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2D layered materials: fundamental properties and device applications
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2D layered materials: fundamental properties and device applications
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2D LAYERED MATERIALS: FUNDAMENTAL PROPERTIES AND DEVICE APPLICATIONS by Huan Zhao A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) December 2019 Copyright 2019 Huan Zhao DEDICATION This dissertation is dedicated to Mrs. Ruoke Shi for all her love and support; And to the memory of my beloved grandmother Li Xiu-Ying who unfortunately couldn’t stay in this world long enough to see her doctor grandson ii Acknowledgment My research accomplishment in this dissertation would not have been possible without the contributions from my supportive family members, insightful mentors, courteous friends, generous funders, and a wide-range of world-class collaborators. I would like to sincerely appreciate those who have supported, encouraged, and inspired me throughout my PhD education. First, I would like to thank my advisor, Professor Han Wang, for his help in my research. Han preceded me through the PhD research at USC and taught me essential skills such as how to present the work and how to collaborate with experts from different fields. In addition, I am extremely grateful to Han for writing strong recommendation letters in my fellowship and award applications, as well as his generous financial support during my PhD life. I would like to acknowledge all my colleagues and collaborators for their strong support and cooperation, including all my present and former labmates, especially those who built the lab with me such as Xiaodong Yan, Yuanrui Li, and Luhao Wang. I also want to acknowledge Prof. Jing Guo’s group, Prof. Jayakanth Ravichandran’s group, Prof. Wei Wu’s group, Prof. P-H Tan’s group, Northrop Grumman Corporation, Prof. Jing Kong’s group, etc. for their friendly support. I feel extremely lucky to have worked alongside with these world- class researchers. iii Last but not least, I would like to express my deep gratitude to my family who always offers me a pillar of support during my graduate study. My special thanks go to Ruoke and my grandparents who helped me make through each step of my PhD program. iv TABLE OF CONTENTS DEDICATION ................................................................................................................... i Acknowledgment .............................................................................................................. ii Abstract ........................................................................................................................... vii 1. Introduction ............................................................................................................... 1 1.1 2D Material Preparation ................................................................................. 2 1.1.1. Chemical Vapor Deposition ................................................................ 3 1.1.2. Mechanical Exfoliation ....................................................................... 5 1.2 2D Material van der Waals Heterostructures ................................................ 11 1.2.1. All-dry Viscoelastic Stamping Method ............................................. 12 1.2.2. Other Flake Transfer Methods........................................................... 17 1.3 2D Material Electronics ............................................................................... 18 1.4 2D Material Nanophotonics ......................................................................... 22 1.4.1. Introduction of 2DM Nanophotonics ................................................ 22 1.4.2. Graphene Photonics: Photodetector, Modulator, and Plasmonics Photodetectors ................................................................................................ 25 1.4.3. Photonics of TMDCs ......................................................................... 30 v 1.4.4. Black Phosphorus for Photonics Application .................................... 32 1.4.5. Outlook .............................................................................................. 33 2. Research Accomplishments in my PhD Study: An Overview ................................. 35 3. Characterizing the Novel Properties of Emerging Low-dimensional Materials with Reduced Symmetry ........................................................................................................ 38 3.1 Spatial-temporal Imaging of Anisotropic Photocarrier Dynamics in Black Phosphorus ............................................................................................................. 38 3.2 Interlayer Interactions in Anisotropic Thin Rhenium Diselenide ................ 51 4. 2D Material Kirigami and Origami ......................................................................... 72 4.1 2D Material Kirigami ................................................................................... 73 4.1.1. Engineering the Optical Response of Monolayer Molybdenum Disulfide Nanoribbons with Kirigami ............................................................................ 73 4.1.2. Hausdorff Dimension, Self-similarity, and Fractal in 2D material Kirigami 82 4.2 2D Material Origami .................................................................................... 88 5. Atomically Thin Femtojoule Memristor ................................................................ 105 5.1 Introduction ................................................................................................ 106 5.2 Sample preparation and characterization ................................................... 107 vi 5.3 Thickness Dependent Ultra-low Power Filamentary Switching and Modeling 111 5.4 Device Characteristics of a 0.9 nm BNOx Memristive Device ................... 119 5.5 Efficient Learning with Ultra-low Power Compound Synaptic Devices ... 122 6. BNOX Memristor Based Boltzmann Machine ....................................................... 125 6.1 Introduction ................................................................................................ 126 6.2 BNOx-WSe2 Device for Generating Dynamically Tunable Sigmoidal Distributions ......................................................................................................... 127 6.3 A Boltzmann Machine Based on the Stochastic Memristor ....................... 133 6.4 A Machine-learning-based Method for Device-circuit Co-design of the Boltzmann Machine ............................................................................................. 138 7. References ............................................................................................................. 144 vii Abstract Since the successful isolation of graphene fourteen years ago, 1-2 the family of two- dimensional (2D) materials have attracted tremendous interests in the research community. Unique and novel physics has been found or proposed in 2D materials, such as Dirac- Fermions, 2-3 valley degree of freedom, 4-5 Weyl Semimetal, 6 and Quantum anomalous Hall Effect. 7-8 In a perspective of electronic device engineering, 2D layered material family contains conductors, semiconductors (both p-type and n-type) and insulators, which is promising for CMOS integration. Compared to traditional silicon electronics, 2D material devices are flexible, transparent, environmentally friendly, biocompatible, and in many circumstances, performs better. In addition, 2D semiconductors have a wide range of bandgaps from sub 0.1 eV to over 3 eV , enabling us to design infrared optoelectronic devices 9- 11 with small bandgap materials, build logic circuits 12-14 with intermediate bandgap materials, and fabricate power electronics with large bandgap materials. 15 With these advantages, it is desired to both explore the exotic fundamental properties of 2D materials and develop concept-new 2D material based electronic devices. 1 1. Introduction Since the successful isolation of graphene fourteen years ago, 1-2 the family of two- dimensional materials (2DMs) has attracted tremendous interests in the research community. There are hundreds of materials in 2D family, 16-17 which can be thin down to few layers owing to the weak interlayer van der Waals interaction. These materials usually possess unique properties that are not observed in their bulk counterparts. Various techniques are developed to prepare such materials and their heterostructures, as well as to encapsulate them. A number of sophisticated experimental tools have been utilized to characterize 2D materials from all perspectives, archiving rich information into the 2D library. Classified by their band- structures, there are metals, 18-19 semi-metals, 20-21 Weyl Semimetals, 22-23 half-metals, 24 semiconductors, 25-27 topological insulators, 28 and insulators 29 in 2D material family, which enables us to build various photonic and electronic devices. Besides, recently magnetic, 30-31 ferroelectric, 32-33 charge-density-wave 34-35 and superconductive 36-37 2D materials have been uncovered, bringing more features into 2D material based functional devices. The most commonly studied 2D materials area graphene, hexagonal boron nitride, transition metal dichalcogenides (TMDCs), black phosphorous, group-IV monochalcogenides, gallium/indium monochalcogenides, layered oxides, halides, etc. Beyond these materials, 2D 2 material superlattices, heterostructures, fractals, as well as 2D material engineered by strain, twisting, doping, functionalization, and suspending have resulted in numerous 2D structures with tunable properties. In a perspective of device engineering, the family of 2D layered materials contains conductors, semiconductors (both p-type and n-type), and insulators, which is promising for CMOS integration. Compared to traditional silicon devices, 2D material devices are flexible, transparent, better biocompatible, and in some cases have better performance. In addition, 2D semiconductors have a wide range of bandgaps from <0.1 eV to >3 eV , enabling us to design infrared optoelectronic devices with small bandgap materials, build logic circuits 12-14 with middle bandgap materials, and fabricate power electronics with large bandgap materials. 15 With these advantages, it is desired to both explore the exotic fundamental properties of 2D materials and develop concept-new 2D material-based devices. 1.1 2D Material Preparation One of the most critical challenges in the 2D material research community is to obtain high- quality, large-scale monolayer 2D materials. Since most of the 2D material applications are in the mesoscopic scale, assembling 2D membrane from microscopic molecules and cleaving 2D flakes from their bulk counterparts are two main approaches to obtain monolayers, which are called “bottom-up” and “top-down” methods, respectively. In this section, I will introduce 3 some “mainstream” methods of producing 2D materials. I will also discuss how to stack 2D flakes to prepare heterostructures in the next section. 1.1.1. Chemical Vapor Deposition Chemical Vapor Deposition (CVD) typically utilizes gas, or solid precursors to have chemical reaction under a controlled environment. 38 The essential setups to perform CVD are a furnace, a gas flow control system, temperature control units, and a vacuum pump with gauge. Catalytically active substrates are widely used in 2D material CVD growth. The mechanism for CVD synthesis is dependent on substrates: a substrate can catalyze the self- limiting growth of monolayer film if its precursor insolubility is low. In other circumstances, substrates are heated up to induce the diffusion or sublimation processes to grow a 2D membrane enriched with the precursor element. To synthesize CVD graphene, acetylene (C2H2) and methane (C2H4) are typically served as a carbon source (Figure 1.1.1). The hydrocarbon precursors are usually heated to 1000 degree Celsius to dehydrogenate on a metal substrate, which is typically Cu or Ni foil. The species formed in the previous reaction tend to nucleate into graphene islands, which eventually enlarge and merge into a full monolayer film with numerous grains. 39 Graphene obtained with this method could reach over 30-inch scale at a relatively low cost. 40-41 The 4 metal substrate can be etched away using metal etcher, resulting in freestanding graphene film which can be easily transferred to arbitrary substrates. Figure 1.1.1 A Schematic of graphene CVD synthesis CVD graphene monolayers typically have worse electrical performance comparing to their exfoliated counterparts. For example, exfoliated graphene sample can have carrier mobility over 200,000 cm 2 V −1 s −1 , 42 when suspended or sandwiched with hBN. However, the mobility of CVD graphene monolayer can reach 37,000 cm 2 V −1 s −1 when an hBN substrate is used, 43 which is an impressive value, but still lower than the exfoliated ones. To synthesize single-crystal graphene in large scale is challenging, as there are always undesired grain boundaries. Another challenge is to efficiently transfer CVD graphene from metal foil to arbitrary substrate, without compromising the sample quality. Nevertheless, the CVD (and MOCVD 44-45 ) method is an economic approach to produce large-scale graphene and many other 2D material monolayers, 46-47 which is a milestone towards industry level applications of 2D materials. Nowadays there are many new-born startups working on wafer-scale CVD 5 graphene synthesis, demonstrating that this technique is drawing interest from the industry side. 1.1.2. Mechanical Exfoliation In 2004, Dr. Geim’s group invented the “scotch tape” method to produce monolayer graphene. 1 The basic idea is to place a piece of thin graphite flake onto a scotch tape, using the adhesive force of the tape to peel off monolayer or few-layer flakes from the bulk graphite. This method can also work for most of the other 2D materials. There are a number of modified mechanical exfoliation methods, which all share similar mechanisms. For the abovementioned “tape method”, the critical parameters are the tape, the graphite, and the substrate. I will break down these parameters in details in the following text. Most of the other 2DMs can also be well exfoliated with the techniques to exfoliate graphene. In terms of the tape, most researchers prefer Nitto blue tapes, which is cleaner than 3M scotch tapes. Nitto blue tape has relative weak adhesive force, which becomes even weaker with elevated temperature. From my experience, at 80 degree Celsius, the blue tape can lose a majority of its adhesively, starting to wrinkle and buckle. Therefore, if someone prefers large flakes regardless of the flake thickness, he or she is recommended to bake the substrate with the tape attached, before separate the tape with the substrate at the elevated temperature. Since graphene flakes contact with the substrate firmer but stick looser towards the tape at 6 high temperature, a significant number of thick flakes will be transferred onto the substrate. Similarly, as blue tapes completely become non-sticky after treated with acetone, immersing the substrate into an acetone bath with tape attached is another approach to obtain large flakes. Once immersed in acetone, the blue tape rolls up and peels off automatically within a minute, leaving the substrate with large (and typically thick) flakes (Figure 1.1.2). Figure 1.1.2 Left, a blue tape heated on a hot plate is attached with a wafer, with graphite flakes on tape. Right, a blue tape with wafer can roll up automatically in an acetone bath. Highly oriented pyrolytic graphite (HOPG) flakes are preferred in tape-based exfoliation method, as they are easy to exfoliate, especially considering the flake size is typical ~ 1 mm. NGS Naturgraphit GmbH, a German company (www.graphit.de) that offers graphene flakes in various scales and shapes (Figure 1.1.3), is another good choice for exfoliation. If using NGS graphite, I would recommend ordering the flakes with ~5 mm scale, which can easily fit the dimension of most of the tapes. Before performing exfoliation, it is 7 recommended to peel off the old grey surface of the bulk graphite by scotch tapes to obtain the highly reflective, metal-like fresh graphite surface (Figure 1.1.3b), which is helpful for obtaining high-quality flakes. Figure 1.1.3 a) Graphite flakes from NGS Naturgraphit GmbH. b) Fresh graphite flake with shinning surface For 2DM researchers, the most popular substrate is Si/SiO2 substrate, where a layer of SiO2 is thermally grown onto Si. Highly doped Si is preferred in most of the electrical measurement, while highly resistive, or intrinsic Si substrates are preferred in most of the optical characterizations, especially those applying transmission light to interact with the material. 