. Vertical red lines indicate appearance of light pulses, and vertical cyan lines indicate the appearance of the gate pulses. Different light pulse height is achieved by sending current pulse of different amplitude through the LED (I L E D ). I L E D values used for different set of experiments are presented in the inset with respective coloured lines. A light pulse with strong intensity (higher I L E D ) creates more e − h pairs, allowing transfer of larger number of holes in the MoS2 -SiO2 interface, hence, a pronounced PPC is observed. The gate pulses used in recovering the PPC (RESET operation) are kept similar in all RESET operations. It is now established that PPC magnitude can be controlled either by setting VBG or by controlling I L E D . A summary of the effect of several control experiments (a)

ILED

20 A 2 A

(b)

ILED

5 2 A 20 A 200 A 2000A 3

0.53 0.50

1

VBG = -40 V

4

12 t (minute)

R 2 /Rd(%)

R (k)

0.56

2000A 200 A

20

-40

-30 VBG (V)

-20

Fig. 7.4 Intensity controlled switching. a Control of switching magnitude with various illumination excitation (I L E D ). b Comprehensive switching response at different V BG , I L E D . Light pulse intensity is controlled by using different values of LED-current (I L E D ) when pulsing

162

7 Switching Operation with Graphene-on-MoS2 Heterostructures

is presented in Fig. 7.4b. To make a comparison of the results obtained at different VBG , PPC response is normalized with respective values of the dark resistance (Rd ) of the sample resulting from different gate voltage settings. For a fixed I L E D , PPC increases almost linearly with higher negative values of VBG . However, the slope of increment is determined by the LED pulse height (I L E D ). Higher I L E D gives better slope of increment. In this context it should be mentioned that various types of device architectures, made of 2D materials, can give non-volatile memory functionality. In their review, Bertolazzi et al. highlight multiple reports which demonstrate nonvolatile memory functionality of several 2D materials based devices [1].

7.4 PPC Dynamics and Near Perfect Charge Retention A detail examination on charge retention time scale is displayed in Fig. 7.5. A different graphene-on-MoS2 device is used in this experiment, where MoS2 of similar thickness is taken with VT H ≈ −10 V, and graphene charge neutrality point (CNP) remain at −8 V (VC N P ). Time evolution of the persistent state (PPC) is studied by monitoring the source-drain current by applying a light pulse of ≈ 0.1 s duration. Temperature of the device is maintained at 110 K. For I L E D = 5 mA (I L E D LED current, it controls the intensity of pulsed illumination), optical power is found to be PL E D ∼ 50 pW µm−2 , and a linear relation for same range of I L E D values is maintained. Figure 7.5a shows time evolution of PPC for two different VBG values. Under strong illumination where I L E D > 50 µA, a logarithmic relaxation in the photoresponse is observed for t  100 s. After this time duration the response becomes

(a) 26

8

8 0

1E2 1E3 1E4

R ()

t (s) -40 V

14

10 t (s)

8 -35 V

2 8

VBG = -30 V

1

-30 V

2 R ()

R ()

(b)

VBG = -40 V

2 100

0.1

1

10

100

t (s)

Fig. 7.5 PPC dynamics and near perfect charge retention. a Logarithmic decay of resistance to nearly relaxation free transition when excited with LED current (I L E D ) of 200 µA for 0.1 s. Solid lines are guide to the eye. (Inset) Persistent state (PPC) monitored over ∼ 12 hrs. b Nearly relaxation free PPC at three different gate voltages (Low PL E D )

7.4 PPC Dynamics and Near Perfect Charge Retention

163

almost constant, indicating nearly relaxation free state (Fig. 7.5a). The circular and square dots indicate measured data points for −40 V and −30 V (VBG ) respectively. Solid lines are guide to the eye, and indicate the presence of two different time scales (two slope in any trace) in the evolution. Here I L E D = 200 µA with 0.1 s pulse duration is used as the illumination excitation. Almost no relaxation is obtained when illumination excitation is kept low I L E D ( 20 µA). Few such traces are presented in Fig. 7.5b, where different panels indicate different VBG settings. Though a small difference in absolute magnitude of PPC is observed, the relaxation free nature remains unchanged within the small range of variation of VBG values. PPC is also found to be stable even after several hours. Such a state, monitored over several hours, is presented in the inset of Fig. 7.5a. Here the PPC state is prepared using I L E D = 5 µA for 30 ms, and monitored for 12 hrs, which is a maximum experimental time scale used here. It is clear from this section that PPC with a limited amplitude (due to small I L E D ) remains in relaxation free state, and hence can be a good candidate for potential optoelectronic memory application. Detail quantitative discussions on the evolution of PPC and the origin of relaxation free nature is presented in following sections.

7.5 Charge Carrier Dynamics and PPC Control experiments with bare graphene and bare MoS2 devices show no PPC (see Sect. 6.1). This indicates the phenomenon to be an intrinsic property of the grapheneon-MoS2 heterostructures. However, PPC has been studied ealier in various other materials. For example, carbon nanotube and some other light absorbing polymer based composites also show electric field tunable PPC [2–5]. Gate electric field dependent trapping mechanism of photogenerated carriers have been attributed to the persistent effect in those materials. In case of graphene-on-MoS2 field effect transistors, a combined effect of carrier localization [6] and gate electric field (E) dependent trapping phenomenon is considered responsible for PPC. For VBG  VT G a schematic of band diagram of graphene with a realistic representation of density of electronic states of MoS2 is presented in the top panel in Fig. 7.6. Instead of sharp termination of density of electronic states at starting of conduction band edge, a band tail extends inside the band gap region of MoS2 (curved line). A variation in VBG allows to move Fermi energy (E F ) through these extended states (shaded region in MoS2 ). Detail study of transport property of MoS2 indicate these states to be strongly localized in nature, and may result from the variation/fluctuation in the potential landscape of MoS2 -SiO2 interface [6]. In presence of E, photo generated electrons and holes get separated in opposite directions (middle panel). Adapting the charge carrier decay kinetics model for semiconductors discussed by Queisser et al. in Ref. [7], the logarithmic decay of PPC (when excited with large I L E D ) is explained (Sect. 7.8). The relaxation free part of PPC, a deviation after the logarithmic decay, can be understood as the effect of electrostatic potential barrier originating from VBG dependent E. At VBG = −50 V, a

164 Fig. 7.6 Charge carrier dynamics and PPC. Schematic illustration of charge carrier dynamics explaining evolution of persistent photoconducting state (PPC). Zero time (t = 0) represent application of light pulse. Direction of electric filed (E) originating from negative gate voltages is indicated by thick arrow. (Inset) Photoresponse in a graphene-on-MoS2 hybrid with thin MoS2 underneath

7 Switching Operation with Graphene-on-MoS2 Heterostructures Graphene

MoS2

SiO2

d

p

+ Si

DOS Ec

EF

localized states x

VBG

t=0 electrons

trapped holes

t >>0 (persistent regime)

R/R (%)

graphene-on-2-layers MoS2

0.6

0.0 0

t (minute)

18

barrier height of 0.8 eV is estimated for a 5 nm thick MoS2 flake on 285 nm SiO2 gate dielectric. Bulk dielectric constant of both SiO2 and MoS2 are assumed to be valid for this estimation. Excitation with LED pulses having smaller illumination powers generate small number of photogenerated carriers. After separation by E these reside on the two sides of MoS2 (bottom panel, Fig. 7.6). However, being smaller in numbers, this charge separation does not alter the E , and 0.8 eV is considered to be strong enough to prevent these to recombine further. The understating of charge retention mechanism signifies the importance of device architecture where sandwiching MoS2 between graphene and SiO2 (back gate dielectric) allows a direct control on the photogating effect, unlike the graphenenanoparticle based hybrids [8] where photosensitive nanoparticles reside on top of graphene. The importance of E is also established with a graphene-on-MoS2 device having thinner MoS2 underneath graphene (bottom-right inset, Fig. 7.6). Presence of only two layer of MoS2 allows a smaller electrostatic potential drop within its ≈ 1.5 nm thickness, allowing a low PPC value such as < 0.5% at 130 K. Lowering of PPC with low MoS2 thickness also allows the elimination of the effect of impurities or surface contamination in photoresponse. This study indicates that MoS2 thickness dependent photoresponse study is essential to optimize the device response for such graphene-on-MoS2 devices. So far all the photoresponses were demonstrated with exfoliated graphene, and MoS2 . For practical applications, it is essential to have large scale devices. Next

7.5 Charge Carrier Dynamics and PPC

165

section (Sect. 7.6) extends the graphene-on-MoS2 based photodetection study with graphene grown by chemical vapor deposition (CVD), which gives a natural route to fabricate large area van der Waals materials [9–14].

7.6 Scalability of Graphene-on-MoS2 FETs

(b)

(a)

Raman: CVD graphene

20 0 1.3

1.4

1.6

 (x1000 cm-1)

1.5

(c) R (k)

R (k)

2.0

counts (a.u.)

To extend the possibility of large scale applications, a graphene-on-MoS2 phototransistor is fabricated with graphene grown by chemical vapor deposition (CVD). The monolayer confirmation comes from Raman spectroscopy as shown in Fig. 7.7b (see Sect. 5.1). An exfoliated MoS2 of having thickness ∼ 4 − 5 nm is selected. The gate voltage dependent resistance modulation, under light and dark conditions, is presented in Fig. 7.7a. Photoresponse shows similar behaviour as it observed in exfoliated graphene devices (Fig. 7.1). However, the response magnitude is found to be smaller. Smaller response can be attributed to the disorder (or defect) assisted low electronic mobility (few hundreds of cm2 V−1 s−1 ) of CVD-graphene used here [15]. Presence of defect is confirmed from the appearance of D-peak (λ−1 = 1348 cm−1 , Fig. 7.7b) in Raman spectroscopy measurement [16–20]. The electronic mobility is atleast an order of magnitude lower in CVD-graphene than the exfoliated graphene devices presented here. Figure 7.7c represents the switching operations performed with light and gate pulses, again resembling the expected operation scheme of graphene-on-MoS2 devices (Sect. 7.3). Results with CVD graphene extend the possiblity of large scale applications of such graphene-on-MoS2 phototransistors.

1.0 -30

-15

0 15 VBG (V)

30

1.08 1.02

CVD T = 110 K

0

70

t (s)

140

210

Fig. 7.7 Scalability of graphene-on-Mos2 FETs. a Transfer characteristics (R − V BG ) of a graphene-on-MoS2 FET prepared with CVD-graphene and exfoliated MoS2 . b Raman spectroscopy showing D and 2D-peak confirming monolayer graphene. c Switching operation at 110 K, V BG = −30 V, and I L E D is 5 mA

166

7 Switching Operation with Graphene-on-MoS2 Heterostructures

7.7 Room Temperature Operation and Long Time Cycles In this section few more switching functionalities have been demonstrated including room temperature operation of graphene-on-MoS2 devices made of both exfoliated and CVD graphene (Fig. 7.8a, b). At room temperature the switching operation is observable at much larger negative VBG values and can be related to the reduced threshold voltage (VT H ) of MoS2 because of thermal broadening. Figure 7.8c indicates the long time cyclic switching with a time period ≈ 2 hours. Temperature of the sample is maintained at 110 K here to perform the SET and RESET operations over days. Owing to relaxation free nature of PPC, a recovery of PPC state (RESET operation) is accomplished with greater than 95% accuracy.

7.8 Theoretical Modelling of PPC This section describes a theoretical formalism which accouts the persistent photoresponse seen in graphene-on-MoS2 hybrid devices. The theoretical treatment presented by Queisser et al. [7] is followed here. In their analysis Queisser et al. showed that a spatial separation between the photocarriers (e − h) leads to a slow relaxation (low recombination rate). In our analysis we give more generalized formulation of their discussion by considering the presence of a gate electric field due to the backgate voltage (VBG ). If a graphene-on-MoS2 device, where MoS2 thickness is d, is illuminated with light at an operational gate voltage (VBG ), photogenerated carriers are momentarily swept to graphene [21, 22] by the interfacial electric field (E; Fig. 7.6). Because of

(a) R (k)

0.45

Exfoliated T = 300 K

0.44 0

R ()

(b)

(c)

40

80

120

760

755

CVD T = 300 K

0

20

t (s)

40

60

0.53

R (k)

Fig. 7.8 Room temperature operation and long time cycles. (a–b) Room temperature switching operation with a exfoliated and b CVD graphene. c Cyclic switching of an exfoliated graphene at 110 K temperature with long time period

Exfoliated T = 110 K

0.51 0

4

t (hours)

8

12

7.8 Theoretical Modelling of PPC

167

the intrinsic n-type doping in MoS2 , graphene-on-MoS2 devices show response only at large negative gate voltages. At such negative voltages electrons gets transferred to graphene and holes remain trapped inside MoS2 . After removing the photoexcitation, photoelectrons from graphene tend to come back towards MoS2 and recombine with holes. Owing to the strong localized nature of electronic states present in MoS2 [6], the volume-density (Z ) of trapped holes is assumed to be uniform. If t = 0 to be the time when light was switched off, at t > 0 electron and holes which are spatially close (near the graphene−MoS2 interface), tend to recombine quickly (middle panel, Fig. 7.6). Here m(t) denotes the photoelectron density at time t present in graphene. At any time (t), photoelectron number in graphene is determined by two physical process (a) quantum tunneling of photoelectrons across the interface and (b) thermal excitation of holes from the hole-doped graphene to MoS2 . Thus the photoelectron number in graphene at any time t is determined by the joint probability of these tow process. For the quantum tunneling process a probability density function p(x, t) is assumed which indicate the probability of finding an hole at any time t and at a distance x from the interface (inside MoS2 ). However, the probability density function from thermal excitation of hole depends on the energy difference E = −E c − (−E F ) = E F − E c (Fig. 7.6). Here E c indicate the energy at mobility edge. Here −E c indicate the energy of a hole in MoS2 . Following the conservation of photocarrier numbers, it is assumed that the number of photoelectrons in graphene at the Fermi energy (E F ) is equal to the number holes in MoS2 at the Fermi energy (E F ). Thus, considering the space dependent probability density function, the recombination rate of holes can be written as [7] − p(x, t) dp(x, t) = , dt τ0 exp(2x/ξ)

(7.1)

where τ0 is the time constant for recombination when there is no spatial separation, and ξ is equivalent of effective Bohr radius arising because of the strong localization in MoS2 . Integrating Eq. 7.1 the probability density function p(x, t) can be evaluated and written as (7.2) p(x, t) = p(x, 0) exp[−(t/τ0 ) exp(−2x/ξ)]. Now invoking the idea of joint probability distribution stated above, the net photoelectron density (m(t)) in graphene can be written as  m(t) = A1 exp [−E/k B T ]

d

p(x, t)d x  d p(x, 0) = A1 exp [(E c − E F )/k B T ] 0

0

exp[−(t/τ0 ) exp(−2x/ξ)]d x.