90 nm SiO2 typically gives the best optical contrast for searching almost all monolayers, especially monolayer hBN. SiO2 thickness at ~ 285 nm is also widely used, as 270-285 nm SiO2 are preferred in identifying atomically thin TMDCs (MoS2, WSe2, etc.), while 300 nm SiO2 is recommended for searching monolayer graphene. Limited by thermal 8 growth time, the surface roughness of a 90 nm SiO2 is typically larger than the 285 nm counterpart, which hinders flake transferring during mechanical exfoliation. Correctly cleaning the wafer can minimize the surface roughness, while a carelessly cleaning turns the wafer surface even worse. If performing dry cleaning, O2 plasma at 60 W RF power is suggested, under 100 mTorr O2 pressure and 1-minute cleaning time. In terms of wet cleaning, I prefer to clean the wafer with the following procedures: acetone 2 min in an ultrasonic cleaner → warm acetone bath at 50 ℃, 1 min → IPA 1 min → DI water spray 10s → N2 dry. It is not suggested to solely clean up the wafer with acetone, as it brings in unwanted residues (Figure 1.1.4). Also, nitrogen gun drying should be performed immediately after taking the wafer out of any volatile solvent, as it is desired to blow away the liquid before it completely evaporates to avoid residues. A clean substrate with an atomically smooth surface is highly desired for obtaining large monolayers using mechanical exfoliation methods. 9 Figure 1.1.4 Left: AFM image of Si wafer before (left) and after (right) cleaning with acetone In some applications, various substrates other than Si wafer are required, which may offer compromised optical contrast. Sapphire, quartz, ITO, mica, etc. are popular substrates for optical measurement, while PDMS, PMA, PV A are commonly used as an intermediate substrate for subsequent material transferring. In general, polymer substrates can result in enhanced yield for exfoliation, owing to their smoothness and excellent adhesion with flakes. High-k dielectrics are preferred in some electrical characterizations, which can offer even better optical contrast than the Si/SiO2 ones, once the dielectric thickness is carefully designed. 10 Figure 1.1.5 Exfoliated graphene monolayer on Au nanoparticle In general, graphene and hBN are easier to exfoliate than 2D sulfides, while sulfides are easier than selenides. Black phosphorus gets oxidized easily in ambient condition, therefore, it is recommended to exfoliate BP inside a glove box filled with inert gas. Figure 1.1.5 and Figure 1.1.6 are examples of my exfoliated monolayer graphene and MoS2. 11 Figure 1.1.6 Exfoliated MoS2 monolayer 1.2 2D Material van der Waals Heterostructures III-V semiconductor vertical heterostructures have revolutionized our lives in many aspects. 48-49 Compared to III-V , high-quality 2D materials vertical heterostructures 17, 50 are easier to fabricate, owing to their van der Waals interactions and daggling-bond-free surface. Interlayer lattice mismatch can induce undesired defects in III-V which hinders the interface quality. On the other hand, 2D materials can be freely stacked together without suffering such defects. By stacking various layered materials together using van der Waals force, 2D heterostructures allow a huge number of combinations that cannot be prepared by other methods. Furthermore, by adjusting the lattice constant and crystal orientations of different layers, new types of complex structures originated from different moiré landscapes can be obtained. 51-52 In addition, 2D homostructures prepared by stacking the same material together with a twist or displacement have also become increasingly popular recently. Here I will 12 introduce some basic methods of stacking 2DMs in the following sections. There are, of course, many other working approaches that are not covered here. 1.2.1. All-dry Viscoelastic Stamping Method In this method, 2D materials are exfoliated onto a PDMS stamp first. Next, the PDMS is placed onto a glass slide. The slide is then turned upside down and aligned on top of a target flake which is on another substrate. A microscope and a set of micromanipulator are typically utilized to align the top and bottom flakes. The last step is to contact the PDMS top layer with the target flake, followed with slowly peeling off the PDMS film, leaving the stacked flakes on the substrate. A schematic to demonstrate this step is shown in Figure 1.2.1, which is originally developed by Andres Castellanos-Gomez et al. 53 Figure 1.2.1 Diagram of the preparation of the PDMS viscoelastic stamp, and the deterministic transfer of a thin flake onto a target flake (for example another thin flake). 13 To my best knowledge, the abovementioned method is the easiest way to deterministically transfer a 2D flake onto arbitrary substrates. It takes less than half an hour for an experienced researcher to perform such a process. Precisely aligning the two flakes with small misalignment (< 2 um) is critical in many scenarios, hence it is worthwhile to build up a system that can perform an accurate alignment. In 2014 I DIYed a deterministic transfer station with a very low budget. Here is how I build it. 14 Figure 1.2.2 A home-made deterministic transferring setup modified from a microscope First, I started from a standard trinocular transmitted and reflected light microscope (OMAX M838TRMD-C30UPB, $3700). I removed the condenser which is only useful for the transmitted light mode but kept the metal ring to serve as a supporter for the future top glass slides. Then the XY stage is removed, flipped and re-mounted onto the microscope, 15 serving as a carrier for micro-manipulator. After flipping and re-mounting, the height of the flipped stage can still be adjusted by the original focus adjustment knob. The last step is to add a manipulator into the flipped stage. I further mount a 1-inch sample stage onto the manipulator with steel coins and a magnet. This coin stage is rotational, as it is connected to the base through a magnet. Figure 1.2.3 A detailed introduction of the DIYed setup During the deterministic transfer, basically we have a top layer and a bottom target layer, and we want to align the two layers before putting them in contact. The top layer is exfoliated onto a PDMS stamp, which is attached to a glass slide. The glass slide is placed on two thicker glass slide supporters which are stuck on the metal ring in my flipped microscope stage. The ring can be fine-tuned in the z-direction with the knob which was used to tune the 16 height of the condenser. The XY movement of the glass slide is realized by sliding it against the two thick slides. I typically add a droplet of water between each thick slide and the top glass slide to lock the z-direction movement of the thin slide, while enhancing the XY sliding between the thin and thick slides. The target substrate is placed onto a home-made rotational stage over the micro-manipulator. The stage is made of two steel coins connected with a magnet, and two additional US copper-nickel quarters as spacers. The benefit of the magnet is that it offers a firm connection while allows us to rotate the coin stage. The flake alignment is performed under a microscope. Once the graphene flake on PDMS is aligned with the target flake, the PDMS moves downside to contact the target flake. Then the PDMS film is slowly peeled off to leave the 2D heterostructures on the target substrate. Figure 1.2.4 shows how a MoS2 monolayer is transferred onto a WS2 mono- and bilayer, through the abovementioned setup. Figure 1.2.4 Left: A monolayer MoS2 on PDMS; middle: 1-2 layer WS2 on Si/SiO2 substrate; Right: MoS2/WS2 heterostructure obtained by PDMS dry transferring. 17 1.2.2. Other Flake Transfer Methods “Wet transfer” methods are flake transfer techniques that utilizing wet etching to detach materials from the original substrate. For example, CVD graphene grown on Cu foil can be wet-transferred onto an arbitrary substrate by putting the sample into FeCl3 to etch away Cu. To transfer 2DM flakes from a Si/SiO2 wafer onto other substrates, hot KOH or NaOH solution are widely used. 54 First, PMMA A3 is spin-coated onto the original substrate at 3000 rpm, followed with a hot plate baking at 150 degree Celsius. Then the substrate is placed on the surface of 1 mol/L KOH or NaOH hot solution (~ 80 ℃). After 2 hours, SiO2 is etched away and Si substrate sinks to the bottom of the solution, leaving the PMMA film floating on the solution. Then the PMMA film is fished up and washed in DI water multiple times before it is finally placed on a target wafer, with microscope-assisted alignment, if necessary. The last step is to remove PMMA with acetone, leaving the flake on the new substrate. “Flake delaminate and stack” is a technique to delaminate a flake from its original substrate and stack it on another substrate. hBN flake can be utilized to pick up 2DM flakes owing to the relatively strong van der Waals force between hBN and the flake. 55 Various polymers such as PMMA and PV A can also act as stamps to peel flakes off from the original substrate. After stacking the flake onto another substrate/flake, the PMMA and PVA can be removed by acetone and DI water, respectively. In such a process, the SiO2 of the original substrates can be reserved, as no etching is involved. Figure 1.2.5 demonstrates the abovementioned technique. 18 Figure 1.2.5 A hBN flake is delaminated from its substrate and transferred onto a graphene flake. 1.3 2D Material Electronics Various 2D material-based electronics have been explored in the past 15 years. The most studied types of devices are transistors, tunneling devices, photodetectors, RF devices, LEDs, memory cells, neuromorphic devices, etc. By combining different devices together, complicated functionality can be demonstrated. For example, CMOS circuits that can process logic computation have been demonstrated by p-type and n-type 2DM semiconductors. Transforming traditional Si electronics to 2DM based electronics seems straightforward: there are metals, p-type semiconductors, n-type semiconductors, and insulators in 2D family, 19 which seems sufficient to build all types of CMOS devices. However, there are a number of challenges. First, we do not have a technique to produce wafer-scale single crystal essential 2DMs, especially 2D semiconductors and 2D insulators. Nowadays the most practical s2DM ynthesis techniques such as CVD and MOCVD can grow these materials continuously at 4- inch scale or beyond with grain boundaries. We have to either be able to synthesize wafer- scale 2D semiconductors in single crystal forms or learn to build circuits with existing of the annoying grain boundaries. Fortunately, the recently developed 2D synaptic devices seem to partially demonstrate defect-tolerate capabilities owing to their stochastic nature. 56 Very recently there is a report that claims the capability of growing 100 mm scale single-crystal hBN film, 57-58 which can potentially serve as a high quality gate dielectric in the future all- 2D circuits. Besides various 2DM film growth techniques, inkjet printed 2D electronics 59-60 might be a new approach to utilize 2DMs. Printed electronics are flexible, less costly, easy to process, and environmentally friendly, compared to traditional clean-room fabricated electronics. In addition, 2DM device fabrication techniques are not as mature as those on Si devices. For example, Si transistors can benefit from the thermally grown SiO2, which is an excellent gate dielectric. Also, during the last decades, clean-room fabrications on Si such as dry/wet etching, anisotropic etching, ion injection, doping, annealing, lithography, contact and 20 interface engineering are fully developed. However, these techniques, although more or less developed in 2DM electronics, are typically not mature enough to meet the industry standard. Nevertheless, 2D materials are believed to be one of the most promising candidates in the post moore era, as suggested in various roadmaps, such as Figure 1.3.1. There are various merits of 2D materials which are not found in most of the other semiconductors. For example, 2D materials are atomically thin, flexible, transparent, and typically environmentally friendly. In the following section, I will introduce some of the key advantages of 2DMs that can benefit their electronic applications. Figure 1.3.1 2017 edition - IEEE International Roadmap for Devices and Systems 2D materials are atomically thin. Leveraged by their thinness, 2D materials have excellent gate tunability in field effect transistor applications. For the same reason, 2DMs are also perfect tunable tunneling barriers, especially when considering the easiness of assembling all-2D tunneling junctions. Recently spin tunneling is also demonstrated in 2D 21 systems. 2DM FETs can easily be fully depleted owing to the thin body. In 2D systems, the movement of electrons and holes are confined into a 2D sheet, giving rise to a number of geometry-confined quantum behaviors. 2D materials are flexible. The high flexibility of 2D materials not only enables electronics on curved systems such as human skins but also opens a door for engineering the device performance via strain, ripple, curvature, etc. Various 2DM devices built on flexible substrates such as PET have been demonstrated (Figure 1.3.2), 61-62 paving the way for next- generation flexible electronics. Devices with flexibility are highly desired in bio-compatible applications, such as micro-robots that can navigate inside a human body. In addition, strain engineering has been predicted or performed to realize bandgap tuning, spin-orbit coupling, phase changing, etc. Figure 1.3.2 A flexible MoS2 FET on PET substrate, adapted from a previous publication 62 2D materials are transparent in their mono- and few-layer forms. For example, monolayer graphene can absorb 2.3% of the incident light, 63 while hBN monolayer is almost 22 completely transparent at the visible light range. In various optoelectronic applications, transparent electrodes are highly desired. Graphene can serve as a tunable transparent electrode in various applications such as photodetectors, photoemission, and energy harvesting. On-screen display is another potential application that utilizes the transparency of 2D materials. 2DM-organic hybrid optoelectronic devices can combine the advantages of both types of novel materials and realize excellent performance. 64 2D materials can be easily assembled to form high-quality junctions. For example, by stacking WSe2 and MoS2 vertically, we have an atomically sharp p-n junction. In addition, this junction is gate tunable, as the electrostatic doping level can be varied by the gate. Similarly, once BP and SnSe2 few layers are stacked together, an Esaki diode can be formed owing to the “broken gap” energy band alignment configuration. 65 Resonant tunneling and negative differential resistance can be observed in such a diode. 2DM heterostructures with more than two different types of materials can offer even more complicated capabilities. For example, assembling MoS2, hBN, and graphene together can result in an ultrahigh on-off ratio flash memory device, 66 where the memory window can be engineered by altering the layer numbers of each material. 1.4 2D Material Nanophotonics 1.4.1. Introduction of 2DM Nanophotonics 23 Since the successful isolation of graphene more than a decade ago, the family of two- dimensional (2D) materials has attracted tremendous interests in the research community. Graphene is the first extensively studied material with true two-dimensional nature. With its unique band structures at the limit of 2D quantum confinement, this honeycomb monolayer of carbon atoms has inspired many interesting applications in nanophotonics and nanoelectronics. The most appealing features of graphene for nanophotonics application originate from its zero-bandgap nature with linear dispersion near the Dirac point. Due to its unique band structure, graphene offers highly sensitive responses to optical signals over a very wide spectral range through various types of light-matter interaction mechanisms. At the terahertz and mid-infrared range, graphene supports localized and propagating plasmons. Due to the controllable Fermi energy in graphene, such plasmonic responses are tunable by electro-static biasing with an external gate, a feature not available in traditional metal-based plasmonic devices. On the other hand, graphene can also be utilized to construct photodetectors and modulators for many optoelectronics applications at near-infrared, visible and ultra-violet spectrum range, leveraging its broadband absorption of light through interband transitions. However, graphene is not suitable for light generation functions due to its metallic nature, for which properties of other 2D materials needs to be explored. Besides graphene, hexagonal boron nitride (hBN) is also a layered material with honey-comb lattice structure. Its large bandgap (6 eV) makes it an outstanding dielectric for other 2D materials, which has enhanced the electronic and optoelectronic performance of various devices. 24 In recent ten years, the research community has witnessed the rise of another family of two-dimensional materials–the single-layer transition metal dichalcogenides (TMDCs), such as molybdenum disulfide and tungsten diselenide. This rich family of mono-molecular-layer semiconductors can cover the energy range 1.5-2.5 eV and beyond, offering new opportunities to construct devices that can perform light generation functions due to its finite and direct bandgap in the monolayer form, such as light emitting diodes (LED) and lasers. In addition, the valley coherence and valley-selective circular dichroism observed in various monolayer TMDCs offer exciting opportunities for the research of novel optical phenomena. Since the beginning of year 2014, we have also seen the arrival of a new member of the 2D material family – black phosphorus. This layered material with a moderate bandgap of 0.3 eV in its thin film form that is widely tunable to around 2.0 eV in its single-layer form bridges the energy gap between zero-bandgap graphene and relatively wide bandgap transition metal dichalcogenides. It can potentially cover a broad wavelength range from mid-infrared to partially visible spectrum for light detection, modulation, and generation applications. Here in the next sections I will review the various topics on the applications of 2D materials for nanophotonics application as introduced above. 25 1.4.2. Graphene Photonics: Photodetector, Modulator, and Plasmonics Photodetectors High speed, broad bandwidth photodetectors are essential for communication, sensing, and digital imaging. Most traditional commercial photodetectors are based on silicon or III-V semiconductors. When photons are absorbed into the photodiode's depletion region, they excite electron-hole pairs and their separation leads to photocurrent generation. This mechanism (usually called photovoltaic effect) was also claimed to be the operational principle of graphene-based photodetectors in early research. 67-68 However, more complex principles have been revealed later. First, the lifetimes of excited carriers in graphene are found to be too short to generate efficient channel current. In addition, the slow electron- lattice relaxation in graphene results in an elevated carrier temperature under light excitation due to a thermal decoupling between the lattice and photo-generated carriers. Therefore, if graphene is doped non-uniformly, “hot” carriers will diffuse due to the electronic temperature gradient, generating a net photocurrent, which is called photo-thermoelectric effect. 69 Furthermore, due to the Auger-type processes in graphene, multiple electron-hole pairs can be generated with merely a single photon, 70-71 which can potentially enhance the detection efficiency. Besides the photo-thermoelectric and photovoltaic effects, bolometric effects in graphene can also play a role in photoresponse 72 . To sum, due to the reduced dimensionality and its metallic nature, the generation of photocurrent in gapless graphene is more complex than that in traditional three-dimensional semiconductors with a sizable bandgap. 26 Graphene Photodetectors Owning to its zero-bandgap nature and the interband transitions of carriers, graphene is able to absorb photons from mid-infrared to ultraviolet wavelengths 9,10 . Unfortunately, the small optical absorption of monolayer graphene arising from its innate thinness has limited the photoresponsivity of graphene-based photodetectors. Although graphene based photodetectors are promising for their ultra-broadband, high speed, and its compatibility to circuits. Its low photoresponsivity compared with traditional semiconductor-based ones remains a major drawback. Recently, several methods have been applied to enhance the optical absorption of graphene-based photodetectors. First, combining graphene with plasmonic nanostructures is able to concentrate light using plasmonic resonances, resulting in a significantly enhanced local electric field. Besides the huge enhancement in quantum efficiency, multicolor detection can also be achieved through the wavelength-dependent photoresponse amplification of plasmonic nanostructures. Second, integrating quantum dots with graphene is another powerful approach to enhance responsivity of graphene photodetectors. The quantum dots assist photogenerated carriers to reach graphene sheets while trap all oppositely charged carriers in quantum dot layer, resulting in a field-effect doping phenomenon. Graphene-quantum dot photodetectors perform tremendous responsivity, but they also suffer low operational speed, due to the long time needed to generate gain. In addition, the working bandwidth in these devices are mainly 27 determined by the quantum dot rather than graphene. Third, integrating graphene with microcavity is another powerful way to increase photoresponse. The cavity-induced optical confinement can enhance photoresponse, but also narrows its bandwidth. Finally, coupling graphene to various waveguide can lead to photodetectors with excellent performance. These devices are marked by high photoresponsivity (~ 0.1 A W -1 ), ultra-wide bandwidth (from visible to infrared wavelengths), high efficiency, high speed (~10 Gbit s -1 ), and small footprint. In graphene-waveguide photodetectors, the waveguide conveys light to graphene either by batt-coupling or evanescent coupling. The latter has been applied to many novel devices like graphene/silicon-heterostructure waveguide photodetectors, though integration with waveguide inevitably leads to larger device dimension. The wide adsorption bandwidth of graphene-waveguide photodetectors gives them advantageous over traditional photodetectors. Graphene Optical Modulators Optical modulators play a crucial role in optical communications. Graphene-based optical modulators are marked by their strong graphene-light interaction, ultrafast operation speed, large bandwidth, and high compatibility to silicon electronics. Despite that the absorption coefficient of graphene is large (~5 ×10 7 m -1 in visible range), the ultra-thin nature of monolayer graphene has limited its absorption significantly. Hence, it is necessary 28 to enhance graphene-photon interaction, typically by waveguide or by optical cavity, which will be discussed in this section. Liu et al. developed the first graphene based modulator in 2011. 73 In their devices, mono-layer graphene was transferred on top of a silicon waveguide, with a 7-nm-thick Al2O3 between them serving as a spacer. A drive voltage is applied between graphene and the waveguide to tune the Fermi level. When the absolute value of Fermi level is over a transition threshold (EF(VD) = hv0/2), interband transitions will be suppressed due to Pauli state blocking, hence graphene stays transparent. On the other hand, if a low drive voltage is applied to keep the Fermi level of graphene close to the Dirac point, optical adsorption will be enabled. Thus light transmission in graphene can be effectively modulated via tuning driving voltage. Graphene Plasmonics Because of its simultaneously high carrier mobility and high conductivity, graphene has also emerged to be a very promising candidate for terahertz to mid-infrared plasmonic devices applications. As a subfield of nanophotonics, plasmonics studies the excitation, propagation, and utilization of the collective oscillation of carriers. There are several types of plasmon polaritons, and for graphene, we are more interested in the surface plasmon polaritons (SPP), the collective excitations of electrons and light at the interface between a conductor and a dielectric. The field of plasmonics has attracted significant interests due to 29 its ability to confine and manipulate light below the diffraction limit and/or produce high local field intensities. Nowadays, plasmonics has triggered a plethora of applications including optical antenna, near-field optical microscopy, chemical and biological sensing and subwavelength optics, to name a few. Despite the fact that noble metals such as silver and gold are still the predominant materials of choice for plasmonics, devices fabricated from these materials face several constraints. For example, their operating wavelengths are hardly tunable once the geometry of the structure is fixed. Moreover, they suffer from large Ohmic losses due to the limitation of carrier mobilities, surface roughness, grain microstructure and impurities. Compared to conventional plasmonic materials, graphene plasmons (GPs) presents the following unique properties: (i) Tunability. Due to the relativistic nature of carriers in graphene, the plasmon mass increases proportionally with the Fermi-level. Therefore, the optical response of doped graphene strongly depends on the doping level, which can be chemically or electrostatically tuned. (ii) Strong field confinement. GPs propagate at a speed comparable to the Fermi velocity vF, which is much smaller than the light velocity. As a result, GPs have plasmon wavelengths that are typically 1~3 orders of magnitude smaller than the light wavelength. (iii) Low losses and long lifetime. The high conductivity of graphene can be translated to a fairy long optical relaxation times (~10 -13 s), compared to ~10 -14 s in gold, indicating less plasmon dissipation and longer plasmon lifetime. (iv) Crystallinity. The strong carbon chemical bonds make graphene structures defect-free 30 over several plasmon wavelengths. While fabrication imperfections limit the performance of nanometallic plasmonic structures. 1.4.3. Photonics of TMDCs Transition metal dichalcogenides (TMDCs) are materials with the chemical formula MX2, where M stands for a transition metal element like Mo, W, Nb, Re, and X is a chalcogen (S, Se, Te). Typically one layer of TMDCs consists of an X-M-X sandwich structure. The inter- layer interaction of TMDCs is the weak Van der Waals force, while the in-plane bonding is the strong covalent bond. Thus, bulk TMDCs can be exfoliated down to few-layer films similar to graphene, extending the zoo of two-dimensional materials significantly. Some 2D TMDCs, such as molybdenum- and tungsten-based dichalcogenides, have an indirect bandgap in multi-layer forms, while they become direct-bandgap-semiconductors in their monolayer forms. 25 Their sizable and tunable bandgap (1-2 eV) not only generates strong photoluminescence, 74 but also open doors to various optoelectronic applications such as photodetectors, energy harvesting and electroluminescence, with operational spectrum range that is different from graphene based devices. In addition, exotic optical properties such as valley coherence 75 and valley-selective circular dichroism 76 have been demonstrated in some 2D TMDCs, making these materials very promising for the discovery of new physical phenomena. 31 2D TMDCs based photodetectors Compared to graphene-based photodetectors, few-layer TMDCs based photodetectors have higher photoresponsivity, though they work mainly at the visible region. High- performance photodetectors have been made by various 2D TMDCs, such as MoS 2, WS2, and ReSe2. Most of these detectors operate at the visible spectrum, as a result of their bandgaps being around 1.5-2.5 eV . At the visible range, these photodetectors possess much better performance than pristine graphene-based photodetectors. 2D TMDCs based LEDs Light-emitting diodes (LED) is widely used for display, lighting, and sensing. Since monolayer TMDCs like WSe2 are direct-bandgap semiconductors, electrons and holes can easily recombine with each other in radiative processes to generate photons. Electroluminescence localized at the contact region and occurred on heavily p-doped silicon substrates has been obtained in single layer MoS2 field effect transistors. WSe2 monolayer lateral diodes have been demonstrated by applying multiple independent gate voltages. Through tuning electrostatic doping, both p-n and n-p diodes can be defined, leading to effective bright electroluminescence. Recently, 2D twisted bilayers with interlayer lattice mismatch and/or rotational misalignment have emerged as a powerful platform for studying unconventional properties 32 such as the moiré-dependent interlayer exciton (IX), 77-78 where electron and hole located in different monolayers are coupled to form a bound state. The moiré landscapes can be manipulated by varying the twist angle in 2D twist bilayers, opening a door for engineering the IX properties and developing its optoelectronic applications. By tuning the twist angle of the heterobilayer, the moiré period will exceed the Bohr radius of the IX, resulting in a periodic potential distribution across the lateral Moiré superlattice. Therefore, IXs will be spatially concentrated into the periodic potential minima, forming uniform periodic quantum-dot-like emitter array. This Moiré quantum-dot array is predicted to emit polarized light with narrow linewidth, as confirmed by a recent optical measurement. 79 1.4.4. Black Phosphorus for Photonics Application Few-layer black phosphorus (BP) is an emerging 2D material with a puckered orthorhombic lattice. Its anisotropic in-plane lattice structure lowered its spatial symmetry, resulting in highly anisotropic electronic and optoelectronic properties. Bulk BP has a moderate bandgap of 0.3 eV , which increases monotonously with reduced number of layers, eventually reaching 1.5-2.0 eV for monolayer. Hence, for photonic applications, black phosphorus can cover the entire mid- and near-infrared range. The moderate direct bandgap of BP bridges the zero-bandgap graphene and relatively wide bandgap TMDCs, making BP a promising material for future electronics and optoelectronics. 33 Black phosphorus mid-infrared photodetectors with high internal gain, broad working range, and large external responsivity (over 80A/W) has been demonstrated using a back gate FET structure. 80 A vertical electrical field from the gate can dynamically tune the photoresponse range of a BP photodetector, from 3.7 um to over 7 um. 81 The operational speed of such device can exceed 1 GHz, as extracted from the carrier lifetime data. As BP has polarization-dependent optical response, polarization-sensitive broadband photodetectors can be realized, with gate-enhanced efficiency demonstrated. 82 1.4.5. Outlook Atomically thin materials such as graphene, transition metal dichalcogenides and the emerging black phosphorus are being developed as the building blocks for a wide range of optoelectronic devices. These materials offer diverse choices including metals, semimetals, and semiconductors with small or large optical gaps allowing for different and new application space even beyond what conventional bulk materials can possibly offer. To fully exploit their potentials, there is an apparent need to gain more fundamental understandings on their intrinsic or extrinsic optical behaviors e.g. excitonics, optical nonlinearity, mechanisms of photoresponse. Furthermore, issues involving low light absorption and short light-matter interaction length of 2D materials need to be addressed. This could open up the new areas of research into the symbiotic relationship between these materials with 34 conventional photonic elements including cavities, waveguides or plasmonic nanostructures. The potential of mid-infrared and terahertz graphene plasmons is also being realized, and they show very attractive features including extremely high field confinement, tunability and long lifetime, which can serve as a platform for efficient light-matter interaction in the quantum optical regime. Beyond the graphene plasmonics, the extraordinary optical nonlinearity and fast modulation speed of graphene are also favored for optical communication applications. One remaining challenge is to extend the operating window of tunable graphene optical response from the infrared toward other regions of the electromagnetic spectrum where it can find a larger range of applications from optical modulation, spectral light detection to sensing. To this end, the development of controllable and stable chemical doping for graphene and even other 2D materials is highly desirable. In addition to the optical properties of a material itself, the availability of hybrid heterostructures will give rise to intriguing optical properties as well as expanded device functionalities involving efficient solar cells, ultrafast optical modulators or detectors and 2D light emitting devices or lasers in the near future. 35 2. Research Accomplishments in my PhD Study: An Overview During my PhD years, my directions for exploring 2D materials are: i) characterizing emerging 2D materials with unrevealed unique properties; ii) developing new formats of 2D structures with existing 2D materials; iii) building devices with unprecedented performance that take full advantages of the unique properties/structures of 2D materials. In my early stage of research, I characterized multiple emerging 2D materials with novel experimental tools. For example, we were the first group to systemically study monolayer ReSe2, 83 an unusual 2D material that has strong in-plane anisotropy and weak quantum confinement. We utilized ultralow frequency Raman technique to probe the interlayer interaction of ReS2. In addition, we were the first group to use scanning ultrafast electro- microscopy (SUEM) to study the carrier dynamics in asymmetrical 2D materials. 