(7.3)

Here A1 is a normalization constant which is independent of gate voltage (VBG ) and time (t).

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7 Switching Operation with Graphene-on-MoS2 Heterostructures

Assumtion of typical sharp-front approximation model (or step junction model [7, 23]) allows considering all trapped holes, which are located within a particular distance xs (t) at any time t  τ0 , to be neutralized. To be precise, xs (t) is the spatial extent inside MoS2 , within which all holes which have lifetime between t and t + τ0 become neutral (recombine) such that t + τ0 = τ0 exp(2xs /ξ). Hence, xs (t) can be written as f or t >> τ0 . (7.4) xs (t) = (ξ/2)ln(t/τ0 ) Thus Eq. 7.3 can be simplified as  m(t) = A1 exp [(E c − E F )/k B T ] = A1 exp [(E c − E F )/k B T ]

d

p(x, 0)d x xs  d

p(x, 0)d x xs

= A1 Z (d − xs ) exp [(E c − E F )/k B T ] = A1 Z d(1 − (xs /d)) exp [(E c − E F )/k B T ]. As per the sharp-front approximation mentioned above, p(x, 0) is assumed to be a constant box-distribution function of height Z and width d. Thus, m(t) can be rewritten as (7.5) m(t) = Z 0 d f (t) exp[(E C − E F )/k B T ] where Z 0 = A1 Z and f (t) = 1 − (ξ/2d) ln(t/τ0 ). Time dependent evolution of m(t) (Eq. 7.4) defines typical time scale of the persistent photoresponse seen in graphene-on-MoS2 hybrids. Assuming a small change in the channel resistance (or conductance) due to an optical illumination, the evolution of channel resistance can be written, following the functional form of n(t), as (7.6) R(t) = R A − R B ln(t/τ0 ), where R A and R B are constants which depend on gate voltage and localization property of electronic states of MoS2 . Thus, at larger LED intensities, owing to such logarithmic dependence (Eq. 7.6), photoresponse (R(t) − R A ) appear nearly time independent at large time (t  τ0 ; see Fig. 7.5a). A nearly relaxation free photoresponse is also observed when the intensity of the LED pulse is low (Fig. 7.5b), inset, Fig. 7.5a). At low pulse intensities the sharpfront approximation tends to be invalid because of the inhomogeneous distribution of trapped holes. Such inhomogeneity may appear because of the formation of discrete hole pockets in MoS2 , such that the continuous probability distribution function ( p(x, 0)) becomes delta function (δ(x − d)), where d is the distance from the interface. In such scenario m(t) ∼ exp(−t/τ ), where τ = τ0 exp(2d/ξ). Assuming τ0 ∼ 10−9 s (typical value), d ∼ 5 nm (MoS2 thickness) and ξ ∼ 0.5 nm (Bohr radius), τ i estimated to be ∼ 108 s, which indicates the lifetime of a persistent state (‘ON’ state) can exceed few years (2 − 5 years)!

7.8 Theoretical Modelling of PPC

169

At a large time, when t >> τ0 , the photoelectron density in graphene becomes nearly time independent and can be written as (Eq. 7.5) m(t)|tτ0 = n e = n 0 exp(−E F /k B T ).

(7.7)

Here n e denote the change in charge density (n e ) in graphene channel and n 0 is a slow varying function of t and remain practically constant over the experimental time scale. Equation 7.7 captures the gate voltage (VBG ) dependence photoresponse characteristics of the device since E F is a function of VBG . In the hole doped regime the E F of graphene can be written as  √ E F = −v F k F = −v F πn e = −v F (π/e)C|VBG − VC N P |,

(7.8)

where n e is the electron density in graphene channel, v F and k F are the Fermi velocity and wave vector of charge carriers in graphene and C is the effective capacitance (here back gate) of the device. Using Eqs. 7.7 and 7.8 the magnitude of photogating can expressed as (VBG = (e/C)n e )    VBG = VC exp β |VBG − VC N P | .

(7.9)

Here β and VC are constants and do not depend on VBG .

7.9 Summary • Induced photoresponse in a graphene-on-MoS2 structure shows both persistent (PPC) and non-persistent (PC) nature. Electrostatic tunability of PC and PPC are demonstrated by controlling back gate voltages (VBG ). Nearly relaxation free nature of PPC allow establishing memory operation, which is controlled by light and gate pulses. • Logarithmic decay and relaxation free nature of PPC is explained using a theoretical model, which considers the physical separation between the photogenerated electrons and holes. Theoretical estimation predicts the charge retention time scale to be as large as few years (2–5 years). • Experiments with CVD graphene allows the possibility of large scale device fabrications for practical applications. Room temperature switching operations of graphene-on-MoS2 transistors are also demonstrated for both type of devices made of exfolitaed and CVD grown graphene. • Owing to large photosensitivity, these study support the fact that graphene-onMoS2 devices can be a potential candidate for optoelectronic memory device applications.

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7 Switching Operation with Graphene-on-MoS2 Heterostructures

References 1. Bertolazzi S et al (2019) Nonvolatile memories based on graphene and related 2D materials. Adv Mater 31:1–35 2. Borghetti J et al (2006) Optoelectronic switch and memory devices based on polymerfunctionalized carbon nanotube transistors. Adv Mater 18:2535–2540 3. Star A, Lu Y, Bradley K, Grüner G (2004) Nanotube optoelectronic memory devices. Nano Lett 4:1587–1591 4. Shi Y et al (2008) Photoconductivity from carbon nanotube transistors activated by photosensitive polymers. J Phys Chem C 112:18201–18206 5. Dutta S, Narayan KS (2004) Gate-voltage control of optically-induced charges and memory effects in polymer field-effect transistors. Adv Mater 16:2151–2155 6. Ghatak S, Pal AN, Ghosh A (2011) Nature of electronic states in atomically thin MoS2 fieldeffect transistors. ACS Nano 5:7707–7712 7. Queisser HJ, Theodorou DE (1986) Decay kinetics of persistent photoconductivity in semiconductors. Phys Rev B 33:4027–4033 8. Konstantatos G et al (2012) Hybrid graphene-quantum dot phototransistors with ultrahigh gain. Nat Nanotechnol 7:363–368 9. Bae S et al (2010) Roll-to-roll production of 30-inch graphene films for transparent electrodes. Nat Nanotechnol 5:574–578 10. Dimitrakopoulos C et al (2010) Wafer-scale epitaxial graphene growth on the Si-face of hexagonal SiC (0001) for high frequency transistors. J Vac Sci Technol B 106:30 11. John R, Ashokreddy A, Vijayan C, Pradeep T (2011) Single- and few-layer graphene growth on stainless steel substrates by direct thermal chemical vapor deposition. Nanotechnology 22:165701 12. Bergeron H et al (2017) Chemical vapor deposition of monolayer MoS2 directly on ultrathin Al2 O3 for low-power electronics. Appl Phys Lett 110 13. Zhu W et al (2014) Electronic transport and device prospects of monolayer molybdenum disulphide grown by chemical vapour deposition. Nat Commun 5:3087 14. Marks TJ, Hersam MC (2015) Materials science: semiconductors grown large and thin. Nature 520:631–632 15. Srivastava PK et al (2015) Defect engineering as a versatile route to estimate various scattering mechanisms in monolayer graphene on solid substrates. Nanoscale 7:16079–16086 16. Ferrari AC et al (2006) Raman spectrum of graphene and graphene layers. Phys Rev Lett 97:187401 17. Ferrari AC (2007) Raman spectroscopy of graphene and graphite: Disorder, electron-phonon coupling, doping and nonadiabatic effects. Solid State Commun 143:47–57 18. Casiraghi C et al (2009) Raman spectroscopy of graphene edges. Nano Lett 9:1433–1441 19. Malard LM, Pimenta MA, Dresselhaus G, Dresselhaus MS (2009) Raman spectroscopy in graphene. Phys Rep 473:51–87 20. Kumar Srivastava P, Ghosh S (2013) Eliminating defects from graphene monolayers during chemical exfoliation. Appl Phys Lett 102 21. He J et al (2014) Electron transfer and coupling in graphene-tungsten disulfide van der Waals heterostructures. Nat Commun 5:5622 22. Hong X et al (2014) Ultrafast charge transfer in atomically thin MoS2 /WS2 heterostructures. Nat Nanotechnol 9:682–686 23. Muller RS, Kamins TI, Chan M (2002) Device electronics for integrated circuits, 3rd edn. Wiley

Chapter 8

Bilayer-Graphene-onMoS2 Heterostructures: Channel Bandgap, Transconductance, and Noise

Graphene-MoS2 hybrid structure shows extremely large photoresponse (Chap. 6). However, zero-bandgap in monolayer graphene permits large background current (Id = IDS in dark). It is seen that a bilayer graphene (BLG) can be utilized to make a BLG-on-MoS2 field effect transistor (FET), which helps reducing Id . Reduction in Id occurs because of a band-gap opening in BLG channel in presence of external electric field (Sect. 2.1.2). A dual gated structure is used to control the bandgap (Eg ) and Fermi energy (EF ) independently, giving full regulation over the lowest current in off-state and the channel conductance of the FET respectively. A larger Eg reduces the dark current (Id < 10 nA) and improves the field control tunability (on/off ratio) of channel conductance. Large on/off ratio helps in attaining high photogating effect, which further helps in achieving large photoresponsivity value (∼109 A W−1 ) while operating at low source-drain bias (VDS = 50 mV). Understanding of capacitive coupling in these dual gated structures is also discussed. Such understanding is essential for finding the linear range of operation of the device. Understanding of electrical noise characteristics and respective mechanism is also a topic of discussion of this chapter. A quantitative characterization of low frequency electrical noise is presented. Understanding of noise mechanism helps controlling various excitation parameters so that the best signal to noise ratio can be achieved.

8.1 Bandgap, Transfer Characteristics and Transconductance 8.1.1 Photogating Effect, Transconductance and Dark Current Electric field controlled photoresponse in graphene-MoS2 devices support the fact that the underlying photoresponse mechanism is a photogating effect (also see Sect. 6.3). Physically photogenerated charges are trapped inside MoS2 and induces © Springer Nature Switzerland AG 2020 K. Roy, Optoelectronic Properties of Graphene-Based van der Waals Hybrids, Springer Theses, https://doi.org/10.1007/978-3-030-59627-9_8

171

172

8 Bilayer-Graphene-on-MoS2 Heterostructures: Channel Bandgap …

carriers in the graphene channel. These induced carriers cause a net channelconductance change, which is probed (or measured) by applying an excitation bias (VDS ). When device is excited with a constant source-drain bias (VDS ), a change in source-drain current (IDS ), upon optical illumination, gives the photocurrent (IP = IDS ). The knowledge that light causes an effective change in gate voltages allows us to write IP as (8.1) IP = IDS = m × I1e . Here I1e is the effective current change because of the trapping of one charge carrier (an electron or hole) and m is total number of trapped carriers, originated from successful generation and separation of photocarriers. Owing to the trapping (or de-trapping) of photocarriers, whcih directly controls the channel conductivity by varying the charge carrier density, the photocurrent signal (IP ) shows a collective result (sum) of all the individual photocarrier generation (or recombination) events. If there is an average np  number of photons fallen on the detector then the average number of photocarrier (m) can be estimated as (Eq. 17.5-2, Ref. [1]) m = ηnp ,

(8.2)

where η is the quantum efficiency. Further, considering the effective gate voltage change model (photogating effect) I1e is estimated following the relation (Sect. 6.3) I1e =

dIDS × VT1eG . dVT G

(8.3)

VT1eG represents effective gate voltage change seen by graphene because of one trapped carrier. It is assumed that trapping of one charge carrier is equivalent of loosing one from the graphene channel. This assumption is equivalent of saying that the image charge on graphene, created by the trapped charge (q), has same but opposite value (−q). Thus, considering the idea of geometrical capacitance, VT1eG is said to be equal to the effective voltage required to add (or remove) a charge (q) to one of the capacitor plate (e.g. graphene). VT1eG is estimated following the relation (similar to Eq. 6.1, where ne = 1) VT1eG =

e . CT G

(8.4)

Here CT G is geometrical capacitance of the device and e is the charge of an electron. CT G is estimated following the relation, CT G =

ε0 εr A , d

(8.5)

where A is the device area, d the thickness of gate dielectric, ε0 the free space permittivity, and εr is the relative permittivity of gate dielectric.

8.1 Bandgap, Transfer Characteristics and Transconductance

173

It is evident from Eqs. 8.1 and 8.3 that photocurrent is directly proportional to dIDS /dVT G , which is estimated from IDS − VT G response of the device. When operating with fixed source-drain bias (VDS ), dIDS /dVT G can be written as dIDS dg = VDS × . dVT G dVT G

(8.6)

Here g = IDS /VDS is the conductance of the device and varies with the source-drain geometry (w/l), carrier mobility (μ) and carrier density (ne ) following the relation (Ohm’s law in 2D [2, 3]) w (8.7) g = ne eμ × . l Here w and l are the width and length of the channel respectively. With the help of Eqs. 8.2–8.7, Eq. 8.1 can be rewritten as e dIDS × CT G dVT G e dg × VDS × IP = m × CT G dVT G e dg × VDS × . IP  = ηnp  × CT G dVT G IP = m ×

(8.8) (8.9) (8.10)

It is clear from Eq. 8.9 that the photoresponse is directly proportional to the product of excitation bias (VDS ) and transconductance (d g/dVT G ) of the device. Thus, the photoresponse (IP ) can be controlled either by increasing the excitation bias (VDS ) or by using a device with improved d g/dVT G . It is important to note that the use of larger VDS certainly improves photoresponse (Sect. 6.6), however, the background dark current also increases. Presence of large dark current (a) adds more low frequency noise (Sect. 8.3.3) and (b) increases standby power consumption rate. Thus, an alternative approach to improve the response, is made by improving the channel transconductance (d g/dVT G ) of the device. Because of the field tunable nature of band-gap the transconductance of bilayer graphene FET is much higher (atleast by an order of magnitude) than that of a monolayer graphene. Use of bilayer graphene, thus, allows improving of the photoresponse without the need of larger VDS . Equivalently, it can be said that a BLG-on-MoS2 device is expected to maintain similar photoresponse value with lower excitation bias (VDS ) compared to graphene-on-MoS2 devices. Use of low VDS also helps reducing the probe/excitation current in the channel (receiver circuit) and helps controlling the receiver circuit noise, allowing an improved signal to noise ratio.

174

8 Bilayer-Graphene-on-MoS2 Heterostructures: Channel Bandgap …

8.1.2 Bilayer Graphene and Channel Bandgap (E g ) Large background current (Id ) is a consequence of gap less band structure of graphene (Fig. 8.1a). Application of gate electric field moves the effective Fermi energy (EF ) up or down allowing a certain number of carriers to take part into the conduction. Number of carriers depend on the electronic density of states available at (and around) the position of the Fermi energy. Typically the electronic states falling within the range of KB T values around EF , take part in electrical conduction. Such thermal broadening around EF allows sufficient number of carriers resulting in a large conductance even when the Fermi energy is at the middle of conduction and valance bands [4, 5]. Three panels in Fig. 8.1a illustrate accessibility of various density of electronic states (ne ) when moving the Fermi energy. EF is moved by changing the potential (VBG ) at the gate electrode. Ideally, i.e. in absence of external impurities/doping, EF stays at the middle when VBG = 0 (left panel). However, a non-zero carrier density because of thermal broadening gives a finite conductance. For VBG = 0 channel conductance becomes even higher as ne is large. Negative and positive values of ne indicate the density of electrons and holes respectively. Electronic bands of bilayer graphene is fundamentally different from monolayer graphene. Interlayer coupling through van der Waals interactions between the two layers give a parabolic band structure at lower energies (Sect. 2.1.2). One of the most interesting facts is that the interaction energy between the two layers can be tuned by applying an external electric field perpendicular to the layers. Such tuning breaks the symmetrical indentification of two sublattices that resides on the two planes. Sublattice symmetry breaking causes a band gap (Eg ) opening (Sect. 2.1.2). Ideally, i.e. in absence of external doping/impurities, zero carrier density (ne = 0) is obtained by placing EF at the middle of Eg .

(a) monolayer graphene n0 n0 CB

EF

(b) bilayer graphene

n0 E DOS

KB T

EF VB

VB

VBG = 0

VBG > 0

VBG < 0

EF

CB

Eg

VBG  0 sub-lattice symmetry braking

KBT

n 0

n=0

n 0

Fig. 8.1 Bilayer graphene and channel bandgap (Eg ). a Schematic illustration of electrostatic tunability of accessible density of electronic states in a monolayer graphene transistor. b Bandgap tunability of bilayer graphene (BLG). (Yellowish shaded region) Accessibility to different density of electronic states in BLG. Accessible density of electronic states determine the channel conductance of the transistor. Horizontal shaded region indicate thermal broadening around EF due to finite temperature T . KB is Boltzmann constant

8.1 Bandgap, Transfer Characteristics and Transconductance

175

Experimentally sublattice symmetry breaking is achieved by applying a gate potential (Fig. 8.1b). An independent control on the Fermi energy and carrier density is obtained by utilizing a top and bottom gate geometry (Fig. 1.1b), which helps controlling carrier densities and effective electric fields on the two layers of BLG. The schematics in the shaded region in Fig. 8.1b illustrate carrier density accessibility when Eg is maintained at a constant value.1

8.1.3 Dual Gated BLG-on-MoS2 Heterostructure Schematic illustration of a dual gated BLG-on-MoS2 device is presented in Fig. 8.2a. Figure 8.2b is a three dimensional view of the stack with atomically thin layers. The bilayer graphene (BLG) on MoS2 flake (≈8–10 layers thick), placed on Si++ /SiO2 substrate, is the main device of interest. Graphene and h-BN combination on the top constitutes transparent topgate. Thin h-BN-graphene layers (∼10 nm) are used to ensure adequate optical transparency to the BLG-MoS2 part. The stacking of layers are done following dry transfer method where van der Waals materials were picked up one by one from multiple Si++ /SiO2 substrates using a special type of home made optically transparent mask (Sect. 4.1.3). The final stack is transferred onto a pre-patterned Si++ /SiO2 substrate where highly doped silicon (Si++ ) acts as a backgate. More details of the transfer technique is available in Sect. 4.1. Standard e-beam lithography and thermal evaporation of metals (Cr/Au) is done to make electrical contacts on these heterostructures for further opto-electronic measurements (Sect. 1.5). Optical image of a completed device is shown in Fig. 8.2c. The false colours are introduced to enhance the contrast of individual layers. A dual gated structure is necessary to control the opening of band gap (Eg ) and the position of Fermi energy (EF ) of the BLG independently. Electrical characteristics of such devices are presented in following sections.

8.1.4 Transfer Characteristics of a Dual Gated BLG-on-MoS2 Device Figure 8.3a demonstrates the evolution of IDS − VT G curves at few selected values of VBG . Many of such traces constitute the colour representation of IDS in the complete operational range of VBG and VT G at 83 K temperature (Fig. 8.3b). In coloured illustration, towards higher negative value of VBG the width of the blue colour (region with lowest IDS ) increases along vertical-axis, indicating an increase in band gap. At VBG = −70 V a charge neutrality point (CNP) with IDS < 7 nA is achieved with VT G = 2.27 V. The flattening of the CNP with respect to the change in VT G (Fig. 8.3a) indicates the movement of EF through the bandgap. However, the second CNP at 1 Schematic

credit: Prof. A. Ghosh.

176 (a)

8 Bilayer-Graphene-on-MoS2 Heterostructures: Channel Bandgap … (b)

GRAPHENE

(c)

Graphene

FEW LAYER hBN BLG

hBN BLG MoS2

E

FEW LAYER MoS2 SiO2

BL G

SiO2

DOPED SILICON

contact

TG

Si/SiO2

Si++

BN

1

MoS2 2

10 m

Fig. 8.2 Dual gated BLG-on-MoS2 heterostructure. a Design scheme of a dual gated BLGon-MoS2 transistor for photoresponse experiment. Thin graphene-hBN layers (∼10 nm) used as topgate, which allow necessary optical transparency to the BLG. b Three dimensional perspective of stacked atomically thin structures. c Optical micrograph of a device. False colour added to enhance the visibility of individual layer

0.25

2

0.20

1

0.15

VTG (V)

(b) 3

IDS (A)

(a) 0.30

VBG (V) -70 -50 -30 -10 10

0.10 0.05 0.00 -3

-2

IDS (A)

0.006 0.036 0.066 0.096 0.126 0.156 0.186 0.216 0.246 0.276

0 -1 -2 -3

-1

0 VTG (V)

1

2

3

-60

-40

-20

0 20 VBG (V)

40

60

Fig. 8.3 Transfer characteristics of a dual gated BLG-on-MoS2 device. a Few IDS − VT G traces taken at different backgate voltages (VBG ). b Colour map of IDS within operative range of topgate and backgate voltages. Dashed lines indicate three CNP positions originating from three different carrier density region of the channel

VT G = 1.71 V for the same VBG = −70 V stipulates the presence of another doping density in the channel, and appears because of the small area of the BLG, which resides under the topgate but not on MoS2 , as specified by the arrow-1 in Fig. 8.2c. The topgate and backgate capacitance of this part of BLG remains unaltered for all values of VBG and VT G , hence, the CNP associated with this region follows a constant slope in VBG − VT G plot (white dashed line). The CNP associated with BLG-on-MoS2 under the topgate (main area of interest) follows a curved line (purple dashed line). This happens because of the change in bottom gate capacitance as the MoS2 conductance changes with different values of VBG . For values of VBG > VTH , the MoS2 conductance becomes so large that it prevents BLG to see more increment of VBG . The effective backgate capacitance becomes zero in this regime, hence, the CNP associated with this region follows a

8.1 Bandgap, Transfer Characteristics and Transconductance

177

horizontal line (purple dashed line) as VBG is increased further. Another CNP, also following the horizontal line at lower negative VT G (red dashed line), originates from extension of the thin strip of MoS2 (marked by arrow-2, Fig. 8.2c) under the BLG in the topgated region.

8.1.5 Transconductance, Mobility and Number Density

-6

IDS

10

dIDS/dVTG

1.5

2.0

2.5

VTG (V)

3.0

-9

2

CNP

1.6

2.1 2.6 VTG (V)

103

1

cm-2)

-3

3

0

12

IDS (nA)

0

104

-1  ne

1.5

2.0

2.5 VTG (V)

-2

ne ( 10

3

100

b  (cm2 V-1 s-1)

6

dIDS/dVTG (100 nA V -1)

a

100 nA

The transconductance sensitivity of the dual gated BLG-on-MoS2 device is high with respect to the topgate compared to the backgate characteristics. Here sensitivity indicates the change in value when gate biases are changed. High topgate sensitivity results from large capacitance because of the low dielectric thickness at topgate (Sect. 8.1.3). Thus, in following discussions topgate characteristics are considered. The transconductance is obtained from the IDS − VT G characteristics of the device. The pink trace in Fig. 8.4a shows the IDS − VT G response at VDS = 2 mV. The VBG and T are maintained at −70 V and 83 K respectively. It can be seen that the lowest current achieved, ∼7 nA, indicates a channel resistance of ∼286 k. l/w being ∼4.4, the sheet resistance near charge neutrality point becomes ∼65 k −1 . Such high sheet resistance is the characteristics of the bilalayer graphene, and is not commonly seen in pristine monolayer graphene. dIDS /dVT G is estimated by taking VT G dependent differentiation of the IDS − VT G curve and is shown by the green coloured trace in Fig. 8.4a. The right-most peak (p1) and deep (d 1) indicate the maximum rate of electron and hole density change on the BLG-on-MoS2 part respectively. However, the peaks and dips at p2 and d 2 arise from a part of BLG-channel, which resides underneath topgate but does not have MoS2 underneath it (see Sect. 8.1.4 for details). Thus, p2 and d 2 do not relate to the photoresponse characteristics here. Photoresponse being directly proportional

-3

3.0

Fig. 8.4 Transconductance, mobility and number density. a IDS and dIDS /dVT G variation as a function of topgate voltage. b Estimation of carrier density modulation (ne ) and field controlled mobility (μ)

178

8 Bilayer-Graphene-on-MoS2 Heterostructures: Channel Bandgap …

to the dIDS /dVT G (Eq. 8.8), the operational spot of the device is chosen such that dIDS /dVT G is sufficiently high or near the maximum. The field controlled evolution of IDS of BLG-on-MoS2 device is the consequence of evolution of the channel conductance (G). Physical origin of conductance change is attributed to the modulation of charge carrier density (ne ) and mobility (μ) [6–9] (Sect. 3.3.4). ne is estimated considering the zero carrier density at CNP (lowest IDS ). Assuming geometrical capacitance to be valid, the carrier density is estimated following the relation (Eq. 6.1) ne e =

ε0 ε r × (VT G − VCNP ). d

(8.11)

Here ε0 , εr and d are free space permittivity, relative permittivity of BN and thickness of BN respectively. The result of such estimation gives a linear change in ne as VT G is varied, as represented by the orange line in Fig. 8.4b. The schematic of CNP estimation is presented in the inset. Typical range of carrier density modulation in graphene FETs remains within ∼1012 cm−2 . Following the linear modulation of carrier density, the field effect mobility is estimated following the relation (using Eqs. 8.7, 8.11) IDS l × wVDS ne e ld IDS = × wε0 εr VDS (VT G − VCNP )

μ=

(8.12) (8.13)

Estimated results are shown by the blue line in Fig. 8.4b. Highly nonlinear nature of μ − VT G line arises due to the consideration of linear variation of ne with VT G . Carrier mobility (μ) certainly can be a function of VT G , owing to the change in the interaction parameters (e.g. electron-electron interaction etc.) as the carrier density (ne ) changes. However, the carrier density can also be nonlinear function, which has been ignored here. For example, in graphene-MoS2 structures negative-compressibility is seen due to the band offset between MoS2 and graphene [10]. Thus, a true mobility can be extracted following the hall coefficient measurement under magnetic field, which allows extraction of true carrier density present in graphene [10]. Figure 8.4b gives only an approximate estimation of carrier mobility. However, these are lower limit, as the carrier density estimation holds the upper limit values. Thus, it can be said that the typical mobility in such BLG-on-MoS2 devices is approximately or greater than ∼1000 cm2 V−1 s−1 . Carrier mobility plays an important role in photoresponse. High carrier mobility allows short carrier transit time allowing large photo gain (Sect. 6.6.2).