84 I also developed various new formats of 2D structures with existing 2D materials. Comparing to studying new 2D materials, building new formats of 2D structures with well- studied 2D materials is another interesting and challenging direction. The new format of 2D materials can be kirigami/origami of 2D flakes, strained/suspended 2D sheets, or lateral/vertical 2D heterostrucures enabled by stacking or chemical synthesis. We have studied the properties of such 2D structures like MoS2 nanoribbons, suspended graphene kirigami, strained ReS2, twisted bilayer ReSe2, graphene/hBN/MoS2 heterostructure, etc. Most importantly, I developed a technique that can deterministically fold a 2D flake without 36 the help of a supporting layer attached on the sample. I am able to reconfigure a device into different forms with this folding technique. Equipped with this technique, we can build twisted 2DM bilayers 2D that can potentially lead to a number of novel physics and emerging device applications. Most importantly, I have built various electronics devices with unprecedented performance originating from the unique properties/structures of 2D materials. For example, it is extremely challenging to deposit large-scale, leakage-free continuous subnanometer- thick oxide with traditional approaches such as atomic layer deposition (ALD), sputtering, and thermal evaporation. However, we can easily obtain such membrane by oxidizing monolayer or bilayer 2D flakes. Using 2D materials, I was able to fabricate a switchable memory device with ~0.9 nm source-drain distance, which is a world record. 85 This device only consumes ~ 1 fJ to write/erase a data bit, which is, to our best knowledge, a world record of low power non-volatile memory device. The device can also serve as an artificial synapse. 86 In addition, once applying a few-layer WSe2 as a resistance-tunable electrode, the statistics of the device switching can be tuned by a gate. Thus, the device can serve as a hardware accelerator to implement Boltzmann machines for solving combinatorial optimization problems (arXiv:1905.04431). Here I will structure the next few charters in this dissertation as the following: first, I will introduce my efforts in characterizing various low-dimensional materials with reduced symmetry. A number of unique characterization tools such as ultralow frequency Raman and 37 scanning ultrafast electromicroscopy were utilized to uncover the unique properties of low- dimensional materials that cannot be efficiently characterized by regular experiment methods. In the second section, I will discuss my effort in developing a technique that can deterministically fold 2D materials, as well as its applications in exploring twistronics and reconfigurable devices. In the third part, I will introduce an atomically thin memristor built with oxidized bilayer hexagonal boron nitride. This ultrathin memristor can be operated at a record-low power consumption level, which opens a door for sub-femtojoule memory device operation. The last research section will be implementing the 2D memristive device into the Boltzmann machine algorithm as a hardware accelerator, and a machine learning based method to design such a device. I will elaborate the abovementioned work in the next few sections. 38 3. Characterizing the Novel Properties of Emerging Low- dimensional Materials with Reduced Symmetry 3.1 Spatial-temporal Imaging of Anisotropic Photocarrier Dynamics in Black Phosphorus Black phosphorus (BP) is a new layered material “re-discovered” from 2014. 27, 87 It has a direct bandgap of 0.3 eV , which can be tunable by layer number and strain from 0.3 eV-2.0 eV . 88-90 BP has a high mobility, which is above 1500 cm2/V.s at room temperature and can be > 50,000 cm2/Vs in bulk at low temperature. 91 The optical properties is also excellent, as it has large optical conductivity in 1 to 5 µm, 92 which has great potential for infrared optoelectronics. The most unique property of layered BP is its strong in-plane anisotropy, such as polarization-dependent photoresponse 93 and highly anisotropic in-plane charge transport. 94 Despite extensive study of the steady-state charge transport in BP, there has not been direct characterization and visualization of the hot carriers dynamics in BP immediately after photoexcitation, which is crucial to understanding the performance of BP-based optoelectronic devices. Here we use the newly developed scanning ultrafast electron microscopy (SUEM) 95-96 to directly visualize the motion of photoexcited hot carriers on the surface of BP in both space and time. 84 We observe highly anisotropic in-plane diffusion of 39 hot holes with a 15 times higher diffusivity along the armchair (x-) direction than that along the zigzag (y-) direction. Our results provide direct evidence of anisotropic hot carrier transport in BP and demonstrate the capability of SUEM to resolve ultrafast hot carrier dynamics in layered two-dimensional materials. This work a collaboration with late Prof. Zewail at Caltech. R.I.P. Scanning ultrafast electron microscopy (SUEM) 95-96 is a newly developed technique that can directly image the dynamics of photo-excited carriers in both space and time, with sub- picosecond temporal resolution and nanometer spatial resolution. Details of the setup can be found elsewhere 95-99 and are briefly summarized here (also illustrated in Figure 3.1.1). Compared to optical pump-probe spectroscopy, SUEM is a photon-pump-electron-probe technique, with sub-picosecond electron pulses generated by illuminating a photocathode (ZrO-coated tungsten tip) with an ultrafast ultraviolet (UV) laser beam (wavelength 257 nm, pulse duration 300 fs, repetition rate 5 MHz, fluence 300 μJ/cm 2 ). A typical probing electron pulse consists of tens to hundreds of electrons, estimated by measuring the beam current through a Faraday cup. The probing electron pulses arrive at the sample after the optical pump pulses (wavelength 515 nm, fluence 80 μJ/cm 2 ) by a given time controlled by a mechanical delay stage (-700 ps to 3.6 ns, with 1 ps resolution). The probing electron pulses induce the emission of secondary electrons from the sample, which are subsequently collected by an Everhart-Thornley detector. 40 Figure 3.1.1 Schematic of the experimental setup. SE: secondary electron To form an image, the probing electron pulses are scanned across the sample surface and the secondary electrons emitted from each location are counted. Since the yield of secondary electrons depends on the local average electron energy, more/less secondary electrons are emitted from regions of the sample surface where there is a net accumulation of electrons/holes. 97 Typically a reference SEM image is taken long before the pump optical pulse arrives and is then subtracted from images taken at other delay times to remove the background. In the resulting “contrast images”, bright/dark contrasts are observed at places with net accumulation of electrons/holes due to higher/lower yield of secondary electrons. In this fashion, the dynamics of electrons and holes after excitation by the optical pump pulse 41 can be monitored in real space and time. 96 An alternative way of visualizing hot carrier dynamics in space and time was recently demonstrated using time-resolved photoemission electron microscopy (TR-PEEM). 100 Figure 3.1.2 SEM image of a typical BP flake used for the SUEM measurements. The orange and yellow arrows denote the armchair (x-) and zigzag (y-) directions of the BP crystal, respectively, as determined by optical Raman measurement. Scale bar: 100 μm. In this work, we demonstrate the direct imaging of hot-carrier dynamics in BP with SUEM. Due to the presence of a surface potential, we observe the motion of hot holes on the surface of BP. With SUEM, we see striking visualization of anisotropic diffusion of hot holes after photo-excitation, from which quantitative transport parameters can be extracted. Our results indicate a 15-times higher diffusivity of hot-holes moving along the armchair direction than that along the zigzag direction, which is a combined effect of anisotropic effective mass and direction-independent electron-phonon scattering. 101 Figure 3.1.2 displays a static SEM image of a typical BP flake measured in this work. BP flakes of 80 nm thickness were mechanically exfoliated from a bulk crystal, and subsequently 42 transferred to an ITO-coated glass substrate. The sample is exclusively handled in an argon glovebox before being immediately loaded into the SUEM vacuum chamber. The arrows in the figure denote the armchair (x-) and zigzag (y-) directions of the BP crystal, determined optically by Raman spectroscopy. 102 Polarization-resolved Raman spectroscopy was performed after the SUEM measurements using a 532 nm Nd:YAG laser in the LabRAM ARAMIS system. A 100× microscope objective was used and the power incident on the BP sample was kept below 500 µW to avoid sample damage. Polarization resolved Raman spectroscopy was conducted with a 532 nm laser with different sample rotating angles. The dependence of the Raman peaks intensity on the rotation angle of the sample basal plane is shown in Figure 3.1.3. The crystal orientation is determined specifically from the intensity of the A g 1 peak, which reaches the minimal intensity when the laser polarization is along armchair (x-) direction. 102 Figure 3.1.3 Raman characterization of the BP flake. Left: the Raman spectra measured with the incident laser at different polarization angles. x denotes the armchair direction and y denotes the zigzag direction. Right: the intensity of the A g 1 peak with the incident laser at different polarization angles. 43 SUEM contrast images of the BP flake shown in Figure 3.1.2 are presented in Figure 3.1.4. A low-pass Gaussian filter is used to suppress the noise of the images for presentation, while raw images are used for quantitative analysis shown later. Images displayed in the first row were taken when the flake is oriented as shown in Figure 3.1.2, whereas images in the second row were taken when the flake is rotated by 90 degree. Figure 3.1.4 SUEM imaging of hole diffusion on the BP surface. First row: the sample orientation is the same as that shown in Fig. 1(b). Second row: the sample is rotated by 90 degrees. The arrows denote the armchair direction. Scale bar: 60 μm. The orange and yellow arrows shown in the two left images denote the armchair (x-) and zigzag (y-) directions of the BP crystal for the original sample orientation (first row) and after the sample is rotated by 90 degrees (second row), respectively. A low-pass Gaussian filter is used to suppress the noise in the images for presentation. Firstly, only dark contrast is observed in the region of the sample excited by the pump laser. The initial shape of the excited spot is elliptical as expected because the pump laser is 44 incident on the sample at an angle. Since secondary electrons are typically emitted only from the top few nanometers of the sample, the observation of only dark contrast indicates that the electrons and holes are separated vertically after photo-excitation, and the holes are accumulated near the sample surface while the electrons are drawn away from the surface. This separation is most likely due to the existence of a surface potential on the BP sample (we observed the same behavior in heavily doped n-type silicon with SUEM also caused by a surface potential), which arises due to the formation of an atomically thin phosphorus oxide layer 103 on the BP surface when the samples are briefly exposed to air (<30 seconds) during their loading into the vacuum chamber of the SUEM. The vertical transport process associated with the surface potential is also reflected in the observation that the intensity of the dark contrast reaches a maximum around 40 ps after the optical pump pulse arrives. At 40 ps delay time, the profile of the spatial distribution of holes follows approximately the shape of the pump beam. As the time progresses, it is clearly observed that the holes preferentially diffuse along the armchair (x-) direction, denoted by the orange arrow, regardless of the relative orientation of the BP flake and the optical pump beam. In this measurement the polarization of the optical pump beam is not specifically chosen. Although it is known that the absorption of BP is strongly dependent on the light polarization, 82 we verified experimentally that the light polarization does not affect the dynamics of the hot 45 holes after photo-excitation, as shown in Figure 3.1.5Error! Reference source not found. Figure 3.1.5 Polarization dependence of the hot hole dynamics in black phosphorus. This measurement was done on a single BP flake with different polarizations of the input pump laser. Although the absorption of the pump laser is different with different polarizations (shown as different shapes and sizes of the induced hole distribution), the subsequent dynamics, namely the anisotropic diffusion, is the same for different polarization directions. The bright spot seen in the last three rows of images is a defect created due to long-time exposure of the sample to the pump laser. 46 In addition to the direct and intuitive visualization of the highly anisotropic transport of photo-excited hot holes in BP provided by the SUEM contrast image, numerical values of transport parameters can be extracted through quantitative analysis of the contrast images. A convenient parameter to describe the spatial distribution of particles is the variance s , which in this case is angle-dependent, defined as s q,t ( )= r r,t ( ) r × ˆ q ( ) 2 d 2 r ò ò r r,t ( ) ò ò d 2 r - r r,t ( ) r × ˆ q ( ) d 2 r ò ò r r,t ( ) ò ò d 2 r æ è ç ç ö ø ÷ ÷ 2 , (1) where r r,t ( ) is the local carrier concentration, and ˆ q is a unit vector pointing to a certain angle q . Here we approximate r r,t ( ) with the measured local intensity I r,t ( ) of the SUEM contrast images, assuming a linear relation between them. This assumption should hold here since the optical excitation is weak and the measurement works in the linear response regime. Figure 3.1.6 shows the calculated s q,t ( ) from the images at different delay times in the first row of Figure 3.1.4, normalized by s q,t ( ) at 40 ps. It is clear that the variance of the spatial distribution increases significantly along the armchair direction, while its change along the zigzag direction is hardly discernible. 47 Figure 3.1.6 The variance of hole-distribution along different directions normalized by that of the initial distribution. In the case when the diffusivity is a constant, the variance of the spatial distribution should be a linear function of time. In the current experiment, however, the diffusivity changes with time due to a decreasing temperature of the hot carriers. As a first-order approximation, we assume the temperature of the hot carriers decays exponentially T t ( )=T 0 exp -t t T ( ) , with a time constant t T controlled mainly by inelastic electron- phonon scatterings. 104 We further apply the Einstein relation D= k B Tm ( ) q , where D is the diffusivity and m is the mobility, and argue that D t ( )= D 0 exp -t /t T ( ) , where D 0 is the diffusivity right after photo-excitation, because immediately after photo-excitation, the lattice is still cold so that the mobility limited by electron-phonon interaction is not largely affected. In this case the time dependence of the variance is: s q,t ( )= 2D 0 q ( )t T 1- exp - t t T æ è ç ö ø ÷ é ë ê ù û ú +s 0 q ( ). (2) 48 Fits of Eq. (2) to experimentally measured variances along the armchair and zigzag directions are plotted in Figure 3.1.7 (Left). From the fittings, the parameters can be extracted as t T » 150 ps , D 0,armchair »1.3´10 4 cm 2 s , D 0,zigzag » 870 cm 2 s , s 0,armchair » 216.7 mm 2 and s 0,zigzag » 405.8 mm 2 . The ratio between the diffusivities along the two directions is approximately 15. This ratio is much higher than that measured by steady-state transport experiments 105 and calculated by first-principles simulations assuming near-equilibrium transport, 101 but close to the value inferred from an optical pump-probe measurement. 22 This observation demonstrates the significant difference between hot-carrier dynamics and near- equilibrium dynamics, and the fact that the measured hot-carrier diffusivity ratio is on the same order of the effective mass ratio 106 indicates that the transport of photo-excited hot carriers is likely more affected by the effective mass of the carriers than their scattering properties. Furthermore, the timescale of carrier recombination can be inferred from the time- dependence of the average intensity of the dark contrast, as shown in Figure 3.1.7 (right). Data collected from three different BP samples are compiled here, and the exponential fit gives a recombination lifetime t R ~550 ps. Within this recombination time, the average diffusion length of holes can be estimated, using Eq. (2), to be 9.7 μm along the armchair direction and 0.6 μm along the zigzag direction. 49 Figure 3.1.7 Left: the variation of hole distribution along the armchair and zigzag directions versus time delay. Dashed lines represent fit with an exponentially decaying diffusivity due to the cooling process of the holes. Right: the average intensity of the hole-distribution versus time delay, indicating the time scale of the carrier recombination process. Dashed line is an exponential fit with a recombination time of 550 ps. To further examine the validity of the extracted model parameters, here we simulate the SUEM contrast images by numerically solving the two-dimensional diffusion equation with time-dependent anisotropic diffusivities and a recombination term: ¶r r,t ( ) ¶t = D x t ( ) ¶ 2 r r,t ( ) ¶x 2 +D y t ( ) ¶ 2 r r,t ( ) ¶y 2 - r r,t ( ) t R , (3) where x and y directions are the armchair and zigzag directions, respectively, and D x and D y are time-dependent diffusivities along the two directions, with values as discussed in the previous sections. The simulated images are shown in Figure 3.1.8, in good agreement with the experimental images shown in Figure 3.1.4, justifying the transport parameters extracted from our analysis of the experimental SUEM images. 