8.2 Gate Capacitance, Excitation Bias and Excitation Frequency

179

8.2 Gate Capacitance, Excitation Bias and Excitation Frequency Gate capacitance coupling with the excitation bias is common in FET devices. Strong capacitive coupling introduces non-linear IDS − VDS response. Thus, photoresponse also becomes a strong nonlinear function at higher excitation bias (>50 mV). Owing to the non-zero bandwidth of Lockin measurement, strong capacitive coupling can also introduce noise via gate voltage modulation. Thus, understanding of excitationbias-limit is essential so that non-linear effects can be avoided. Following sections discuss basic results of capacitive coupling obtained in BLG-on-MoS2 devices.

8.2.1 Topgate Capacitance and Excitation Bias (VDS ) Figure 8.5a shows two probe IDS − VDS characteristics of the device when excited the source-drain with DC bias. Different coloured lines are the results from similar experiments performed at different topgate voltages (VT G ), which are indicated in the top-left inset with respective coloured symbols. At higher carrier densities IDS varies almost linearly with VDS (red and gray traces). However, towards the lower carrier densities, pronounced non-linearity in IDS − VDS relation is observed (blue, violet, green and yellow traces). Non-linearity at higher VDS appears owing to the strong capacitive coupling of the topgate with VDS . Because of the common ground between VDS and VT G , the effective topgate potential gets altered along the channel (bottom-right inset, Fig. 8.5a). For example, the net potential, seen by the right end of BLG channel, is VT G − VDS , whereas the left end sees the potential VT G . When dIDS /dVT G is large, a small change in VDS appears as a change in VT G . Thus, blue, violet, green and yellow traces in Fig. 8.5a show nonlinear response when VDS increased by few tens of millivolts. The

0

(b) 100

10 1

IDS (A) -15

50 1V TG

(V) 3 VTG

A

IDS

VDS (mV)

IDS (A)

10

IDS (A)

(a)

VDS Graphene

hBN

-10

VBG

MoS2

BLG

-10 -5

0

0 5

-50

10

SiO2 Si++

-0.10

-0.05

0.00 VDS (V)

0.05

0.10

-100

15

1.5

2.0

2.5

3.0

VTG (V)

Fig. 8.5 Topgate capacitance and excitation bias. a Evolution of source-drain characteristics at different VT G . b Colour representation of IDS in the operational range of VT G and VDS values

180

8 Bilayer-Graphene-on-MoS2 Heterostructures: Channel Bandgap …

curvature in IDS − VDS curves are understood from the curvature of IDS − VT G at the operational spot of VT G . Detail evolution of source-drain current in the complete operational range of VDS and VT G values are shown as a colour map of IDS in Fig. 8.5b. To avoid complexity arising from non-linear response, most of the photoresponse experiments are performed at lower VDS values. The highest value of VDS = 50 mV is used for photoresponsivity measurement, while most of the sensitive experiments the source-drain bias is kept limited to only few hundred microvolts (∼200 µV).

8.2.2 Excitation Frequency Versus Transfer Characteristics Lockin measurement technique requires an excitation carrier frequency. The detection of signal at the same phase of the carrier frequency gives the expected DC response of the signal (SRS Lockin 830 manual). Low noise bandwidth of the detection process allows measuring of clean signal. The phase information is a measure of the other nonlinear components (e.g. capacitive, inductive etc.) in the circuit. Graphene-MoS2 samples show strong evolution of phase component at higher X ) and out-phase frequencies. Figure 8.6a, b shows evolution of the in-phase (IDS Y (IDS ) response respectively. At lower excitation frequencies (5 kHz), the in-phase component remain very high compared to the out-phase component. At relatively higher frequencies (10 kHz), the out-phase component become dominant. Out of the phase component indicates the presence of non-linear components such as capacitors etc. Origin of capacitance in the external circuit may appear because of the coaxial cables used to connect the sample and instruments. Another source of capacitance can come from the metal-graphene contact pads (Sect. 2.2.2.2). The topgate capacitance can also add phase because of the strong coupling between VT G and VDS (Sect. 8.2.1). Depending on the effective value of different capacitance sources, (b)

0.5

0.1 10.1 20.1 30.1 40.1

IXDS (A)

0.4 0.3

5.1 f 15.1 25.1 35.1 45.1

0.0

(kHz)

-0.1 Y IDS (A)

(a)

0.2 0.1 0.0 -0.1

-0.2 -0.3

0.1 10.1 20.1 30.1 40.1

-0.4 1.5

2.0

2.5

VTG (V)

3.0

1.5

2.0

5.1 15.1 25.1 35.1 45.1

2.5

f (kHz)

3.0

VTG (V)

Fig. 8.6 Excitation frequency versus transfer characteristics. a In-phase (θ = 0◦ ) component X ) of I ◦ (IDS DS − VT G characteristics at different excitation frequencies (f ). b Out-phase (θ = 90 ) Y ) of I component (IDS − V characteristics DS TG

8.2 Gate Capacitance, Excitation Bias and Excitation Frequency

181

these contribute at different frequencies. The following section gives a qualitative discussion of the contributions from different source of capacitance.

8.2.3 Channel Impedance and Phase An insight  to the capacitive coupling is obtained from the resultant current X 2 Y 2 ) + (IDS ) ) and respective phase component (θ = (180◦ /π) (IDS = (IDS   Y X × tan−1 IDS ). Figures 8.7a, b colour presentation of estimated IDS and θ values /IDS using the results shown in Fig. 8.6a, b respectively. At lower frequencies (10 kHz), the evolution of phase do not alter the magnitude of IDS . A negative phase indicate a capacitive contribution to the overall impedance. The regaining of net magnitude of IDS , even with non-zero θ, indicates that the sample capacitance as the contributing factor. However, at larger frequency values (10 kHz), the amplitude of IDS starts deviating from the expected values, indicating contributions from other parts of the circuit such as co-axial cable etc. It is evident that various source of capacitive coupling gives frequency dependent output at higher excitation frequencies. However, the net IDS remain unchanged with f  10 kHz. Thus, a low excitation frequency (typically 200 Hz) is used to avoid Lockin carrier frequency dependent response. IDS(A) 0.01 0.06 0.11 0.16 0.21 0.26 0.31 0.36 0.41 0.46

VTG (V)

2.8 2.4 2.0 1.6 1.2

10

20

30

f (kHz)

40

(b) 3.2

 (o) -90

2.8

-70 -50

VTG (V)

(a) 3.2

2.4

-30 -10

2.0

10 30

1.6

50 70

1.2

10

20

40

90

f (kHz)

 X )2 + (I Y )2 ) (IDS  Y X DS  ◦ −1 − f . b Evolution of phase (θ = (180 /π) × tan IDS /IDS ) in

Fig. 8.7 Channel impedance and phase. a Evolution of total current (IDS = in the operational range of VT G the operational range of VT G − f

30

182

8 Bilayer-Graphene-on-MoS2 Heterostructures: Channel Bandgap …

8.3 Low Frequency Noise Characteristics 8.3.1 Temporal Evolution of IDS and Power Spectral Density Source-drain current (IDS ) of a BLG-on-MoS2 device, under constant excitation bias (VDS ), shows a temporal variation around a mean value owing to various intrinsic mechanisms like substrate induced trapping de-trapping mechanism (exchange noise), change in disorder configuration (configuration noise), carrier localization in one dimensional conductance channel, percolation and excited carrier density fluctuation etc. [9, 11–13]. Owing to current crowding at contacts, contact noise can also contribute when channel resistance is comparable to the contact resistance at BLGmetal junctions [14, 15]. Figure 8.8a shows some examples of temporal evolution of IDS measured in a BLG-on-MoS2 device. Different panels indicate results obtained when operating the device at different topgate voltages (VT G ). Respective values of VT G are indicated in the inset of Fig. 8.8b by the symbols of respective colours. To make a quantitative estimation of noise power, time dependent traces are recorded at a fixed sampling frequency (512 Hz). The internal buffer of SR-830 Lockin amplifier is used to record the data at such high frequency. Noise power densities (Si(X ) (f ) and Si(Y ) (f )) of individual channels are estimated from the power spectral density (PSD) analysis of the individual time-series data which are recorded X Y X ) and Channel-2 (IDS ) simultaneously. Time dependent IDS and from Channel-1 (IDS Y are fed into a PSD analysis software, which follows a digital signal processing IDS technique developed by Ghosh et al. [16] and gives frequency dependent Si(X ) (f ) and Si(Y ) (f ) values respectively. Similar PSD analysis can be done using commercially available softwares such as LabView from National instruments. -18

 = 1.5

IDS

3 nA

Si (f) (A2 Hz-1)

10-19 10-20 10

-21

IDS (nA)

(b) 10

(a)

100 10 1 VTG (V) 3

 = 0.9

10-22 10-23

=1

10-24 0

5

10

15 t (s)

20

25

0.1

1 f (Hz)

10

Fig. 8.8 Temporal evolution of I DS and power spectral density. a Time series of source-drain X is only presented here. b Power spectral current at few selected VT G (inset,(b)). Evolution of IDS density of IDS , where symbols are the experimental results and connecting lines are guide to the eye. (Inset) Symbols of respective colours indicate the VT G values at which time-series data were recorded and respective power spectral density are presented, as shown in a and b respectively

8.3 Low Frequency Noise Characteristics

183

For a resistive sample Si(Y ) (f ) appears from various other sources such as instrument-noise, ground-noise etc. (Sect. A.1), which causes an additional noise power in the Channel-1. Thus Si(X ) (f ) contains noise power from both the sample and Si(Y ) (f ). Hence, effective sample noise power is estimated following the relation Si (f ) = Si(X ) (f ) − Si(Y ) (f )

(8.14)

The frequency dependent noise power (Si (f )) at some values of VT G is presented in Fig. 8.8b. The symbols indicate estimated values at respective frequencies, and the connecting lines are guide to the eye; the overall spectral response is 1/f α in nature. At low carrier densities (cyan, violet, blue) BLG-on-MoS2 shows a pure 1/f dependence (α ∼ 1, bottom and middle gray lines). However, at higher carrier densities (red, dark-yellow, green, yellow symbols) Si (f ) deviates from 1/f nature and varies as 1/f 1.5 . A vertical shift of the spectral density happens because of the differences in background current (IDS ) arising from different VT G settings (inset). Frequency dependent evolution of noise power confirms that the noise magnitude increases at lower frequencies. The background noise value also depends on the background current used to characterise the device. Such study gives a quantitative  2 ) present in a signal (IDS ) when measuring estimation of noise magnitude ( IDS at a non-zero bandwidth (f ) and excitation bias current (IDS ). Thus, a control on the backgrond noise is achieved by controlling the bandwidth of measurement and excitation bias current.

8.3.2 Evolution of Noise with Gate Voltage and Frequency Bandwidth BLG-on-MoS2 devices show a strong evolution of frequency dependent noise power (Si (f )) as a function of topgate voltage. Figure 8.9a shows the estimated noise power in the operational range of VT G values. Noise power is estimated from various timeseries data (Fig. 8.8a), which are recorded at various VT G values. Symbols indicate noise power values at the respective operational spot of VT G , and the connecting lines are guide to the eye. Three different sets of coloured symbols show the evolution of noise power at three different frequencies. Because of the 1/f α nature of noise power (Fig. 8.8b), the low frequency component always remain at higher values for all gate voltages. The gray line in Fig. 8.9a is the IDS − VT G curve, and highlight the fact that the evolution of Si (f ) has a correlation with the evolution of IDS . Effect of noise appears as a random fluctuation in the measured IDS values. The standard deviation in the IDS is estimated following the relation ID =

   2 IDS  = Si = Si (f ) × f .

(8.15)

8 Bilayer-Graphene-on-MoS2 Heterostructures: Channel Bandgap … 0.25 f (Hz) 1 8

10-10 -11

10

-12

10

10-20

1.2 V

10-21

TG

(V) 3.0

10-22 10-24 1.5

2.0

2.5

3.0

10-9

1.28 2.12

400 300

f (Hz) 0.25 1 8 IDS

10-23

(b)

500

200

1.58 2.36

1.94 VTG (V) 2.58 3.02

10-10 ID (A)

10

-19

ID (A)

-18

Si(f) (A2 Hz-1)

(a) 10

IDS (nA)

184

10-11

100 0

10-12

1

VTG (V)

10

f (Hz)

Fig. 8.9 Evolution of noise with gate voltage and frequency bandwidth. a Evolution of noise power as a function of VT G . Symbols indicate experimentally obtained values. Evolution of IDS is shown by the gray line. (Inset) Magnitude of noise current as a function of VT G . Three colour lines are the results from three different frequency-bandwidth values (f ). b Noise current magnitude (standard deviation) as a function of frequency bandwidth (f ). Symbols are experimental results and connecting lines are guide to the eye. Different set of coloured symbols represents VT G dependent evolution

Here it is assumed that the noise is purely 1/f is nature (Si = Si (f ) × f ). A more general approach to find ID is to integrate Si (f ) within the desired bandwidth, and can be written as   f2  2 ID = IDS  = Si = Si (f )df . (8.16) f1

Here f = f2 − f1 is the bandwidth of frequency within which frequency dependent noise power (Si (f )) has effective contribution to the signal. ID estimation directly relates the noise power to the magnitude of fluctuations in IDS (i.e. noise current). VT G dependent evolution of ID is shown in the inset of Fig. 8.9a. Three lines correspond to different frequency bandwidths used when estimating ID (Eq. 8.15 is used here). Frequency bandwidth (f ) dependent evolution of ID is shown in Fig. 8.9b. Different coloured symbols are the estimated results for different VT G values, the connecting lines are guide to the eye. Lower bandwidth shows low noise-current (ID ). ID tends to saturate at larger f values because of the negligible contributions from higher frequency values (Sect. 8.3.1). Bandwidth dependent noise current estimation is essential to understand the photoresponse limit of BLG-on-MoS2 heterostructure based devices. Low bandwidth certainly gives less noise-current. For example, a f = 0.25 Hz reduces the noise current by a factor of 2 compared to 3 Hz value (VT G = 2.36 V). Such quantitative investigation helps selecting proper range of frequency bandwidth of the measuring instrument so that extremely sensitive photodetection experiment can be performed (Chap. 10).

8.3 Low Frequency Noise Characteristics

185

8.3.3 Noise and Excitation Current

(b)

I2.5 DS

2 Si/IDS |f = 8 Hz

IDS

-21

10

10-6

10-22 10 I (nA) 100 DS

100

Si/I2DS

Si (A2)

10-20

10-20

IDS (nA)

(a)

Si (A2)

Frequency normalized noise power (Si ) has a strong dependence on IDS . Figure 8.10a shows current dependent variation of frequency normalized noise power (Si ). From 2 (Sect. 3.3.4); the empirical relation proposed by Hooge, Si is expected to vary with IDS 2 the gray line is a fit of the function S0 × IDS where S0 is fitting parameter. Symbols indicate the measured noise magnitude at respective IDS values. The topgate voltage (VT G ) is kept fixed at 2.37 V at all IDS values. It is evident that at higher IDS noise 2.5 2 fit is observed, and IDS appears to magnitude increases, however, a deviation from IDS be a better functional representation (inset, Fig. 8.10a). Different coloured symbols in the inset of Fig. 8.10a are the Si values estimated at different bandwidth values. 2 when exciting IDS dependent response is further tested by normalizing Si with IDS the sample at a fixed VDS but with different VT G values. Green circles in Fig. 8.10b are the experimental results, the connecting green lines act as guide to the eye. Pink line 2 ) indicates evolution of IDS as VT G changes. Normalized noise magnitude (Si /IDS appears a function of VT G . The response at the left side of the CNP appears non trivial because of the appearance of multiple peaks/dips in IDS − VT G characteristics (Sects. 8.1.4, 8.1.5). Thus only right side of the CNP is taken for further analysis. 2 is seen to follow a However, at the high conductance region (shaded region) Si /IDS similar trend of increment (or decrement) as IDS does with VT G . It is evident from Fig. 8.10a that the noise power changes by two orders of magnitude when IDS is changed by one order of magnitude, suggesting that the noise current can be tuned over a wide range of values by choosing appropriate bias current (IDS ). However, the exact mechanism of dependence of Si on IDS still remains elusive. In following section an attempt has been made to understand the origin of Si further.

10-21

10-7 Si|f = 8 Hz

10

S0I2DS (S0 = 1.610-6)

10-22 10

100 IDS (nA)

1.5

2.0

2.5

3.0

VTG (V)

Fig. 8.10 Noise and excitation current. a Frequency normalized noise power (variance of IDS ) at various excitation bias. (Inset) Evolution of Si − IDS at three different f values. b Current normalized variance of IDS and IDS as a function of VT G

186

8 Bilayer-Graphene-on-MoS2 Heterostructures: Channel Bandgap …

8.3.4 Normalized Noise and Mobility Fluctuation Typical sources of 1/f noise in a substrated-graphene transistor are mobility fluctuation or number density fluctuation of charge carriers [6–9, 11]. Mobility fluctuation relates to the electron-phonon scattering (Hooge model, Sect. 3.3.4), whereas the trapping/de-trapping mechanism of charge carrier leads to a number density fluctua2 ) is proportions (McWhorther model, Sect. 3.3.4). Current normalised noise (Si /IDS −1 tional to ne when mobility fluctuation is the dominant source of noise (Sect. 3.3.4). 2 shows n−2 However Si /IDS e dependence when number density fluctuation is dominant (Sect. 3.3.4). 2 − ne dependence. Circles are the Figure 8.11a shows multiple feature of Si /IDS experimental results and lines of different colours are the fit functions. At low number densities (green shaded region in the inset) a n−1 e dependence is observed, indicating that the carrier mobility fluctuation is the dominant source of noise. However, at 2 higher densities, n2.5 e and ne dependent nature of Si /IDS is observed. Si follows a relatively simple relation with IDS , as shown in Fig. 8.11b. Two (unlike −1 2 varies as IDS (cyan colour line) at three) density regions are seen here where Si /IDS 2 low density region and IDS (pink colour line) at high density region. Shaded region of respective colours in the inset show the respective partitions as a function of VT G .

8.3.5 Dark Noise Versus Single Electron Signal The dominant source of noise in BLG-on-MoS2 device is flicker noise (1/f type) (Sect. 8.3), and is termed as dark noise (ID ). Low dark noise is always desired so that extremely low intensity can be measured. At sufficiently low intensities, device receives a discrete amount (quantum) of energy owing to the impingement of discrete number of photons (Sect. 3.3.1). Ultimate detection challenge lies in identifying the quantization, i.e. resolving photon numbers. A single photon leads to a quantum change in VT G , adding one charge (1e) into the channel. Hence, a quantum change in IDS (I1e ) happens upon photoillumination (cross ref). However, the noise current (ID ) should be so low that the respective change in IDS due to the addition of an electron to the channel can be measured unambiguously. A comparison between dark noise (ID ) and the signal, owing to the addition of a single charge (I1e ) is presented in Fig. 8.12. Experimentally obtained results of ID values are presented by the green circles, whereas the pink line indicates estimated value of I1e using Eqs. 8.3 and 8.4. At present, I1e values remain much lower in all values of VT G when compared with the noise current magnitude ID . The shaded region indicates the closest match attained between I1e and ID . The closest match near 2.4 V happens because of the large gain (∝ dIDS /dVT G ) of the device, allowing a large signal i.e. large I1e (Fig. 9.2b), while IDS remain sufficiently small resulting low value of 1/f -noise i.e. low ID (Fig. 8.10).

8.3 Low Frequency Noise Characteristics

(b)

10

10

10-6

10-6 -7

10

 ne

2.4 V (V) 3.2 TG  ne  ne-1

1015

ne (m -2)

10 2.4 V (V) 3.2 TG

 I2DS

 I-1 DS

2.5

10-7

100

IDS (nA)

-7

IDS (nA)

100

Si/I2DS

10-6

Si/I2DS

2 Si/IDS

10-6

Si/I2DS

(a)

187

10-7 2 Si/IDS |f = 8 Hz

10

1016

100 IDS (nA)

Fig. 8.11 Normalized noise and mobility fluctuation. a Normalized variance of IDS as a function of carrier density. (Inset) Shaded region of different colours indicate respective range of power-law 2 − n representation. b Normalized variance of I fit in Si /IDS e DS as a function of IDS . (Inset) Shaded 2 −I region of different colours indicate respective range of power-law fit in Si /IDS DS curve 10-10 10-11 ID (A)

Fig. 8.12 Dark noise versus single electron signal. Frequency normalized noise magnitude of current i.e. standard deviation of IDS (ID ) and expected signal from single photon absorption event (I1e ) at various VT G values

10-12 10-13

I1e ID

10-14 1.2

1.6

2.0

2.4

2.8

3.2

VTG (V)

ID being larger than I1e , a poor signal to noise ratio is expected as far as detection resolution of single photon is concerned. However, it is seen that the careful design of the device helps improving I1e , hence SNR can be improved such that the photon number in an optical pulse can be identified unambiguously (Chap. 10).

8.4 Summary • Photoresponse in graphene-MoS2 based heterostructures can be improved by increasing the transconductance of the channel. Photoresponse in grapheneMoS2 devices is proportional to the transconductance. This is a consequence of photogating effect. Electric field controlled high-tunability of transconductance makes BLG a preferable choice over monolayer graphene. Large transconductance is helpful in improving gain without using higher excitation bias. Bandgap tunability of BLG allows large channel resistance, which lowers the dark current which, in turn, reduces receiver circuit noise.

188

8 Bilayer-Graphene-on-MoS2 Heterostructures: Channel Bandgap …

• A dual gated structure helps controlling the bandgap and carrier density in the conduction channel independently. The intrinsic n-type nature of MoS2 restricts accessing the high conductance tunability at the positive side of backgate voltages, thus restricting the range of operation to the negative side of VBG . • Various source of capacitive coupling gives frequency dependent output at higher excitation frequencies. A phase sensitive measurement reveals that cable capacitance and topgate capacitance restricts the frequency of excitation carrier to a limit of 109 A W−1 ) while working with low excitation bias (VDS = 50 mV). High responsivity and tunable dark noise allow attaining extremely low noise equivalent power (NEP). Low NEP improves the detection limit of such photodetectors, which helps distinguishing noise from few photons. Photon noise is utilized as a photodetection parameter and to identify photon distribution statistics of an illumination source. A detailed study of photoresponse characteristics of BLG-on-MoS2 devices and quantitative study of photon noise from an LED source is presented in this chapter. Study of photon noise reveals the dynamic range of these detectors when detecting photons.

9.1 Photoresponse Characteristics 9.1.1 Photocurrent Evolution with Gate Electric Fields A complete dependence of IP in the operational range of backgate and topgate voltages (VBG , VT G ) is depicted in Fig. 9.1a. Figure 9.1b illustrates the electric field directions originating from respective bias combinations in four quadrants of the plot. The null response for VBG > 0 originates from n-type nature of the MoS2 . For VBG < 0 and VT G < 0 the electric field is so strong that EF lies deep inside the valence band where the available density of states are so large that no further change in EF happens because of addition/removal of small number of electrons to the BLG. Conductivity remains almost unaltered because of photogating effect in this regime. The effective region of interest remains confined at VBG < 0 and VT G > 0. With photogating effect, both positive and negative IP can be obtained, depending on the choice of VBG

© Springer Nature Switzerland AG 2020 K. Roy, Optoelectronic Properties of Graphene-Based van der Waals Hybrids, Springer Theses, https://doi.org/10.1007/978-3-030-59627-9_9

191

9 Photoresponse and Photon Noise in Bilayer-Graphene-MoS2 Hybrids

(a) 3

VTG (V)

IP (A)

-0.047 -0.034 -0.022 -0.009 0.003 0.016 0.028 0.041 0.053

IP (A) -0.04 0.00

(b)

0.04 3

2

2

1

1

0

0

-1

-1

-2

-2

VTG (V)

192

VTG

VTG IDS

A

A

VDS

VBG

A

VBG

A

-3

-3 -60

-40

-20

0

VBG (V)

20

40

60

Fig. 9.1 Photocurrent evolution with gate electric fields. a Colour map of photocurrent (IP ) in the operational range of backgate and topgate voltages (VBG , VT G ). b Scheme of electric field direction inside the heterostructure for positive and negative values of VBG and VT G

and VT G , as shown in the right-inset of Fig. 9.1a corresponding to the VBG = −60 V (white dashed line on colour plot).

9.1.2 Photoresponsivity in BLG-on-MoS2 Device Figure 9.2a shows the photoresponsivity (γ) of the device as a function of PLED . Different coloured symbols represent similar experiments carried out at different VT G , keeping VBG fixed at −70 V. At a constant VT G , responsivity increases as illuminated power decreases. For similar PLED , photoresponsivity attains higher value when VT G is changed from higher doping density to CNP, and is attributed to the improved dIDS /d VT G (Eq. 8.8). However, the non-monotonic behaviour at lower intensities can be explained from the highly non-linear nature of the IDS − VT G curve near CNP. At lower intensities a photoresponsivity of ∼109 A W−1 is achieved, even with a small source drain bias of 50 mV. Tunability of IP and γ with respect to the change in VT G is shown in Fig. 9.2b. It is evident that IP and γ increases (or decreases) whenever dIDS /d VT G increases (or decreases). IP varies linearly with dIDS /d VT G because of the photogating effect, as explained earlier (Eq. 8.8). Transfer of photogenerated carriers of similar amount causes more (or less) change in IP for a higher (or smaller) value of dIDS /d VT G .