50 Figure 3.1.8 A simulation of Black Phosphorus carrier dynamics In summary, we use SUEM to directly visualize the dynamics of photo-excited hot holes on the surface of black phosphorus. The highly anisotropic in-plane charge transport of black phosphorus is confirmed in our experiment, and we further find that the ratio between the diffusivities of hot holes along the armchair direction and the zigzag direction is much larger than that measured at near-equilibrium conditions, illustrating the drastic difference between hot carrier dynamics and near-equilibrium carrier dynamics. This study 51 demonstrates the capability of SUEM in deepening our understanding of hot carrier dynamics in low-symmetry layered materials. This work is the first study of 2D materials using SUEM technique. 3.2 Interlayer Interactions in Anisotropic Thin Rhenium Diselenide ReSe2 was an emerging 2D material at the time we studied it. Our group were the first group to report the properties of monolayer ReSe2. One unique property of layered ReSe2 is that it is anisotropic in the plane, due to its reduced lattice symmetry. In this work, 83 we study the interlayer phonon vibration modes, the layer-number-dependent optical bandgap, and the anisotropic photoluminescence (PL) spectra of atomically thin rhenium diselenide (ReSe2) for the first time. The ultra low frequency interlayer Raman spectra and the polarization- resolved high-frequency Raman spectra in ReSe2 allow the identification of its layer number and crystal orientation. Furthermore, PL measurements show the anisotropic optical emission intensity of the material with its bandgap increasing from 1.26 eV in the bulk to 1.32 eV in the monolayer. The study of the layer-number dependence of the Raman modes and the PL spectra reveals relatively weak van der Waal’s interaction and two-dimensional (2D) quantum confinement in the atomically thin ReSe2. The experimental observation of the intriguing anisotropic interlayer interaction and tunable optical transition in monolayer and 52 multilayer ReSe2 establishes the foundation for further exploration of this material in the development of anisotropic optoelectronic devices functioning in the near-infrared spectrum, which is important for many applications in optical communication and infrared sensing. In the past few years, the transition metal dichalcogenides (TMDC) family 107-112 of two- dimensional (2D) materials have attracted great interest among the physicists, chemists, engineers and material scientists due to their unique physical and chemical properties resulting from 2D quantum confinements, unique lattice structures and interlayer coupling (or the absence of it in their monolayer form). From 2014, 2D materials with strong in-plane anisotropic properties such as black phosphorus 27, 105, 113-115 ave been proposed for developing new devices with promising applications in electronics, 116-117 optoelectronics 92, 118-121 and thermoelectrics. 122 However, the selection of 2D materials with strong in-plane anisotropy has so far been very limited and only sporadic studies have been devoted to transition metal dichalcogenides materials with strong in-plane anisotropy, which is yet to convey the full picture of their anisotropic optical and phonon properties, and the anisotropy in their interlayer interactions. In this work, we study the anisotropic interlayer interactions in atomically thin rhenium diselenide (ReSe2) – by investigating its ultralow frequency interlayer phonon vibration modes, the layer-dependent optical bandgap, and the anisotropic photoluminescence (PL) spectra for the first time. The ultra-low-frequency interlayer Raman spectra combined with 53 the high-frequency Raman measurements allow deterministic identification of the ReSe2 layer number and crystal orientation. The PL measurements show anisotropic optical emission intensity, which depends on the polarization of the incoming light with bandgap increasing from 1.26 eV in bulk to 1.32 eV in monolayer, consistent with theoretical results based on first-principle calculations using density functional theory (DFT). A systematic study of the polarization-resolved high-frequency Raman spectra in mono- and bi-layer ReSe2 is also carried out for the first time. Study of the layer dependence in the high- frequency Raman modes and PL indicates relatively weak van der Waal’s (vdW) interaction and 2D quantum confinement in atomically-thin ReSe2. The results reveal the intriguing interlayer interaction and anisotropic optical transition in single- and multi-layer ReSe2, which offers the potential for developing anisotropic optoelectronic devices in the near infrared spectrum range. ReSe2 is one of the layered transition metal dichalcogenides (TMDCs) with van der Waals interaction between layers. As shown in Figure 3.2.1a, every unit cell of monolayer ReSe2 contains four formula units, which includes two categories of rhenium (Re) atoms together with four categories of selenium (Se) atoms. The Se atoms on top and bottom sandwich the Re atoms in the middle to form a monolayer lattice of ReSe2. Unlike common TMDCs such as MoS2 and WSe2, which crystallize in the hexagonal (H) phases, ReSe2 crystal displays a distorted CdCl2-type lattice structure. 123 Due to Peierls distortion, 124 54 adjacent Re atoms are bonded in the form of zigzag four-atom clusters, 125 which align along the direction of the lattice vector a to form Re chains (see Figure 3.2.1b). Calculations have revealed that such a distorted octahedral (1T) crystal structure has lower energy than its hexagonal counterpart, thus being more stable. 126 This clustering of Re atoms has also been discovered in ReS2 crystals, 123, 127 contributing to distort the lattice geometry and stabilize the crystals. The distorted 1T nature of ReSe2 has conferred this materials strong in-plane anisotropy in their optical 128-130 and electronic 131 properties. Figure 3.2.1c shows the Brillouin zone of the monolayer ReSe2, which is a hexagon with unequal side length. The bandstructure of monolayer ReSe2 predicted by first-principles calculations is also demonstrated in Figure 3.2.1d. Perdew-Burke-Ernzerhof (PBE) exchange-correlation function under general gradient approximations (GGA) was applied in the calculations. Spin- orbit coupling (SOC) was taken into account and ultrasoft pseudopotential was applied. The calculated bandgap is 1.15 eV . It is well known that GGA tends to underestimate the bandgap of 2D materials, 132 so the real intrinsic bandgap is likely to be larger than 1.15 eV as confirmed by our experimental results to be discussed later. From the energy band diagram, the bottom of the conduction band is located at the Γ point, while the top of the valence band is located near the Γ point, making monolayer ReSe2 an indirect bandgap semiconductor. 55 Figure 3.2.1 (a) The unit cell of ReSe2 crystal. a, b, and c are the three lattice vectors. Re atoms and Se atoms are colored with blue and yellow, respectively. (b) The top view of ReSe2 crystal. The clustering of Re atoms forms the Re chains along lattice vector a direction, as shown in the red dotted line box. (c) The Brillouin zone of ReSe2. (d) The calculated bandstructure of ReSe2 monolayer. K path is shown in the Brillouin zone. The arrow indicates the transition from the top of the valence band to the bottom of the conduction band. Fermi level has been set to zero. Experiments and results: To investigate the interlayer interactions in this 2D material with reduced symmetry, ReSe2 flakes were prepared on Si/SiO2 substrates by the standard micromechanical exfoliation method. 133 Mono- to few-layer samples were first located by optical contrast using an optical microscope and then the layer numbers were verified based on the height information measured by Atomic Force Microscopy (AFM). Figure 3.2.2 shows the optical micrograph and the AFM data for mono- and few-layer ReSe2 flakes. According to the AFM morphology, the thickness of mono-layer ReSe2 is about 0.7 nm, which is in agreement with 56 the interlayer distance obtained by powder diffraction. 134 ReSe2 samples in their mono- to few-layer forms are robust in air and show no clear signs of degradation after at least several months in ambient environment. Figure 3.2.2 : (a) The optical and AFM images of monolayer and few-layer ReSe2. (b) The AFM height data measured along the pink and blue dotted lines shown on the left. The interlayer shear (C) and layer-breathing (LB) Raman modes of a layered material directly reflect its interlayer van der Waals (vdW) coupling. 135-141 These modes only occur in multi-layers of ReSe2, but not in the monolayer samples. As shown in Figure 3.2.3a, the C and LB modes often occur at the ultralow frequency region (<50 cm -1 ) of Raman spectra in TDMCs because the vdW coupling is a much weaker interaction compared to the intra-layer modes where the lattice atoms interact through the much stronger atomic bonding. In general, there are N-1 pairs of C modes and N-1 LB modes in an N layer 2D layered material. For in- plane isotropic materials, like graphene 135 and MoS2 136 , each pair of C modes is doubly degenerate and has the same frequency. For an in-plane anisotropic 2D material of ReSe2, each pair of C modes is not degenerate in principle, which means that there are 2(N-1) C modes with different frequencies in an N layer sample and these 2(N-1) C modes can be 57 divided into two categories based on the vibration directions. Although ReSe2 is an anisotropic material, the lattice constants of directions a (6.7 Å) and b (6.6 Å) are almost equal, which suggests that each pair of C modes of the material tend to overlap together because of their small frequency separation. Indeed, first principle calculations using DFT (Figure 3.2.3b) predict two C modes at 12.1 cm -1 and 13.2 cm -1 , respectively, and an LB mode at 24.8 cm -1 . Figure 3.2.3a exhibits the ultralow frequency modes in 1L, 2L, 3L, 6L and 10L ReSe2. The spectrum for bilayer ReSe2 has the C mode at 13.5 cm -1 and the breathing mode at 25.0 cm -1 . Since the theoretical difference between the two C modes in frequency is as small as 1 cm -1 , the peak measured at 13.5 cm -1 for bilayer ReSe2 should correspond to the degeneracy of the two calculated C modes at 12.1 cm -1 and 13.2 cm -1 . Figure 3.2.3b shows the lattice vibration displacement directions for the three modes. Figure 3.2.3 (a) Interlayer Raman modes in monolayer and few-layer ReSe2. C and LB denote shear and breathing modes. Note that the two peaks around 5 cm-1 marked by stars are not Raman signals. They are due to Brillouin scatterings of silicon. (b) Schematic of the three low-frequency phonon vibration modes of bilayer ReSe2 obtained from first- 58 principles calculations. From left to right, they correspond to the two shear modes located at 12.1 cm -1 , 13.2 cm -1 and one breathing mode located at 24.8 cm 1 . Given an N layer ReSe2, we use CNN-i and LBNN-i (i=1, 2…, N-1) to denote the N-1 C modes and N-1 LB modes. Here, CN1 and LBN1 (i.e., i=N-1) are the highest frequency C and LB modes, respectively. As shown in Figure 3.2.3a, no peaks corresponding to interlayer Raman modes were detected in the monolayer sample. The C21 and LB21 are observed at 13.5 cm -1 and 25.0 cm -1 in the bilayer flake, respectively. However, only C32 (9.5 cm -1 ) and LB32 (17.7 cm -1 ) are detected in trilayer ReSe2. The C31 and LB31 modes are silent. Moreover, only the CNN-1 and LBNN-1 are observed in the 6-layer and 10-layer samples. The likely reason for the absence of other C and LB modes is their Raman-inactive nature or their much weaker electron-phonon coupling compared to the lowest frequency modes, which is similar to the case of the highest frequency C modes in multi-layer graphene. 135 Figure 3.2.4 Polarization-resolved Raman peak intensity of bilayer (a) and trilayer (b) ReSe2. The intensity of each peak has been normalized with respect to the intensity of the Si peak. The dots in both figures are from experiment, while the lines in both figures are theoretical fits from the Raman tensor analysis. Figure 3.2.4 shows the polarization dependence of the C and LB modes measured in bilayer and tri-layer ReSe2. Due to the reduced in-plane symmetry in ReSe2 lattice, the 59 intensity of the C and LB modes show a strong dependence on the polarization angle of the incident laser beam. This clearly reveals the interlayer coupling characteristics and the anisotropic interlayer vibration modes in ReSe2, which suggests that the ultralow frequency interlayer Raman measurements can serve as an unequivocal way to determine the layer number in ReSe2 samples and their crystal orientation. The intra-layer Raman modes of layered materials correspond to the Raman active intra- layer phonon vibration. The layer-number dependence of these high-frequency Raman modes (>50 cm -1 ) can also provide insight into the interlayer interaction in 2D materials. At the high-frequency region of the monolayer ReSe2 Raman spectra, in principle, there should be 36 normal vibration modes including 18 potential Raman modes due to the presence of 12 atoms in each unit cell of the ReSe2 crystal lattice. We detected 16 distinctive Raman peaks in the spectral range between 100 cm -1 and 320 cm -1 in the Raman spectrum of monolayer ReSe2, as depicted in Figure 3.2.5a. Figure 3.2.6 shows the layer number dependence of the ReSe2 Raman spectra for monolayer, bilayer and four-layer samples. Bulk ReSe2 displayed very weak Raman intensity, compared to its few-layer counterparts. For all of the peaks, except the one near 176 cm -1 , Raman intensities of monolayer samples are slightly weaker than those in the 3-4 layer samples. This is attributed to its small volume in the unit cell and the multiple reflection interference in the multilayer structures contained ReSe2 flake, SiO2 and Si substrate. 142 For most of the Raman modes, thick samples have red- shifted peak positions compared to thinner samples. A detailed discussion of layer-number dependence of high-frequency Raman modes is included in the discussions section. 60 Figure 3.2.5 (a) Raman spectra of monolayer ReSe2 in the 100 cm -1 to 300 cm -1 spectral range under the excitation of 532 nm green laser beam at different polarization direction incident normal to the sample. (b) The dependence of Raman intensity on the polarization of the incident laser beam for three typical peaks located at 125 cm -1 (red dots), 160 cm -1 (blue triangles) and 176 cm -1 (green diamonds). The symbols are experimental data while the three curves in corresponding colors are fits from the Raman tensor analysis. (c) The lattice vibration modes of the three peaks shown in (b) obtained from first-principles calculations. Due to the reduced in-plane symmetry, the intensity of the intra-layer Raman modes in ReSe2 also exhibits strong polarization dependence. By varying the polarization direction of the incident laser beam, we investigated the polarization dependence of various Raman modes of monolayer ReSe2. Measurements were carried out from 0 degrees to 360 degrees 61 with twenty-degree steps. Figure 3.2.5a is the plot of Raman spectra under different polarization directions. There are no obvious shifts of peak positions when tuning the polarization direction of the incident laser beam. However, the peak intensity of all the Raman modes varies significantly, with a period of 180 degrees. This dependence can be clearly observed in the polar plots of the peak intensity as a function of the polarization angle. Figure 3.2.5b shows the plots for the peaks at 125 cm -1 , 160 cm -1 , and 176 cm -1 . Since modifying the relative angle between laser polarization direction and crystal orientation leads to a variation of Raman intensities, we can utilize polarization-resolved Raman measurement as a non-destructive tool to identify the crystal orientation of ReSe2. This is the first systematic study of high-frequency Raman spectra in mono- and bi-layer ReSe2. Our results are also consistent with a previous study 143 that showed Raman measurement data for 5 layer and thicker ReSe2 samples. 