9.1.3 Illumination Power and Photoresponse Figure 9.3a shows evolution of IDS − VT G characteristics of BLG-on-MoS2 device (coloured lines) with the variation of optical power (PLED ). Here VT G is varied continuously for different fixed values of PLED including zero value (dark), while VDS and VBG are kept constant at 50 mV and −70 V respectively. To have benefit in

9.1 Photoresponse Characteristics

193

(b) 20

1.5 0.5

9

7

10

6

10

105 10-5

VTG (V) 2.40 2.64 2.80 2.96 3.12 ) 3109/(1+50P0.85 LED

10-3

0

0.5 0.0

-20

10-1 101 PLED (fW m-2)

0.0 dIDS/dVTG  IP

-0.5

-40

103

1.0

IP (A)

 (A W-1)

108

dIDS/dVTG (A V-1)

10

1.5

2.0

2.5 VTG (V)

3.0

x 109 (A W-1)

(a)1010

-0.5 -1.0 -1.5

Fig. 9.2 Photoresponsivity in BLG-on-MoS2 device. a Photoresponsivity of the device at various LED power values (PLED ). Different sets of colour symbols represent results from similar experiments performed at various topgate voltages (VT G ). Solid line is the fit function of form A/(B + PLED ), here A, B are fitting parameters. b Comparison of transconductance (dIDS /d VT G ), photocurrent (IP ) and responsivity (γ) as a function of VT G . Here VBG = −70 V, VDS = 50 mV, and PLED = 0.04 fW µm−2

(a) 10

(b) 3.0

1

-2

PLED (fW m )

1.5

2.0 2.5 VTG (V)

3.0

1.45

2.5

2.45

VTG (V)

IDS (A)

Dark 0.374 4.628 24.42 63.44 152.7 430.6

IDS(A) 0.45

3.45

2.0

4.45 5.45

1.5 10-2

10-1 100 101 PLED (fW m-2)

102

6.45 7.25

Fig. 9.3 Illumination power and photoresponse. a Topgate transfer characteristics at dark (black line) and at different illumination powers (coloured lines). The backgate voltage was set at -70 V with VDS = 50 mV. b Colour map of source-drain current (IDS ) in the operational range of VT G −PLED

photocurrent from both A and B excitons of MoS2 , wavelength of 609 nm is used (Sect. 5.9). In presence of optical illumination CNP appears at lower value of VT G , which decreases further with increasing PLED . The left shift of CNPs, with respect to the value at dark, happens because of the backgate generated electric field, which transfers photogenerated electrons to BLG from MoS2 . This reduces the effective hole-doping (p-doping) in the BLG because of electron-hole (e − h) recombination. As an equivalent statement, it can be said that the effective gate voltages to the BLG changes in presence of light, resulting a different doping density (photogating effect). Application of higher PLED generates more electron-hole pairs (e − h) allowing more pronounced photogating. Reduction in effective VBG also reduces the effective bandgap, causing an increase in the lowest achievable value of IDS (IDS at CNPs) for larger PLED (coloured lines, Fig. 9.3a).

194

9 Photoresponse and Photon Noise in Bilayer-Graphene-MoS2 Hybrids

The power dependent evolution of photogating effect is better visualized in (PLED ,VT G ) space by representing IP values in colour scale (Fig. 9.3b). The low current values (red-region) indicate the low carrier density near the charge neutrality point (CNP). Two distinct rate of photodoping effect are observed from two distinct slopes of the CNP in (PLED ,VT G ) space. At lower power, the device shows a very low photodoping rate (low vertical shift) compared to the high power regime (large vertical shift). The yellowish horizontal area arise from photo inactive region of BLG under the topgate (Sect. 8.1.4).

9.1.4 Excitation Bias and Non-linear Response Figure 9.4 illustrates the change in photocurrent (IP ) with different source-drain and topgate excitation biases. Figure 9.4a shows few traces of IP at some fixed values of VT G (coloured lines). Respective VT G values of these traces are indicated by the solid circles of respective colours in the inset. Away from the CNP, IP increases linearly with VDS , which is understood from photogating effect. A fixed illumination power causes a constant photodoping leading to a fixed amount of change in channel conductivity. Increase in VDS gives a higher value of IDS , resulting in larger IP (IP = δσ/σ × IDS , σ being the sample conductivity). Thus, increasing VDS may be an apparent choice to enhance the photoresponse, however, this also increases the dark current (Id = IDS at dark), limiting the noise equivalent power (NEP) of the detector. At a fixed VDS , the IP increases towards CNP because of the increase in dIDS /d VT G (Eq. 8.8). A higher slope in IDS − VT G curve increases photogating effect, as a small change in VT G can lead to a higher change in IDS . A deviation from linearity of IP − VDS curve near the CNP and towards higher value of VDS (Fig. 9.4a, cyan trace) can be attributed to the strong dependence of IP on dIDS /d VT G due

0

1

50 1 VTG

(V) 3 VTG (V) 1.28 2.08 2.64

-1 -2 -0.10

100

-0.05

0.00 VDS (V)

VDS (mV)

IP (A)

1

(b)

10

IDS (A)

(a) 2

-50

1.68 2.48 3.2

0.05

0

0.10

-100

1.5

2.0 2.5 VTG (V)

3.0

IP (A) -2.80 -2.30 -1.80 -1.30 -0.80 -0.30 0.20 0.70 1.20 1.70 2.00

Fig. 9.4 Excitation bias and non-linear response. a Photocurrent (IP ) evolution as source drain excitation (VDS ) is changed. Multiple traces results form different VT G (inset). (Inset) Symbols of respective colours show VT G selection on IDS − VT G curve. b Colour representation of photocurrent evolution in the operational range of VDS and VT G

9.1 Photoresponse Characteristics

195

to the large topgate capacitance. As VDS increases the effective gate voltage along the channel length changes; thus, effective value of dIDS /d VT G gets altered resulting non-linear IP . The asymmetric response of the device, at larger excitation bias, is further highlighted in Fig. 9.4b. The symmetric response would have similar coloured features (IP ) around the VDS = 0 line.

9.1.5 Quantum Efficiency (QE) of BLG-on-MoS2 To estimate the quantum efficiency of the device, light on/off cycles are performed for various power settings. Respective temporal evolution of photocurrent values are presented in Fig. 9.5a. Here the temperature of the device is maintained at 42 K temperature. VDS , VBG and VT G are kept fixed at 10 mV, -40 V and 1.46 V respectively. For any particular PLED (here λ = 635 nm), IP tends to saturate after a few seconds, which is the typical response time of such devices (Fig. 6.7). Knowing the response mechanism as photodoping effect (Sect. 8.1.1), the effective number of photoelectrons can be estimated using the following the formula (Eq. 8.8) CT G IP × m= e



dIDS d VT G

−1

.

(9.1)

Here CT G and e are the topgate capacitance and charge of a single electron respectively. dIDS /d VT G is the slope in IDS − VT G curve where light on/off experiments are performed. CT G can be estimated following the formula (Eq. 8.5) CT G =

(a)

(9.2)

10

QE|t = 0.3 s

365

0.5

0.7 57/(14+PLED )

167 77.6

0.3

28.7

0.2

7.23

0.1

0.52 PLED (fW m-2)

0.0 0

5

10

15 t (s)

20

25

30

1

101 100 10-1 10-2 10-3 t (s) 0.1

QE (%)

0.4

QE (%)

IP (A)

(b)

969

0.6

ε0 εr A . d

0.1

1

10

1 10 100 PLED (fW m-2)

1000

Fig. 9.5 Quantum efficiency (QE) of BLG-on-MoS2 device. a Temporal evolution of photocurrent (IP ) at various illumination power (PLED ). b Quantum efficiency (internal) of the BLG-onMoS2 FET at various illumination powers. (Inset) Temporal evolution of quantum efficiency

196

9 Photoresponse and Photon Noise in Bilayer-Graphene-MoS2 Hybrids

Here d and εr are thickness and dielectric constant respectively, of boron nitride, which is used as a topgate dielectric. ε0 is the free space permittivity and A is the device area. Now, the photon number at any time (from t = 0) is calculated with following the equation: AtPLED np = , (9.3) EP where PLED and EP are the illumination power density (per unit area) and energy of a single photon respectively. Hence, the quantum efficiency (QE) can be written as QE =

m × 100. np

(%)

(9.4)

In this experiment dIDS /d VT G = 2.77 µA V−1 , EP = 3.1 × 10−19 Joule (λ = 635 nm), boron nitride thickness (d ) is ≈ 8 nm and εr of BN [1] is considered to be 4. Using Eqs. 9.1, 9.3 and 9.4, the time dependent quantum efficiency of the device is estimated from Fig. 9.5a and results are shown in the inset of Fig. 9.5b. Time dependence in quantum efficiency is a natural consequence of electrostatic field (E) controlled photoresponse in such BLG-on-MoS2 (or graphene-on-MoS2 [2–4]) devices. The initial rise is due to the instrument response time. However, for first few seconds effective photoresponse remains high because of E. After few seconds E reduces because of trapping of charges in MoS2 -SiO2 interface (Sect. 6.3), causing a reduction in QE value. To present the true capacity of these detectors, only QE values around t ≈ 0.3 s are considered. Illumination power (PLED ) dependence of QE is shown in Fig. 9.5b. QE is found to attain a maximum value ≈ 4% for at low intensities. Typically, QE attains much higher values (>20%) in graphene-on-MoS2 devices (Sect. 3.7.3). Though QE can vary with various parameters such as excitation wavelength, gate bias voltage etc., true reason for such low values of QE in BLG-on-MoS2 devices is not understood and remains to be investigated further.

9.1.6 Thermal and Shot Noise Limited Noise Equivalent Power and Specific Detectivity Total electrical noise in graphene-MoS2 hybrid devices appears from various sources of noise including 1/f noise (Sect. 8.3). However, operation at higher frequencies (f ) removes the contributions from 1/f noise, which appears only at low frequencies (Fig. 8.8b). Thus, thermal noise (IJ ) and shot noise (IS ) set the ultimate lower limit of noise equivalent power (NEP) when device operates at larger frequencies such that IF2  IJ2 + IS2 . Hence NEP can be written as (Sect. 3.2.2)

9.1 Photoresponse Characteristics

197

√ 4KB T /R + 2eId NEP = γ

(9.5)

2 Here noise from the photon source (IPD , Eq. 3.7) is excluded to avoid defining NEP a function of light source. Here symbols have their usual meaning. Figure 9.6 represents the noise equivalent power (NEP) and specific detectivity (D∗ ) of a BLG-on-MoS2 photodetector assuming Eq. 9.5 to be true. At low VDS (50 mV), dark current (Id ) of the device remains controlled, however, high γ value allows NEP to attain extremely low values as presented in Fig. 9.6a. The gate voltage dependence of NEP arises from the dependence of γ and Id on VT G . Different coloured lines indicate NEP at different PLED . At low optical power the NEP is as low as 3 × 10−22 W Hz−1/2 . Knowing NEP, the specific detectivity (D∗ ) of the device is estimated following Eq. 3.11 and presented in Fig. 9.6b. A specific detectivity of more than 1018 Jones (cm Hz−1/2 W−1 ) is achieved near VT G ∼2.40 V. Such low NEP and high D∗ make these detectors as highest photosensitive detectors available till date, while operating at low source-drain bias (50 mV) and high temperature (83 K). As discussed earlier (Sect. 3.2.2), NEP indicates the lowest optical power measurable by the detector. For example, a NEP value of 3 × 10−22 W Hz−1/2 indicates that a change of 3 × 10−22 Joule energy per unit second is detectable by the detector. In the present experiment a single photon energy value is approximately 3.3 × 10−19 Joule (λ = 609 nm), and is much larger than the detection limit of the detector. The low NEP values indicate the possibility of resolving single photon by these detectors. However, it should be noted that the NEP values mentioned here are the thermal and shot noise limited values (Eq. 8.8). Signal quality at lower frequencies, however, is limited by the flicker noise, giving a large noise in current (Fig. 8.8). Thus, when operating the device in a frequency bandwidth range which allow flicker noise, a

(a)

(b)

PLED (fw m -2) 0.0045 0.0398 0.3742

10-20

1018

D* (cm Hz1/2 W-1)

NEP (W Hz-1/2)

10-19

1017

10-21

PLED (fW m -2) 0.0045 0.0398 0.3742

16

10

10-22 2.3

2.4

2.5

2.6

VTG (V)

2.7

2.8

1015

2.3

2.4

2.5

2.6

2.7

2.8

VTG (V)

Fig. 9.6 Thermal and shot noise limited noise equivalent power and specific detectivity. a Noise equivalent power of a BLG-on-MoS2 device in a range of interest of VT G . Three different lines represent the values √ for three different illumination powers (PLED ). Here, NEP is estimated using the relation NEP= 4KB T /R + 2eId /γ. b Specific detectivity of the device (D∗ ) for the similar optical powers shown in (a)

198

9 Photoresponse and Photon Noise in Bilayer-Graphene-MoS2 Hybrids

larger value of NEP is expected, hence a restriction on the detection limit is noted (Sect. 8.3.5). The photodetection limit of BLG-on-MoS2 devices is learnt by studying the photoelectron generation noise (Sect. 3.3.2). Following sections describe detection of ‘noise-signal’ arising from extremely low intensities, comprising single or few photons, even with low frequency (0.1 < f < 10 Hz) measurement probes, thus indicate the measuring limit of such device.

9.2 Photon Noise 9.2.1 Photon Absorption and Receiver Circuit Noise A schematic illustration of photoelectron ‘noise-signal’ is presented in Fig. 9.7. A photon (yellow arrow), when absorbed by the MoS2 , generates an electron-hole pair (e − h), and the electron gets transferred to the BLG giving a small rise in EF by an amount EF , which causes a small change (IDS ) in IDS . IDS appears as an additional noise current in the IDS time series data. To evaluate the contributions from few photons, the complete experiment is done at extremely low values of LED intensities. LED is excited with extremely low bias currents (ILED ) allowing only few photon generation via random optical transitions. At fixed ILED , the temporal evolution of IDS in the operational range of a BLG-on-MoS2 device is monitored continuously. Random impingement and absorption of photons introduce a noise in IDS (Fig. 9.7). Power spectral density analysis of such time series data allows extraction of the noise contribution arising from the photons. Knowing the gain of the detector, the single-photon contribution to the noise is estimated. When normalized

E

GRAPHENE MoS2

IDS

hBN

BLG

BLG

-

MoS2

+

IDS

EF

t

SiO2 Si++

K

Fig. 9.7 Photon absorption and receiver circuit noise. Low intensity detection scheme in a BLG-on-MoS2 device. When a photon is absorbed by MoS2 it creates an electron-hole pair (cyan and red circles respectively). Upon reaching to BLG, electron causes a change in current (IDS ). This change in IDS appears as temporal fluctuations in IDS values. Uncorrelated appearance of the photons cause fluctuations at random time

9.2 Photon Noise

199

with single photon contribution, noise magnitudes obtained at various ILED values, give the average photon numbers detected by the device.

9.2.2 Illumination Power and Spectral Density of Noise To capture the noise contribution originating from small number of photons, many time series data of IDS are taken with data acquisition speed of 512 Hz and illuminating the sample with extremely low values of PLED (Fig. 9.8). Power spectral density (PSD) analysis, of the time series data is performed at low frequency (f ) range to extract frequency dependent contribution of photoelectron generation noise (Sect. 3.3). To achieve extremely low PLED , the LED current (ILED ) is maintained at various low values. At a fixed (VT G , VBG ) time series data is taken with arbitrarily low ILED resembling dark, and then ILED is increased in small steps. Figure 9.8a shows three such time series data taken at different PLED values including dark condition, where PLED = 0. It is evident that the fluctuations in IDS increase as the PLED increases. Further, quantitative analysis of photon noise are done by estimating the frequency dependent noise power from these time series data. Figure 9.8b shows such power spectral density (PSD) (Si (f ) − f ) analysis for three different illumination powers. A 1/f dominated nature of the spectral is observed (gray line). At fixed f the higher PLED gives a higher value of Si (f ), indicating contributions from larger number of photons. Frequency normalized variance (IL2 ) is estimated using the formula IL2 = Si (f ) × f .

(9.6)

(a)

(b)

-2

)

0.3 nA

2.87  10 -4

10

10

0 5

10

100 10 1.2

-22

3.0 VTG (V)

1.1 10-23 1/f

ILED

IDS

17.9  10 -3

0

1/f1.5

10-21 Si(f) (A2 Hz-1)

dark P LED (fWm

IDS (nA)

This relationship is used to estimate the photon noise contribution.

15 t (s )

20

25

30

dark 2.910-4 1810-3 PLED (fW m-2)

-24

0.1

1 f (Hz)

10

Fig. 9.8 Illumination power and spectral density of noise. a Temporal evolution of source-drain current (IDS ) recorded with different illumination powers (PLED ). Backgate and topgate voltages (VBG , VT G ) are set at -70 V and 2.30 V respectively, position of which is indicated by an orange circle on IDS − VT G curve (inset,b). b Power spectral density of current-noise (Si (f )) at different PLED . Si (f ) extracted from the similar time series data shown in (a). (Inset) Symbol indicate operating point on IDS − VT G curve

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9 Photoresponse and Photon Noise in Bilayer-Graphene-MoS2 Hybrids

9.2.3 Photon Noise, Dark Noise and Gate Electic Fields The values of variance (IL2 ) obtained from the IDS time traces (Fig. 9.8) are represented by filled circles (pink) in Fig. 9.9a when exciting the sample with PLED corresponding to respective LED currents (ILED ) mentioned on the horizontal axis. Each data point is obtained from a time series window of 27 s. IDS values are acquired at 512 Hz speed in this time-window using ‘internal data buffer’ of SR830 Lockin amplifier from ‘Stanford Research System’. The slope of the low pass filter and time constant (tc ) settings of Lockin amplifier are kept at 24 dB/Oct and 10 ms respectively, allowing an equivalent noise bandwidth (ENBW) value of f ≈ 8 Hz, which is estimated following the relation (see SR830 manual, Stanford Research Systems) f =

5 . 64 × tc

(9.7)

Thus, meaningful power spectral density analysis (PSD or Si(f )) of the time series data remains within 8 Hz bandwidth. Before estimating the power spectral density, a digital filtering of the raw time series data is done to obtain a sharp cut-off frequency (see Ref. [5]). Si(f ) values are estimated using these processed data. To improve the quality of Si(f ), at each LED excitation current, IDS time series data is acquired 15 times. Si(f ) is estimated from each such similar time series data, and finally average Si(f ) value is considered. The complete data acquisition and processing are done in automated manner using LabView interfacing with the instrument (Sect. 4.4). Each data point takes about 10 minutes time to complete. Circles in Fig. 9.9a represent the variance (IL2 ) obtained following the Eq. 9.6. 40

10

1.2

VTG (V)

20 15

10-23 10-24

25

3.0

I2L |f = 8 Hz IDS

10-2

10-1 100 ILED (A)

101

10 5 102

10-20

2

IDS (nA)

10

10-21

IDS (nA)

-22

30

I2(D,L) (A2)

I2L (A2)

10-21

(b) 10-20

35

100

Exp Fit

 I2D (A )

-20

(a)10

10-21 10-22

I2L I2D

10-23 -22

10

10

100 IDS (nA)

10-23 10-24

10-2

10-1 100 ILED (A)

101

102

Fig. 9.9 Persistent current and dark noise. a Variance of current-noise (IL2 ) and source-drain current (IDS ) at multiple photoexcitations (ILED ). (Inset) Shaded region indicates the range of IDS values (average) attained when recoding time-series data with the sequence of ILED values. Orange circle indicate the initial spot selected for the experiment. b Comparison between variance obtained in presence (IL2 ) and absence (ID2 ) of light. (Inset) VT G dependent variance of IDS in dark. Green circles are experimentally obtained values and black line is a non-linear curve fit. Non-linear fit function is used to interpolate variance of IDS for an arbitrary IDS in the given range

9.2 Photon Noise

201

10-20 100

10-22

10 VBG (V)

1 1.5

8 (-70, 2.30) 8 (-80, 2.60) 8 (-90, 2.91)

IL2 (A2)

IDS (nA)

10-21

f (Hz) (VBG (V), VTG (V))

10-23

-70 -80 -90

2.0 2.5 VTG (V)

3.0

10-24 10-3

10-2

10-1 100 ILED (A)

101

102

Fig. 9.10 Static electric field and photon noise. (Right panel) Evolution of noise power (IL2 ) as a function of ILED . Here IL2 = Si(f ) × f , and Si(f ) is the frequency (f ) dependent power spectral density, extracted from the similar time series data shown in Fig. 9.8a). Three different coloured symbols indicate values extracted from similar set of experiments performed at three different combinations of top and backgate voltages as indicated by the symbols of respective colours in left-panel. (Left panel) Symbols show three different operating point on IDS − VT G curves aiming low dark current (Id ) at larger electric field i.e. at larger gate voltages (VBG , VT G )

Because of persistent nature of photoresponse in such devices (Chap. 7), a drift (increase) in IDS is observed after completion of each set of experiment with fixed illumination power and shown by the gray line in Fig. 9.9a (right-vertical axis). The shaded region in the inset shows similar IDS values in the IDS − VT G presentation, whereas the circle shows initial position. Increase in IDS also causes an enhancement in 1/f noise (Sect. 8.3.3) and affects the Si(f ) (or IL2 ) values. A direct measurement of dark noise (inset, Fig. 9.9b) allows the extraction of IDS dependent contribution of dark noise (ID2 ), which are presented in Fig. 9.9b (empty circles). At reasonable photoexcitation IL2 attain much higher values than ID2 indicating direct contribution from photon induced noise-current. The difference between IL2 and ID2 allows the estimation of the number of photons detected by the sample (Sect. 9.2.4). Figure 9.10 (right panel) shows IL2 − ILED plot for three different combinations of VBG and VT G , which are indicated by the similar coloured symbols in the leftpanel in Fig. 9.10. A prominent increase in IL2 is correlated with the larger number of photon absorption events, owing to the increase in the incoming photon flux at higher ILED values. Larger number of photoabsorption events transfers more photoelectrons (e) to graphene, hence, the fluctuations in IDS (IL2 ) appear more. Details of photon counting analysis are shown in following section (Sect. 9.2.4).

202

9 Photoresponse and Photon Noise in Bilayer-Graphene-MoS2 Hybrids

9.2.4 Photon Noise If there is an average np  number of photons impinging in a given time window (τw ), there is an average m = ηnp  photoelectron events which contribute to the measured ‘noise-signal’; here η is the quantum efficiency of the device. At a fixed ILED , the contribution of photons to the measured noise power is estimated by subtracting the light to dark variance values (IL2 −ID2 ; Sect. 9.2.3). Thus average number of 2 , photoelectron generation, corresponding to a ILED value, is equal to (IL2 −ID2 )/I1e 2 where I1e is the variance originated from a single photoelectron generation event. 2 is estimated following the relation (Eqs. 8.3, 8.4) The square root of I1e I1e =

dIDS dIDS e × VT1eG = × . d VT G d VT G CT G

(9.8)

Here VT1eG is the effective gate voltage change because of one electron addition to the BLG channel. CT G and e are total topgate capacitance and charge of a single electron respectively. Value of dIDS /d VT G depends on the choice of operational point in IDS − VT G curve (left panel, Fig. 9.10). Three different panels in Fig. 9.11 represent the results obtained from three different sets of VBG , VT G values. In all three panels the vertical axes represent the 2 , whereas the horizontal photoelectron numbers estimated using (IL2 − ID2 )/I1e axes represents the photoelectron numbers estimated from the optical power density (PLED ) corresponding to the LED excitation current ILED . The photoelectron numbers starts increasing from values close to one (vertical axes), indicating detection capability of single photon absorption event. The detection ability is more apparent

(IL2-ID2 ) /I21e (count)

(a)

104 3

10

(b) VBG = - 70 V m0.8

104 3

10

(c) -80 V m0.8

104 3

10

-90 V m0.8

102

102

102

101

101

101

100

100

100

10-1 10-1 100 101 102 103 104

10-1 10-1 100 101 102 103 104 m = NP (count)

10-1 10-1 100 101 102 103 104

Fig. 9.11 Photon noise. a–c Generated photoelectron number (m) versus detected photoelectron 2 ). Here I 2 is the single electron variance expected at the operating number ((IL2 − ID2 )/I1e 1e gate voltage combinations. Three different panels are to show the similarity of results obtained from similar experiments performed for three different sets of VBG and VT G . The solid lines are fit of the function f (x) = x0.8 which is a close match to f (x) = x resembling the Poissonian statistics of random events i.e. the appearance of photons

9.2 Photon Noise

203

in the right most panel, which corresponds to VBG = −90 V, VT G = 2.91V . The apparent detection ability of one photon noise is achieved owing to low NEP, high dIDS /d VT G resulting from increased bandgap, at proper choice of VBG and VT G . Many PLED values at low ILED do not give measurable power owing to the limited sensitivity of commercial detectors. The power calibration is extrapolated consider3/2 ing ILED dependence of PLED to get the PLED values at these ILED (Fig. 4.28b). To obtain average photoelectron numbers (m) on the horizontal axes, PLED is normalized with respect to the total data acquisition time (τw ), photon energy (EP ), device area (A) and quantum efficiency (η) of the device such that m = NP τw η,

(9.9)

2 correspondence where NP = PLED A/EP (Fig. 9.11). The m vs (IL2 − ID2 )/I1e n is shown by x functional dependence where n = 0.8. The horizontal and vertical dashed-lines indicate one-photoelectron-generation versus one-photoelectrondetection events. n = 0.8 is the close match to the value n = 1 expected from a true Poissonian statistics arising from random events, related to the random impingement of photons. This gives an additional support to the understanding of photon-noise measured in BLG-on-MoS2 sample.