62 Figure 3.2.6 Layer-dependent Raman spectra of ReSe2 in the 100 cm -1 to 300 cm -1 range. The monolayer, bi-layer and 4-layer flakes with the same crystal orientation were measured with the same polarization of the incident laser beam. To understand the corresponding lattice vibrations of each Raman mode, we calculated the phonon modes of monolayer ReSe2. Among 36 normal modes of phonon vibrations, there are 18 Raman modes, 15 infrared modes, and three acoustic modes. Hence, the lattice vibration in each Raman mode can be rather complex. Density functional theories were applied to identify the vibrations of each Raman mode. The calculated modes match well with the measured peaks. We found that the vibration in each mode contains multiple components along with different lattice directions. In addition, since there are four Se basis atoms and two Re basis atoms in each unit cell, the intensity of vibration could vary significantly in atoms with different positions. We selected the 125 cm -1 , 160 cm -1 , and 176 cm -1 peaks and showed the lattice vibration and atom displacement directions for their corresponding phonon modes in Figure 3.2.5c. Due to the complexity of lattice vibrations in 63 monolayer ReSe2, it is hard to find a pure Eg or Ag mode in each Raman response as the case in MoS2, thus we identify these modes as Eg-like or Ag-like modes based on their more dominant vibration directions. The 125 cm -1 mode is an Eg-like mode, as the vibration is mostly in-plane and symmetric. The 160 cm -1 and 176 cm -1 peaks are Ag-like modes since the main vibrations are in the one-dimensional vertical direction. The interlayer coupling and 2D quantum confinement in atomically thin ReSe2 samples also result in the dependence of their bandgap on layer number, which can be revealed from photoluminescence (PL) measurements. We carried out PL measurements on monolayer, few-layer, and bulk ReSe2 samples (Figure 3.2.7a). For each sample, only one main PL peak was found. However, the PL spectrum of bulk ReSe2 has a relatively broader peak, which is likely the combination of two split peaks. A detailed discussion of the PL split at low temperature can be found in the discussion section. Due to the indirect bandgap nature, the peak intensity is relatively weak for monolayer ReSe2, and increases monotonically when adding layer numbers (Figure 3.2.7b). Thus, monolayer samples are relatively noisy, but better signal-to-noise was obtained in few-layer samples. The measured bandgap enlarges with decreasing layer numbers, ranging from 1.26 eV of bulk to 1.32 eV of monolayer crystals (Figure 3.2.7ab), demonstrating the same trend in the layer-number dependence of the bandgap as predicted by previous first-principle calculations of ReSe2 bandgap at different thicknesses. 126 64 Figure 3.2.7 (a) PL spectrum of ReSe2 in different layers; (b) the layer-dependent PL intensity and bandgap of few-layer ReSe2. (c) Polarization-dependent PL intensity of six- layer and ten-layer ReSe2. To further study the anisotropic optical absorption, we conducted the polarization- dependent PL measurements on few-layer ReSe2 flakes by rotating the polarization of the incident laser beam. Since the PL signal of very thin ReSe2 is relatively weak due to its indirect bandgap, we chose multi-layer samples to obtain a higher signal-to-noise ratio. Multi-layer ReSe2 regions of different thickness (6-layer and 10-layer) were selected from a single continuous flake sample, and thus should have the same crystal orientations, which is also confirmed by Raman measurements. By varying the polarization direction of the excitation laser beam, we were able to obtain the polarization dependent PL peak intensities. 65 As shown in Figure 3.2.7c, the peak intensity of two flake regions with 6-layer and 10-layer ReSe2 vary with polarization angles at a period of 180°, revealing their anisotropic energy- band information. PL measurement of 3L-, 6L- and bulk ReSe2 were also carried out at 80 K (Figure 3.2.8a) We found that all the peak positions blue-shifted compared to the ones at room temperature for each same sample. We found that the PL peak of all three samples splits into two adjacent peaks with an energy difference around 0.02 eV . Similar to the case at room temperature, all the two peaks redshift slightly as the layer number increases. To reveal the PL peak split of ReSe2, we calculated the energy band structure of bulk ReSe2 using DFT with spin-orbit effect considered (Figure 3.2.8b). Since we use a GGA method, the calculated bandgap tends to be slightly underestimated compared to the measured values. Figure 3.2.8 (a) PL spectrum of ReSe2 samples at the temperature of 80K. The intensities of each peak are rescaled to fit the figure. (b) The calculated bandstructure of bulk ReSe2. The bottom of the conduction band is at Γ point, whereas the top of the valence band is near the Γ point. Those local maxima away from the Γ point can contribute to van Hove Singularities. The energy of the transition B is about 20 meV higher than that of the transition A at the Γ point. 66 At low temperature, the PL intensity is weakr than that at room temperature for multi- layer samples, which is also found in some other indirect bandgap TMDCs, such as few-layer MoSe2. In addition, like other TMDCs, 144-145 the bandgap of all samples increases at a lower temperature. This bandgap decreasing at high temperature is universal in semiconductors, 146 due to the increased electron-photon interaction as well as the temperature-dependent lattice length. Taking the bandgap of bulk ReSe2 as an example, the bandgap increased by around 0.1 eV when temperature decreased from 300 K to 80 K. Hence, it would be possible to tune the optical properties of ReSe2 through thermal engineering. At low temperature, the PL peaks of ReSe2 flakes split into two adjacent peaks with an energy difference of 0.02 eV . The low-energy peak located at around 1.37 eV always has higher intensity. For example, in the 6L ReSe2 flake, the peak at 1.37 eV has a full width at half maximum (FWHM) of around 0.03 eV , and the peak at 1.39 eV has an FWHM around 0.02 eV . At room temperature, however, the 6L ReSe2 flake sample has an FWHM of 0.11 eV , which is much larger than that in the two separate peaks at low temperature. The PL peaks of all the other samples also exhibit a significantly broadened FWHM at a higher temperature. The abovementioned PL peak splitting is discussed in the next section. Discussions Ultralow-frequency Raman modes. Our ultralow frequency Raman measurement is the first experimental study of interlayer vibrations of few-layer ReSe2. These interlayer Raman modes are important since they offer information about interlayer charge exchanges, screenings, and scatterings. The frequency of the observable C and LB modes of multi-layer layered materials can be calculated by this equation, 136 67 respectively, where N is the layer number, . Using this formula, the layer number can be determined by the peak positions of the C and LB modes. Compared to AFM data, measurements of ultralow frequency Raman modes provide a more accurate method for identifying ReSe2 layer numbers. Our first-principle calculations were able to accurately predict the C and LB Raman modes of bi-layer and tri-layer ReSe2. High-frequency Raman modes. The high-frequency Raman spectra of ReSe2 corresponding to the intra-layer modes are distinctively different from that in other typical TMDCs such as MoS2 and WSe2. Here, we would like to compare the Raman spectra of few-layer ReSe2 with those of few-layer MoS2. First, atomically thin ReSe2 layers have more than ten measured Raman peaks while MoS2 flakes only have two high-frequency Raman active peaks, 147 which are the E2g 1 mode and A1g mode. In addition, the lattice vibrations in each ReSe2 Raman mode are much more complex than those in MoS2 layers. It can be easily identified that the E2g 1 mode of MoS2 is the in-plane opposite vibrations of two S atoms and one Mo atom, while the A1g mode is the opposite vibration of two S atoms in the vertical direction. For ReSe2, however, it is hard to identify such a pure vibration mode due to the rather complicated crystal lattice. ReSe2 from monolayer to bulk has a Ci symmetry, and the corresponding irreducible representation is Γ=A′+A″, in which A′ is Raman active. Therefore, all the Raman modes in ReSe2 are A′ mode with the same format of Raman tensor: 68 In addition, it is also observed that most of the peak positions for monolayer and few- layer ReSe2 samples red-shift with increasing layer numbers (Figure 3.2.6). Considering van der Waals force only, when the layer number increases, the vdW interaction between layers tends to suppress lattice vibrations, making the lattice more “stiff”. Thus, the vibration energy of each vibration mode could become higher with increasing the layer number, resulting in the blue-shifts of the corresponding Raman peaks. 141 On the other hand, if we consider long- range Coulomb interactions, the increased dielectric tensors with the layer numbers can lead to an increase in Coulomb screenings. This results in a softer Coulomb interaction between atoms, and thus the Raman peak tends to redshift. 148 Here, we would like to compare ReSe2 with WeSe2, whose atomic mass is almost equal to ReSe2. The layer-number dependent behavior of high-frequency modes in WSe2 is similar to those in MoS2, A1g and E2g modes are blue-shift and red-shift from monolayer to bulk, respectively. 149 The frequencies of C and LB modes in bilayer WSe2 are 16.5 cm -1 and 28.2 cm -1 respectively, 137 which are higher than those in bilayer ReSe2. The vdW interaction can be measured by the interlayer force constant ~ m 2 , 135 where m is atomic mass of monolayer TMDCs, ω is the Raman frequency of interlayer vibration modes. Since the m is almost the same for each other, the interlayer C and LB coupling of WSe2 is about 27% and 49% stronger than that of ReSe2, respectively. This indicates that the interlayer vdW interaction of ReSe2 is much weaker than that of WSe2. Moreover, the long rang Coulomb interaction is estimated by calculating the dielectric tensors and Born effective charges with DFT. The long rang Coulomb interaction in ReSe2 is close to that of WSe2. Based on the above discussions, the observed red-shifts of Raman peaks with increased ReSe2 layer numbers indicate that interlayer van der Waals interaction is not strong enough to dominate the layer dependence of phonon behavior. The relative weak interlayer coupling of few-layer ReSe2 has also been evidenced by its layer-number dependent PL emission, which will be discussed later. 69 For both ultralow-frequency and high-frequency in-plane Raman modes, the peak intensities vary periodically with the polarization directions of the incident laser beam, which is direct evidence of the anisotropy crystal. Once combining high-frequency and low- frequency Raman measurements, both crystal orientation and layer numbers of ReSe2 flakes can be clearly identified. Photoluminescence. For layered materials, the quantum confinement in the vertical direction can be enhanced once the layer number reduces and the interlayer interaction disappears in monolayer samples. Hence, many TMDC crystals have indirect energy bandgap in their bulk and multi-layer forms, but possess direct bandgap in their monolayer form. 147, 150-151 The photoluminescence measurements of mono- and few-layer ReSe2 samples revealed that the optical bandgap decreases with increasing layer numbers (Figure 3.2.7b), which is similar to other 2D semiconductors, such as MoS2, 74 black phosphorus, 152 and ReS2. 127 Similar to ReS2, the layer-number dependence of the bandgap of few-layer ReSe2 is much weaker than that in other 2D semiconductors. Many TMDCs such as MoS2 and WSe2 have strong PL emission in monolayer flakes with direct bandgap, however, the PL peak intensity of few-layer ReSe2 increases monotonically when increasing the layer number (Figure 3.2.7b). The layer- number dependence of the PL peak intensity is much weaker compared to other TMDCs such as MoS2 and WSe2, indicating a relatively weak layer-number dependence of quantum confinement and interlayer interactions. In this case, when adding layers, PL intensity increases due to the increased quantity of materials. The PL peak at room temperature is most likely the combination of multiple peaks. From Figure 3.2.8b, the valence band of bulk ReSe2 near Γ point is relatively flat. The indirect inter-band transitions start from the top of valence band, which is close to Γ point and is 0.01- 0.03 eV higher in energy than the highest valence band energy at Γ point. At room 70 temperature, thermal fluctuation energy is in the scale of kT, where k is Boltzmann constant and T is room temperature (~300 K). The estimated thermal fluctuation energy is 0.03 eV . This energy is large enough to modify the energy of some of the electrons at Γ point to the extent of 0.01-0.03 eV , and thus may trigger the direct inter-band transitions. Hence, the transitions excited by the laser excitation may happen in multiple positions of the valence band near Γ point, resulting in a broadened PL spectrum. The energy difference between the two split PL peaks at 80 K is 0.02 eV . Since the thermal fluctuation energy at room temperature is higher than 0.02 eV , it is understandable that these two peaks cannot be distinguished at room temperature. It is well-known that MoS2 PL has two peaks with energy difference of 0.15 eV due to spin orbit coupling (SOC) induced split of valence band. From our calculation, the SOC induced band splitting does not occur at the transition position, so the split of PL peak cannot be attributed to SOC effect. In addition, the SOC induced energy split is over 0.1 eV according to the calculation, which is much larger than the split energy we observed. Impurities and defects can also lead to PL peak split, but they are not likely to contribute to the split we observed since we consistently observe two peaks with stable peak positions in different samples with different layer number. Furthermore, as we can observe similar peak split in the bulk sample compared to in trilayer sample, it is unlikely that the split is due to trion or exciton PL peaks in ReSe2 samples. From the band structure, bulk ReSe2 is an indirect bandgap semiconductor. The bottom of the conduction band is at Γ point, whereas the top of the valence band is near the Γ point. It is the most likely that those local maxima away from the Γ point contribute to van Hove Singularities, giving rise to the side peak and corresponding splitting. As marked in Figure 3.2.8b, the energy of the transition B is about 20 meV higher than that of the transition A at the Γ point. This is consistent with experimental observation in Figure 3.2.8a. Meanwhile, consider the small energy difference (around 20 meV), phonons may play an important role for the observed peak splitting. 71 In summary, we report the first experimental observation of the anisotropic interlayer C and LB vibration modes and the anisotropic layer-number dependent photoluminescence in mono- and few-layer ReSe2. A systematic study of the angle-resolved polarization Raman measurements on intra-layer Raman modes of mono- and bilayer ReSe2, as well as their layer-number dependence, is also carried out for the first time. The ultralow frequency Raman modes can be used for the identification of layer number and crystal orientation in ReSe2. The optical bandgaps of ReSe2 are revealed to vary from 1.32 eV in the monolayer to 1.26 eV in the bulk, which agree well with the first-principle calculations. Unveiling the interlayer Raman modes and the layer-number dependent optical bandgap in ReSe2 advances the understanding of this 2D TMDC material with unusually complex lattice structure while opening the door to potential applications in near-infrared polarized optoelectronics devices. Finally, the experimental demonstration of anisotropic phonon and optical properties also provides direct experimental evidence of the highly anisotropic nature of mono- and few- layer ReSe2, which may be utilized to construct advanced semiconductor devices. Furthermore, besides tuning ReSe2 bandgap via modifying layer numbers, strain engineering 151 and electrostatic gating 27 might also be utilized to control the energy bandgap. Since the indirect bandgap of ReSe2 is just slightly smaller than the direct inter-band transition energy as shown in the energy band structure, it might be possible to tune ReSe2 into a direct bandgap material with bandgap engineering, which is desirable for various applications like light emission. The tunable bandgap in the near-infrared (NIR) spectrum range can make ReSe2 an interesting material for exploring novel device applications in NIR optoelectronics. 72 4. 2D Material Kirigami and Origami Kirigami and Origami are paper cutting and folding art, respectively. Since 2DMs are atomically thin and ultra-flexible, it can also be cut or folded, just like a piece of paper. Cutting and folding of 2DMs can give rise to various novel features that cannot be found in normal 2DMs. Kirigami and Origami can engineer the geometric dimensionality. For example, in the next section, I will demonstrate how 2D flakes can be cut into mathematically 1.x-dimension fractals, as defined by Hausdorff dimension theory. Another example is that complicated 3D structures can be made out of 2DM folding, such as the paper airplane toys. In addition, kirigami and origami can engineer the energy band-structure of 2DMs. Graphene nanoribbon is one of the most studied graphene kirigami system, which has drawn tremendous attention of the device engineers owing to its bandgap opening. 153-154 Twisted bilayer graphene, 155 a novel system prepared by graphene stacking or folding, recently has initiated rich new physics such as superconductivity, van Hove singularity, etc. In a word, 2DM kirigami and origami techniques are powerful tools to engineer the essential properties of such materials, giving rise to numerous new applications. 