9.2.5 NEP and D∗ from Photon Noise Noise equivalent power (NEP) and specific detectivity (D∗ ) of the device are also estimated following photon-noise experiments. Figure 9.12a shows PLED dependence of D∗ for three different operational combinations of VBG and VT G . These are the same three spots as indicated by their respective coloured symbols in IDS − VT G curves (a)

(b) D* (cm Hz1/2 W-1)

NEP (W Hz-1/2)

10-20 VBG (V), VTG

10-21 10-22 10-4

VBG (V), VTG

1018

10-19

(V)

-70, 2.30 -80, 2.60 -90, 2.91

10-3

10-2

PLED (fW m-2)

10-1

100

(V)

-70, 2.30 -80, 2.60 -90, 2.91

1017 1016 1015 10-4

10-3

10-2

PLED (fW m-2)

10-1

100

Fig. 9.12 NEP and D∗ from photon noise. a NEP extracted from photon noise at various PLED . Three different coloured symbols indicate the selection of three different sets of VBG and VT G values. b D∗ at various PLED for similar set of VBG and VT G values shown in (a)

204

9 Photoresponse and Photon Noise in Bilayer-Graphene-MoS2 Hybrids

shown in the left panel of Fig. 9.10. Figure 9.12a shows the NEP of the device. At a fixed illumination power, D∗ can maintain almost similar value while reducing the dark current (Id ) further by choosing different VBG and VT G combinations. The reduction in Id is achieved by increasing the bandgap in BLG. It should be mentioned here that noise from background radiation is expected to have insignificant contribution to NEP and D∗ presented in Fig. 9.12. Background noise, because of the presence of blackbody radiation may limit the detector sensitivity and performance. However, such background limited performance (BLIP) of a detector has less relevance in visible band compared to infrared band because of lower photon flux in the visible band [6–8]. For example, assuming blackbody radiation (emissivity = 1) at room temperature (300 K), background photon flux (ϕP ) is estimated to be ∼0.04 m−2 s−1 (band radiance ∼4π × 10−21 W m−2 in 4π solid angle, within the spectral band of 0.45 µm to 0.75 µm [9]). Such photon flux is many orders of magnitude lower than the lowest photon flux used in our experiments. D∗ of the presented device is estimated to be ∼4 × 1014 Jones when dark noise (all electrical noise including 1/f noise) is considered. Here NEP ∼10−18 W Hz−1/2 is used, which is estimated following 1/f noise analysis at VT G = 2.362 V, VBG = −70 V, IDS = 2 mV. D∗ ∼1018 Jones does not cross the theoretical limit when radiation-background limited detectivity is considered within the optical band of 0.45 µm to 0.75 µm. The theoretical limit of detectivity for an ideal detector with η = 1 is estimated to be ∼1021 Jones (see previous para).

9.3 Summary • Bilayer graphene (BLG) on MoS2 devices show extremely low noise equivalent power (NEP < 10−21 W Hz−1/2 , Thermal and shot noise limited) and large specific detectivity (D∗ > 1018 cm Hz1/2 W−1 (Jones)) while operating at ∼80 K temperature. Such low NEP and high D∗ values mark these detectors as highest sensitive photodetectors while operating at such high temperature (>> 4.2 K). Low dark current (Id ) and large responsivity (γ) values enable achieving of such low NEP and large D∗ . • High sensitivity allows characterising photon statistics of an illumination source (LED). Inspite of the presence of 1/f dominated noise at low frequencies (0.1 > f > 10 Hz), BLG-on-MoS2 is able to identify the difference in noise caused by few photons. • Variance of photon noise magnitude shows a close match (80%) with mean photon number. Such a match indicates that photo emitting statistics of LED follows Poisson statistics. Photon statistics is verified over a wide range of photoabsorption events starting from single photon. Such results indicate a wide dynamic range of ∼80 dB.

9.3 Summary

205

• Photon noise characterization indicates single photon detection capability of BLGon-MoS2 devices. However, a careful design scheme is necessary when intended number-resolved photon number detection. The following chapter presents a number resolved photon detection aspects of BLG-on-MoS2 devices.

References 1. Xue J et al (2011) Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride. Nat Mater 10:282–285 2. Roy K et al (2013) Graphene-MoS2 hybrid structures for multifunctional photoresponsive memory devices. Nat Nanotechnol 8:826–830 3. Zhang W et al (2014) Ultrahigh-gain photodetectors based on atomically thin graphene-MoS2 heterostructures. Sci Rep 4:3826 4. Long M, Wang P, Fang H, Hu W (2019) Progress, challenges, and opportunities for 2D material based photodetectors. Adv Funct Mater 29:1–28 5. Ghosh A, Kar S, Bid A, Raychaudhuri AK (2004) A set-up for measurement of low frequency conductance fluctuation (noise) using digital signal processing techniques. arXiv 0402130. http:// arxiv.org/abs/condmat/0402130cond-mat/0402130 6. BLIP condition in point-to-point optical communication (1967) Proc IEEE 55:189–192 7. Barhydt H (1976) Performance of nearly BLIP detectors in infrared sensors. Optical engineering, vol 15 8. Rosencher E, Vinter B (2004) Optoelectronics, 2004 edn. Cambridge University Press, Cambridge 9. Blackbody radiation calculator (online resources). https://www.spectralcalc.com/blackbody_ calculator/blackbody.php

Chapter 10

Number Resolved Single Photon Detection

Extremely low noise equivalent power and large detectivity allow BLG-on-MoS2 devices useful for single photon detection. Tuning gain and noise magnitude, it is possible to select an operational range of frequency-bandwidth where a single photon signal is distinguished from the background noise. Various measures were taken to tune the gain. For example, a short channel device is used to increase photogain etc. This chapter discusses detailed characterisation of a number-resolved single photon detector made of BLG-on-MoS2 structures. Histogram of photon statistics confirming the photon number resolution is also presented.

10.1 Fundamentals of Graphene-on-MoS2 Detectors Signal to noise ratio in graphene-on-MoS2 devices In a graphene-MoS2 planar photodetector [1–4], the circuit current (IP ) always flows inside the graphene plane (top panel, Fig. 10.1a). Graphene remains physically isolated (by a van der Waals gap) from the photoactive part (MoS2 ). Electrostatic field (from gate) across the graphene-MoS2 interface takes one type of photocarrier (electron or hole) selectively to graphene and the other carrier (hole or electron) remain trapped inside MoS2 or in MoS2 -SiO2 interface. When graphene receives photocarriers, it shows a change in conductivity. Thus, graphene acts as a receiver circuit here. The net conductivity change depends on the Coulomb interaction and screening mechanism across the graphene-MoS2 interface (Chap. 6). Since MoS2 acts almost as an insulator, the screening effect is negligible, and hence, trapped carrier holds the image charge that is transferred to graphene by gate electric field. Thus, the photocurrent is determined by the photogenerated trapped states inside MoS2 . However, once generated, owing to the absence of perturbation current (i.e. probe current or circuit current) and the strongly localized nature of electronic states [5], the photocurrent (IP ) remains free from gain noise (Sect. 3.3.3). The ultra-low thickness of MoS2 ( 1.6’. Deposition of an over-layer is also observed (irregular structures) which contains higher copper densities, coming because of the elemental copper deposition. Figure B.1e shows the zoomed image of the smooth-looking region. It is believed that the under layer contributes to photoconduction whereas the over layer mostly contains elemental copper and photo-inactive.

B.2

Current-Voltage Characteristics of Cux S Film

Electrical contacts are made using conducting epoxy (Ag-epoxy) in order to study photoresponse characteristics of these hybrids. Apart from the vertical growth of Cux S on graphene, film also grows laterally on top of the non-conducting epoxy mask. Thus, to study the graphene-Cux Sinterface characteristics, electrical contacts are made on graphene and the laterally grown Cux S. 2-probe current-voltage characteristics for two different pairs of contacts are presented in Fig. B.2b. The contact-A and contact-B differ by contact-area resulting different saturation current. A Schottky barrier is likely to form between grapheneCux S and Cux S-Ag-Epoxy interfaces. Assumption of a back-to-back diode model helps explaining both the linear and non-linear nature of the curves obtained from different pair of contacts (Fig. B.2c, d). Here IDS = Isat [exp(eVDS /nkB T ) − 1] diode equation is assumed, where n is the non-linearity factor whereas other symbols have usual significance. To fit the linear response Isat,1 = Isat,2 = 5 × 10−7 A is used. For non-linear curves Isat,1 = 1.3 × 10−8 A and Isat,2 = 4.0 × 10−7 A are chosen. Physically equal saturation current indicate comparable Schottky junction area, i.e. equivalent area of contact. Different saturation current indicate different are of contact. Here the current-voltage characteristics is better explained by assuming the n-type doping of Cux S.

262

Appendix B: Electrochemically Grown Photoactive Material on Large Area Graphene

Fig. B.2 Type of contacts. a Scheme showing device contact configuration. A, B have different contact area. b 2-probe response between graphen/Cux S/A, and graphen/Cux S/B. c scheme of back to back diode model. d Resulting curves from the model. Figures reprinted with permission [22]. Copyright (2012) American Chemical Society

B.3 Photoresponse Study of Graphene-Cux S Hybrid Devices Photoresponse characteristics of the grown film is tested by placing electrical contacts on the graphene-Cux S hybrid (see Sect. B.2). A schematic of such device is presented in Fig. B.2a, where contact-A and contact-B are made by utilizing conducting epoxy (Ag-epoxy). Figure B.3a shows the current-voltage characteristics of the device in dark (black-line) and light (red-line) conditions. An illumination of AM1.5 with 1000 W m−2 power density is given here. In presence of light, increase in current indicates the decrease in sample resistance due to the optical absorption property of Cux S film. In this 2-probe current-voltage characteristics, graphene acts as one contact and the other contact stays on the laterally grown Cux Sn which stays

Appendix B: Electrochemically Grown Photoactive Material on Large Area Graphene

263

Fig. B.3 Photoresponse study. a I − V characteristics of Cux S film grown on graphene substrate. b I − V characteristics of Cux S film grown on ITO substrate. Inset show time dependent light on off cycles. Figures reprinted with permission [22]. Copyright (2012) American Chemical Society

outside the overlapping region of graphene-Cux S. The effective contact area between graphene-Cux S being much larger than the epoxy-contact area, it is assumed that the region surrounding the contact play least role in photoconduction. Similar photoresponse study is carried out with Cux S film grown on ITO-coated glass. Here a current density of 3 µA mm−2 is used. The 2-probe measurements are done by taking ITO as one contact and a Ag-epoxy contact which is placed on the laterally grown part of Cux S. The similar photoresponse of Cux S films grown on graphene and ITO indicate that graphene can act as equally good conducting electrode as ITO, which has a wide range of commercial applications. The ITO used here has a sheet resistance of ∼10 −1 . The large resistance difference between between graphene and ITO does not appear in the current-voltage characteristics because of the large resistance of Cux S film which is semiconducting in nature. It can be said that large area photo-active material can be grown on graphene to make graphene-Cux S hybrid. Simple electrochemical growth technique is utilized to make such hybrid structures. Photoconductivity is tested of the as-grown film which shows similar response as the Cux S film grown on ITO. Simple electrochemical growth method can be utilized to prepare large area hybrid devices for large scale applications.

References 1. Konstantatos G et al (2012) Hybrid graphene-quantum dot phototransistors with ultrahigh gain. Nat Nanotechnol 7:363–368 2. Roy K et al (2013) Graphene-MoS2 hybrid structures for multifunctional photoresponsive memory devices. Nat Nanotechnol 8:826–830

264

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3. Roy K et al (2013) Optically active heterostructures of graphene and ultrathin MoS2 . Solid State Commun 175–176:35–42 4. Jariwala D, Marks TJ, Hersam MC (2016) Mixed-dimensional van der Waals heterostructures. Nat Mater 16:170–181 5. Pradhan A et al (2017) Ultra-high sensitivity infra-red detection and temperature effects in a graphene-tellurium nanowire binary hybrid. Nanoscale 9:9284–9290 6. Long M, Wang P, Fang H, Hu W (2019) Progress, challenges, and opportunities for 2D material based photodetectors. Advanced functional materials 29:1–28 7. Islam S et al (2019) Ultra-sensitive graphene-bismuth telluride nano-wire hybrids for infrared detection. Nanoscale 11:1579–1586 8. Lee I et al (2020) Photoinduced tuning of schottky barrier height in graphene/MoS2 heterojunction for ultrahigh performance short channel phototransistor. ACS nano 14:7574–7580 9. Levendorf MP et al (2012) Graphene and boron nitride lateral heterostructures for atomically thin circuitry. Nature 488:627–632 10. Georgiou T et al (2012) Vertical field-effect transistor based on graphene WS2 heterostructures for flexible and transparent electronics. Nat Nanotechnol 8:100–103 11. Nguyen VH, Mazzamuto F, Bournel A, Dollfus P (2012) Resonant tunnelling diodes based on graphene/h-BN heterostructure. J Phys D Appl Phys 45:325104 12. Choi MS et al (2013) Controlled charge trapping by molybdenum disulphide and graphene in ultrathin heterostructured memory devices. Nat Commun 4:1624 13. Huang C et al (2014) Lateral heterojunctions within monolayer MoSe2 -WSe2 semiconductors. Nat Mater 13:1096–1101 14. Lee C-H et al (2014) Atomically thin PN junctions with van der Waals heterointerfaces. Nat Nanotechnol 9:676–681 15. Sarkar D et al (2015) A subthermionic tunnel field-effect transistor with an atomically thin channel. Nature 526:91–95 16. Pizzocchero F, et al (2016) The hot pick-up technique for batch assembly of van der Waals heterostructures. Nat Commun 7 17. Purdie DG et al (2018) Cleaning interfaces in layered materials heterostructures. Nat Commun 9:1–12 18. Masubuchi S et al (2018) Autonomous robotic searching and assembly of two-dimensional crystals to build van der Waals superlattices. Nat Commun 9:1413 19. De Fazio D et al (2016) High responsivity, large-area graphene/MoS2 flexible photodetectors. ACS Nano 10:8252–8262 20. Polat EO, et al (2019) Flexible graphene photodetectors for wearable fitness monitoring. Sci Adv 5, eaaw7846 21. Pataniya PM, Sumesh CK (2020) WS 2 nanosheet/graphene heterostructures for paper-based flexible photodetectors. ACS Appl Nano Mater 3:6935–6944 22. Padmanabhan M, Roy K, Ramalingam G, Raghavan S, Ghosh A (2012) Electrochemical integration of graphene with light-absorbing copper-based thin films. J Phys Chem C 116:1200– 1204 23. Kochat V et al (2011) High contrast imaging and thickness determination of graphene with in-column secondary electron microscopy. J Appl Phys 110:014315