73 4.1 2D Material Kirigami In this section, I will introduce how we cut 2D materials and how we explore novel properties of such kirigami systems. In the first part of this section, I will demonstrate how we engineer the optical properties of monolayer MoS2 by cutting it into 5 nm scale nanoribbons. In the second part, I will discuss how I proposed to generate 1.x fractal dimensionality on graphene, and its application as a high-performance antenna. 4.1.1. Engineering the Optical Response of Monolayer Molybdenum Disulfide Nanoribbons with Kirigami Molybdenum Disulfide (MoS2) is a promising material for the next generation electronics and optoelectronics devices. The properties of MoS2 can be tuned by external perturbations. Cutting the monolayer MoS2 into quasi-one-dimensional MoS2 nanoribbons (MNRs) is an effective approach to engineer the properties MoS2. Here, we study the optical response of MNRs systematically. MNRs with different widths are prepared by direct Helium ion beam milling. The special polarization behavior of Raman modes can be explained by the anisotropy of light absorption in MNRs, which is proved by the polarized optical contrast. This work is a collaboration with Prof. P-H Tan’s group and Prof. Wei Wu’s group. MoS2 is an indirect bandgap semiconductor in bulk, transforming to direct bandgap semiconductor when reduce to monolayer. Monolayer MoS2 has valley-selected and tight 74 binding exciton ( ∼1.1 eV) and trion ( ∼40 meV). MoS2 field-effect transistor (FET) has high on/off ratio (10 8 ) and mobility (200 cm 2 V − 1 s − 1 ), and shows a metal-insulator transistor (MIT) behavior under high level doping. Geometry of 2D materials plays a critical role in further tuning their properties. By patterning 2D materials into narrow (sub-20 nm) ribbons, interesting phenomenon and novel properties can arise. A variety of properties of MoS2 nanoribbons (MNRs) have been calculated by theory. Monolayer (1L) zigzag MoS2 nanoribbons are predicted with the ferromagnetic and metallic behavior, irrespective of the ribbon width and thickness, and 1L armchair MoS2 nanoribbons are nonmagnetic and semiconducting, and the band gaps converge to a constant value of 0.56 eV as the ribbon width increases. Moreover, these properties of MNRs can be tuned by strain and electric field. However, the experimental study of the MNRs is still very limited due to the many challenges in patterning high quality sub-20 nm 2D material ribbon. Here, we prepared MNRs with different widths between 5 and 15 nm using direct Helium ion beam milling. High optical anisotropy of MNRs is revealed by the systematic study of optical contrast and Raman spectroscopy on MNRs. The Raman modes in MNRs show strong polarization dependence. Besides, there are additional emerging modes activated by the edges. The polarization behavior of Raman modes is due to the anisotropy of the light absorption in the nanoribbons that is a result of the1D quantum confinement in 75 patterned MNRs. The polarized optical contrast gives the evidence of such anisotropy in the nanoribbons. Raman spectroscopy is one of the most widely used measurement techniques that can reveal rich characteristics of 2D TMDCs. In bulk MoS2, there are two prominent modes, E2g (383.6 cm −1 ) and A1g (408.7 cm −1 ), which correspond to two sulfur atoms and molybdenum atom of the same layer moving in the opposite in ‐plane direction and two sulfur atoms of the same layer moving in the opposite direction out ‐of ‐plane, respectively. The E2g and A1g modes reduce to E′ (385.3 cm −1 ) and A′1 (404.5 cm −1 ) modes from bulk to 1L, respectively. The E2g ‐like mode shows an anomalous redshift, instead of a blueshift as for the A1g ‐like mode, from 1L to bulk, due to the dominance of long range Coulomb interaction. External perturbations, such as strain, temperature, and electric field, can be used to tune the properties of 1L ‐MoS2, and are reflected in the E′ and A′1 modes. For example, the E′ and A′1 modes soften as temperature increases from 77 to 623 K. Therefore, Raman spectroscopy is a useful tool to study optical properties of MoS2 with external perturbations, including the MNRs. Figure 4.1.1a shows the optical image of the MNRs with varied widths, from 5 to 15 nm. The MNR arrays are patterned by direct helium ion beam milling, which is a great tool to generate finite 2DM kirigami. These five nanoribbons arrays are patterned along the same direction within a single ‐crystalline region of a 1L ‐MoS2 flake. Moreover, the atomic 76 force microscope (AFM) is used to identify the width of the nanoribbons, as shown in Figure 4.1.1b. The AFM image shows that the nanoribbon arrays are uniform with the equal spacing and width, as shown in Figure 4.1.1c. The second harmonic generation (SHG) spectra (Figure 4.1.1d), which can be observed in the 1L ‐MoS2 as an effective tool to identify the lattice orientation, are employed to determine the ribbon crystal orientation. The intensity of SHG is proportional to sin2φ, where φ is the angle with respect to the zigzag orientation. Thus, the SHG intensity would reach the maximum when the laser beam is polarized along the armchair direction, which is 30° with respect to the zigzag direction. As shown in Figure 4.1.1d, the nanoribbon direction has an angle, about 7°, with respected to the zigzag orientation. The schematic diagram of the MNRs is shown in Figure 4.1.1e where the direction of the ribbon with respect to the MoS2 crystal orientation is clearly indicated. 77 Figure 4.1.1 Characterization of the MoS2 nanoribbons. a) Optical image of 1L ‐MoS2 nanoribbons. The nanoribbons with different width are milled in each 10 × 10 μm square. The ribbon direction is marked by the black arrow. b) Atomic force microscopy image of MoS2 nanoribbons with 15 nm width. c) Height data with respect to the distance along cyan line marked in (b). d) Second harmonic generation. The signal intensity depends on the incident laser polarization angle. The armchair and zigzag directions are marked by green and blue dash lines, respectively. e) Schematic diagram of the MoS2 nanoribbon. The armchair (A) and zigzag (Z) directions are marked by the blue and pink arrows, respectively. In the pristine 1L ‐MoS2, the most prominent Raman peaks are E′ and A′1 modes, which are at ≈384 and 405 cm −1 , respectively. Unlike black phosphorus or ReSe2, the in ‐plane crystal structure of 1L ‐MoS2 is isotropic, therefore the Raman intensity of 1L ‐MoS2 is independent of the polarization of the incident laser beam. However, it becomes strongly anisotropic when the 1L ‐MoS2 is patterned into nanoribbons. Figure 4.1.2a plots the Raman 78 spectra of the MoS2 nanoribbons with 15 nm width depending on linear polarization direction of the laser beam. As shown in Figure 4.1.2b, the polarization angle of both the incident laser beam and scattered Raman signal is tuned by the same λ/2 plate, and the scattered light does not pass any polarizers after the λ/2 plate. We denote the angle between the polarization of the incident laser beam and the direction parallel to the nanoribbon as θ. The detector efficiency is sensitive to the polarization of the scattered light. After we calibrated this detector efficiency difference, this polarization result is equivalent to the case to rotate the samples with a fixed polarization of the incident laser beam. The polar plot of E′ and A′1 peak intensity, Irb(E′) and Irb(A′1), with respect to the θ is shown in Figure 4.1.2c. Both Irb(E′) and Irb(A′1) reach the maximum value when the incident laser beam is perpendicular to the ribbon direction, and when the incident laser beam is parallel to the ribbon direction the intensity becomes the minimum. It is different with the Imono(E′) and Imono(A′1) (E′ and A′1 intensity of monolayer MoS2), which are the same for both the directions. The Raman intensity in Figure 4.1.2c can be described as asin 2 (θ)+b (a and b are constant), which is similar to the behavior of the G mode in the graphene nanoribbons. Moreover, Irb max (A′1)/Irb min (A′1)≈4, which is larger than that of the E′ modes (≈2). The polarized Raman spectra are the direct evidence of the structural anisotropy of the MNRs. 79 Figure 4.1.2 Polarized Raman spectra of the MoS2 nanoribbon. a) Raman spectra in the E′ and A′1 peak regions of the MoS2 15 nm nanoribbons with respect to the polarization angle of the incident laser beam. b) Schematic diagram for the polarized Raman measurement, the half ‐wave plate is used for both incident and scattered light. The polarization angle θ is with respect to the direction of the nanoribbons. c) Polar plot of the experimental θ ‐ dependent intensity of the E′ and A′1 modes. Optical contrast has been used to identify layer number of 2D materials on dielectric substrate, which can be measured by the reflection spectrum (I2dm(λ)) from the flake region of 2D materials on the substrate and that (Isub(λ)) from bare substrate not covered by 2D material flakes. The resulting optical contrast δ(λ) is then defined as δ(λ) = (Isub(λ)– I2dm(λ))/Isub(λ). The optical contrast is so sensitive that the change of electronic band 80 structures can be revealed from its optical contrast spectrum, as demonstrated in twisted multilayer graphenes, WS2 and WSe2 flakes. The optical contrast of MNRs with different widths and that of pristine 1L ‐MoS2 under XX polarization are shown in Figure 4.1.3a. The optical contrast of MNRs is quite different from that of pristine 1L ‐MoS2, indicating a significant change of band structures after formation of MNRs. The optical contrast of MNRs is also very sensitive to its width. With decreasing ribbon width, the optical contrast is decreased. It suggests that narrower nanoribbons give the weaker absorption, which results from the more disordered overall crystal structure due to the defects created at the edges. Figure 4.1.3 Optical contrast of MoS2 nanoribbons with different width and polarization. a) Optical contrast of MoS2 nanoribbons with different width and that of pristine 1L ‐MoS2 under XX polarizations. b) Optical contrast of MoS2 nanoribbons with 15 and 5 nm under different polarizations (XX and YY). The contrast of monolayer MoS2 with the same polarizations is shown in the inset. 81 It is expected that the optical contrast of the pristine 1L ‐MoS2 flake does not exhibit any anisotropy under XX and YY polarization configurations because of its isotropic structure. Indeed, in the inset of Figure 4.1.3b, the optical contrast of the pristine 1L ‐MoS2 is almost identical under XX and YY configurations. However, for the 15 nm MNR, the contrast under the YY configuration is smaller than that under the XX configuration within the measured spectrum range. The larger optical contrast of a 2D material flake means that the flake exhibits stronger absorption in the corresponding wavelength. It has been evident in the δ(λ) difference between AB ‐stacked and twisted bilayer (or four ‐layer) graphenes. Therefore, the different δ(λ) between the two configurations indicates that 15 nm MNR exhibits bigger absorption for the incident light under the XX configuration than that under the YY configuration. The 5 nm MNR gives similar results, as demonstrated in Figure 4.1.3b. The optical contrast data discussed above are consistent with the result based on Raman spectroscopy. The Raman scattering is a third ‐order process which involves the absorption of an incident photon, the creation (or annihilation) of a phonon, and the emission of a scattered photon. Thus, the intensity of Raman mode is proportional to , where and is the optical transition matrix element (related to the adsorption) of the incident and scattered light, and Mph is the matrix element of the electron–phonon interaction. In 2D materials with reduced crystal symmetry, such as ReSe2, all the three terms contribute to the polarized Raman modes, and Mph plays a more dominant role. Here, we consider the 82 intensity of E′ modes in 1L ‐MoS2 nanoribbons, which is not sensitive to the polarization of the incident laser beam in pristine 1L ‐MoS2, and . Larger absorption under the XX configuration leads to stronger Raman intensity. We find that . This indicates that Mph has no contribution to the polarization of the E′ mode, which is different from the anisotropic 2D materials with reduced symmetry, such as black phosphorus and ReSe2. Because the phonon vibration in MNRs is very similar to that in pristine 1L ‐MoS2, it is reasonable that we observe similar electron–phonon interactions in both of them. In conclusion, All the Raman modes in MNRs show polarization ‐dependent intensity. The E′ and A′1 peaks are broadened resulting from the phonon confinement effect with the reduction of nanoribbon widths. The relative intensity of A′1 modes in MNRs to pristine 1L ‐ MoS2 can be used to probe the width of each nanoribbon. The polarization behavior of Raman modes is found to result from the anisotropy of the light absorption in the nanoribbons, which is supported by the optical contrast measurement. By patterning isotropic 2D materials, such as MoS2, into nanoribbons, one can obtain high anisotropic optical properties. 4.1.2. Hausdorff Dimension, Self-similarity, and Fractal in 2D material Kirigami 83 Once a 2DM flake such as a monolayer graphene is exfoliated across an pre-defined trench, it becomes partially suspended, which is a free-standing pure 2D system that are not available in bulk materials. Due to the negative thermal expansion if 2D nanosheets, ripples can be formatted after thermal annealing. Figure 4.1.4 is the AFM and SEM images of wrinkled suspended MoS2 monolayer. Figure 4.1.4 Periodic Ripples in suspended monolayer MoS2, which are formatted after thermal annealing. Left: AFM image; right: SEM image The suspended membrane can be further patterned into arbitrary shapes under sub 10 nm resolution, using He focused ion beam milling. Figure 4.1.5 is an example of patterned suspended graphene. 84 Figure 4.1.5 An optical image of a suspended graphene (a), and the FIB microscopy (b) Giving the capability of obtaining free-standing 2D systems with arbitrary patterns, I proposed to reduce the dimensionality from two to 1.x by creating fractal structure in suspended 2D systems. In 1967, a paper titled “How long is the coast of Britain? Statistical self-similarity and fractional dimension” 156 introduced the concept of fractional dimension in geometry with self-similarity. Examples are Koch curves, Cantor set, and Sierpinski triangle. See Figure 4.1.6. 85 Figure 4.1.6 (a) 1-4 scale Koch snowflake curves. (b) A Sierpinski triangle Fractals with scaling and self-similarity can be characterized by non-integer Hausdorff dimensions with the following expression: d ≡ lim 𝜀 →0 ln𝑁 (𝜀 ) ln (1/𝜀 ) where is the geometry of the measuring tool such as the length of a ruler. N is the measurement, namely the number of rulers a measured line or area segment can be decomposed into. 1/ is a scale factor, denoting how an n+1 scale self-similarity system shrinks with respect to its n scale counterparts. For example, in a n-scale Koch snowflake curve, the number of line segments is 4 n-1 , while the length of an n+1 scale segment is 1/3 of the length of the n-scale. In this case, d = ln(4)/ln(3) = 1.26. A Sierpinski triangle is a union of 3 copies of itself, as it is self-similar. Each copy shrinks by a factor of 1/2 when increasing level numbers, resulting in a Hausdorff dimension of ln(3)/ln(2) ≈ 1.58. 86 From the discussions above, we found that 1.X non-integer dimension could be realized in 2D fractal. For example, if we cut a free-standing graphene into a form of the Sierpinski triangle, we reduce the dimension to 1.58, which is a powerful approach to perform dimension engineering. In principle the cutting resolution should be infinitely small, as a real fractal is infinitely self-scaling. However, in real applications, as long as we cut the material with a minimal scale that is far smaller than the characteristic scale of the particles we study, we should able to obtain a fractal that effectively equals to the infinite scaling one. For example, if we are studying the THz graphene plasmonics in a fractal, the minimal scale we cut should be much smaller than ~ 1 m, such as 10 nm, which is fairly challenging, but still feasible. On the other hand, if we are working on centimeter-scale RF antenna, we only need to mill the fractal into ~ 100 m level. Our collaborator in Northrop Grumman Corporation simulated the performance of a 30*30 cm graphene Sierpinski triangle antenna, finding it can be operated at GHz level with excellent performance (Figure 4.1.7). 87 Figure 4.1.7 (a) A design of a graphene fractal antenna; (b) The multiple band responses at RF region. 88 4.2 2D Material Origami Origami offers a distinct approach for designing and engineering new material structures and properties. The folding and stacking of atomically-thin van der Waals materials, for example, can lead to intriguing new physical properties including bandgap tuning, Mott insulator transition, Van Hove singularity and superconductivity. On the other hand, achieving well-controlled folding of van der Waals materials with high spatial precision has been extremely challenging and difficult to scale towards large area. Here, I will introduce a deterministic technique to fold van der Waals materials at a defined position and direction using micro-fluidic forces. The underlying mechanism and energetics of folding are determined by molecular dynamics simulations. Electron beam lithography (EBL) is utilized to define the folding area, which allows high precision control of the folding geometry, direction and position beyond 100 nm resolution. Using this technique, a single-atomic-layer van der Waals material or their heterostructures can be folded without the need of any external supporting polymer layers in the final folded structure. In addition, arrays of patterns can be folded across a large wafer area using this technique and electronic devices that can reconfigure device functions through folding are also demonstrated. Such scalable formation of folded van der Waals material structures with high precision can lead to the creation of new atomic-scale materials and superlattices as well as opening the door to new ways of 89 realizing foldable and reconfigurable electronics devices at micrometer and sub-micrometer scale. Graphene and other atomically-thin van der Waals materials have demonstrated exceptional mechanical properties 157-159 such as high flexibility, low bending stiffness, and superior layer strength. Leveraged by these unique properties, two dimensional (2D) materials can be folded into various super-lattice structures, giving rise to exotic physical properties emerged from the folded edge, the interface, the layer misalignment, and interlayer misorientation. Recently twisted bilayer graphene (tBLG) with a carefully designed twist angle has shown intriguing electronic properties such as Mott insulator transition, 160-161 Van Hove singularity, 162-165 and superconductivity, 166-168 providing a powerful avenue towards exploring Moiré physics and twistronics. 52 As these properties are dictated by precisely tuning of the interlayer misorientations, a simple, clean, technique that can create twisted 2D materials with high controllability and scalability is highly desirable. In previous literature, twisted bilayer graphene can be obtained by consecutively transferring two graphene monolayers synthesized by chemical vapor deposition (CVD). 169- 172 However, it is difficult to control the twist angle of CVD graphene flakes, since it is hard to know the crystal orientation of each layer without sophisticated characterization tools such as transmission electron microscopes (TEM). 173 In addition, even if the crystal orientation of 90 two graphene monolayer is well identified, it is still challenging to align them with a precisely controlled rotational angle. Other approaches to prepare tBLG such as direct CVD synthesis 174 and “tear and stack” method, 160, 166 offer either limited controllability of the twist angle or poor scalability. Here we report a universal technique for folding 2D materials at a pre-defined position and direction using micro-fluidic forces. This technique can easily prepare highly controllable tBLG and other twisted 2D materials without manually aligning and stacking the flakes, nor identifying the crystal orientation. Using this method, both micrometer-scale exfoliated 2D material flakes and wafer-scale CVD-grown 2D material arrays can be folded in seconds, with sub-micrometer spatial accuracy. Figure 4.2.1 illustrates the folding process, which starts with spin-coating 3% wt. polyvinyl alcohol (PVA) solution onto a 90 nm SiO2/Si wafer followed by two-minute baking at 90℃ to form a uniform PVA layer, typically with a thickness of ~40 nm. Then two-dimensional material sheets are transferred onto the PVA layer. PVA is naturally water-soluble, 175 where typically a 40 nm PVA film can be dissolved in warm water within a few seconds. However, high dose electron beam (EB) irradiation can crosslink the PVA molecules due to a thermal induced autoignition process. 176 Therefore, the exposed PVA areas become insoluble in water, in which case PVA functions as a negative resist. 177-178 To fold a 2D material sheet, the electron beam lithography irradiation process will create exposed and unexposed regions of the PVA precisely along the predesigned folding edges. The subsequent immersion into warm deionized (DI) water (50 ℃) will 91 remove the unexposed PVA region and therefore the 2D flake over this part of PVA becomes free-standing, while the exposed PVA region as well as the flake over this region will remain intact. Furthermore, by directing the DI water flow from the unexposed PVA side towards the exposed PVA side, the now free-moving 2D material sheet above the unexposed PVA region will be folded towards the unexposed region to form the folded structure with well- defined position and direction. The spatial control of the folding technique is defined by the electron beam lithography process, which is below 100 nm. 178 The details of this technique are introduced below: First, 3% wt. polyvinyl alcohol (powder purchased from Sigma-Aldrich) water solution is spin-coated onto Si/SiO2 substrate, followed with a two minutes baking at 90 ℃ to form a uniform PVA layer, typically with a thickness of ~40 nm, confirmed by AFM. Then 2D materials are transferred onto PVA/Si/SiO2 substrate with either mechanical exfoliation method 1 or PDMS stamp based dry transfer technique. Thin samples are identified by optical contrast. The next step is to expose the desired leftover sample area by a standard electron beam lithography technique, with a dose of ~ 5000 C/cm 2 , to crosslink the PVA. After EBL, the sample is immersed into DI water with folding direction upward to minimize water bubbles generated in the folded flakes. If necessary, the PVA layer underneath 2D material flake can be removed by spincoating a PMMA layer on top of the folded structure and wet transferring the flake onto an arbitary substrate using KOH solution (1 mol/L, 90 °C, 2h) to remove SiO2, 54 followed with H2/Ar (1:3) annealing for 3 hours at 350 degree Celsius. 92 Figure 4.2.1 A step-by-step illustration of the folding technique A few-layer exfoliated graphene flake before and after folding is demonstrated in Figure 4.2.2a, which shows a sharp edge after patterning. The folding edge is precisely aligned with the EBL-defined PVA edge, which is critical for accurately controlling the folding direction via changing the PVA boundary direction. Figure 4.2.2b shows the atomic force microscopy (AFM) image of a folded graphene flake after removing PVA, demonstrating the high quality of the interface and the folding edge. 93 Figure 4.2.2 (a) A few-layer graphene flake on PV A/SiO2/Si substrate before and after folding. The AFM image inset shows the folding crease is well aligned with the user-defined PV A edge. (b) An AFM image of a folded graphene sample (after PVA layer is removed) showing the high-quality interface, as well as the well-defined folding edge and folding angle. The inset is the optical microscope image of the same sample, where the area for taking AFM imaging is outlined by a dash line. Scale bar is 5μm in (a) and 1 μm in (b). Figure 4.2.3 shows the scalability of the method for folding 2D material sheet using patterned CVD graphene array. The CVD graphene sample was transferred onto a Si/SiO 2 substrate and patterned into arrays of different length scales before they are further transferred onto PVA/Si substrate using polydimethylsiloxane (PDMS) stamp. 53 All the patterns were fold in a single process and the yield is 100%. 94 Figure 4.2.3 Deterministic folding of patterned CVD graphene monolayer array under different scales. Dashed and solid arrows inidcate the direction of the triangle tip before and after folding, respectively. Scale bar: 5 μm This fluidic-flow assisted folding also allows the precise control of the folding angle of the resulting structure, utilizing EBL to define the direction of the folding boundary. An angular rotation θ of the folding boundary can result in a 2θ change in the interlayer twist angle, as shown in Figure 4.2.4a. Figure 4.2.4b demonstrates the excellent controllability of the folding direction and the resulting twist angles in patterned graphene sheets. By varying the direction of the folding edge, different twist angles such as 30 °, 60 °, and 90 ° could be formed in the folded graphene patterns. For CVD 2D materials with isolated domains, the flake edge is always aligned with a certain axis in a crystal Bravais lattice. Therefore, the macroscopic twist angle after folding is also the twist angle between the lattice of the top layer and bottom layer. For exfoliated flakes, since a 2D material flake has significant cleavage tendency at the direction of its 95 lattice axis, most likely the macroscopic folding angle is the same as the atomic misorientation angle (Nano Lett. 12, 1, 293-297, 2012; Phys. Rev. B 96, 165418, 2017), especially when a cleave edge is straight and the flake shape looks regular. Figure 4.2.4 Twisted bilayer graphene with controllable misorientation angle realized by folding for exploring novel physics a) Controlling the folding direction in a graphene sheet by altering the direction of the folding edge. An angular rotation between the folding edge, namely the crosslinked PV A edge, and the graphene sheet results in a 2 angular twist between the top and bottom layers in a folded bilayer structure. (b) Folded twisted bilayer graphene demonstrates 30 °, 60 °, and 90 ° twist angles. In each sample, the PVA layer under the graphene sheet is patterned in a pre-designed direction that leads to the desired twist angle after folding. The folding edge is precisely aligned with the PV A edge, resulting in accurate twist angle control. Scale bar: 5 μm The accurate control of the folding direction allows the formation of van der Waals heterostructures with a deterministic inter-layer twist angle. For example, by folding a monolayer graphene into a twisted bilayer with well-defined 12° misorientation angle, a strong G band Raman enhancement can be observed under 532 nm green laser (Figure 4.2.5). 96 The enhancement of the G band intensity by more than 30 times results from the Van Hove singularity 165 caused by a rotational lattice misalignment. 160, 164, 166, 174, 179-182 The twisted angle that can lead to Raman enhancement is proportional to the photon energy of the incident laser. The insignificant D band of the folded bilayer graphene at ~ 1300 cm-1 suggests the sample is of high quality. Figure 4.2.5 G band Raman enhancement of a twisted bilayer graphene sample prepared by folding a monolayer graphene with a misorientation angle of 12 °. The Raman spectrum of an exfoliated mono- and bi-layer graphene flake is also plotted for reference. The wavelength of the incident laser is 532 nm. Scale bar: 5 μm. To understand the fundamental interactions underlying the folding process, we carried out molecular dynamics (MD) simulation to model the folding of a monolayer graphene. Figure 4.2.6 presents configurations and energetics of graphene during folding. Snapshots 97 (a) – (d) show graphene folded at various angles under the flow of water from the unconstrained side. After folding was complete, we turned off the water flow and found that the folding angles remain unchanged. Figure 4.2.6 Snapshots (a), (b), (c) and (d) show graphene bent under water flow at angles of 0º, 90º, 150º, and 180º, respectively. Here, oxygen and hydrogen atoms in H2O and carbon atoms in graphene are red, white and cyan spheres, respectively. Yellow spheres represent molecules in the water wake. Note that only half of the water in the MD box is shown in order to visualize the folding of graphene. Figure 4.2.7(a) shows the accumulated work on graphene done by water flow, which reaches equilibrium values of 15 and 23 meV for the two graphene configurations, indicating that graphene sheet with boundary orientation angle 𝜑 = 12˚ is slightly harder to fold in water than 𝜑 = 0˚. Figure 4.2.7(b) shows the change of the internal energy of graphene with 98 the increase of the folding angle. The energy barrier of folding a single C atom is estimated to be around 2 to 3 meV, indicating a small value of the out-of-plane bending modulus of graphene. Figure 4.2.7 (a) shows per-atom accumulated work done on graphene by water flow as a function of time. φ represents the orientation angle of the boundary between fixed and free portions of graphene with respect to the y-axis of the simulation box. Figure (b) shows changes in the internal energy of graphene as a function of the folding angle θ. The internal energy increases with θ, reaching a maximum value for θ = 120º and decreases after. The potential energy barrier for graphene folding is around 2 to 3 meV . Not only does the water fold the graphene, but the graphene affects the water flow. At the onset of graphene folding, we observe an interesting phenomenon in the formation of a wake in the water jet impinging directly on graphene; see the movie in the supplementary materials. The wake evolves into a U-shaped pattern as the folding angle increases. The velocity profile in the wake indicates a Levi distribution and the average wake velocity is 300 m/s. 99 We also calculate the free-energy difference, F, between folded and unfolded states using Jarzynski’s equality 183 : exp (−βW) ̅̅ ̅ ̅ ̅ ̅̅ ̅ ̅ ̅ ̅ ̅̅ ̅ = exp (−β∆F) (1), where W represents the work done during folding of graphene. The free-energy difference between a folded and unfolded (initial) states of graphene is calculated from MD trajectories in the canonical (NVT) ensemble. The ensemble average in Eq. (1) involves 20 different initial configurations for each folded state. The free-energy difference per carbon atom increases slowly until the folding angle reaches 90º. Thereafter, the free energy increases more rapidly and reaches a maximum value in the fully folded state. Entropy decrease in graphene sheet is 0.6 𝑘 𝐵 and 0.9 𝑘 𝐵 for 𝜑 = 0˚ and 12˚ respectively, indicating that 45% to 60% degrees of freedom for free C atoms has been lost after folding. The experiment and simulation discussed above show that folding of graphene by water flow is feasible. Next we demonstrate the capability of re-configuring 2D material based devices into various functionalities via our folding technique. Folding can engineer the electrical properties of layered materials by re-shaping the van der Waals sheets’ geometry, changing the stack order, and induce interactions at the interface and folding edges. Such changes can also lead to reconfigurable characteristics at the device level. Figure 4.2.8 shows the re-configuration of a transistor into a floating gate memory device through the folding of 2D material heterostructure involving multiple material layers. As shown in Figure 4.2.8a, a 100 heterostructure consisting of 10 nm hexagonal boron nitride (hBN) sheet, a 10 nm black phosphorus (BP) sheet and a few-layer graphene sheet was first created, which forms a dual gate transistor structure with BP as the channel material (Figure 4.2.8a and b, left panel). The BP transistor exhibits ambipolar conduction behavior where both the electron and hole branches can be reached through electrostatic modulation, which has been widely reported in previous studies. 116, 184-186 After folding the heterostructure using the fluidic-flow assisted method along the middle of graphene, the graphene layer becomes embedded inside the BP- hBN stack, serving as a floating gate, where the bottom gate acts as a control gate (Figure 4.2.8a and b, right panel). Figure 4.2.8 Re-configure a dual gate BP transistor into a floating gate memory device through folding. (a) left: the optical image of the as-fabricated graphene/h-BN/BP heterostructure; right: the image of the sample after folding. Scale bar: 10 um. (b) is the sample schematic before and after folding. 101 A positive control gate voltage (Vcg-max) can shift the threshold voltage of the device positive and therefore vary the hysteresis windows ΔVth, by increasing the amount of charge stored in the graphene floating gate. Applying a negative control gate voltage, on the other hand, can deplete the stored electrons in the floating gate, which reversibly recovers the Vth back to the original value. Hence, by successively sweeping Vcg and measuring Ids, we are able to continuously tune Vth and obtain different programming states. Figure 4.2.9a is a family of Id-Vcg curves measured by varying the maximal value of Vcg, which shows the memory window ΔVth is dictated by Vcg-max, as clearly demonstrated in the inset. To recover a device from positive Vth state back to its original state, a negative gate voltage sweep is performed, resulting in a Vth almost identical to its original value. Figure 4.2.9 Dependence of the threshold voltage on control-gate voltage Vcg, under different Vcg maxima were applied before each measurement. I-V transfer characteristics under different programming voltages Vcg-max are plotted. The inset graph shows a linear relationship between the threshold voltage shift versus the maximum control gate voltage. Number 1 to 4 demonstrates source-drain current measured under different programming state, which shows a complete programming cycle. Red curve: initial state, marked as stage 1; Black curve: transfer curve measured after applying a large control gate 102 voltage (28 V) at the positive direction, which shows Vth shift, marked as stage 2; Orange curve: Ids measured with a large negative control gate voltage (-15 V) sweep, which is to erase the state programmed in stage 2, marked as stage 3; green curve: I-V transfer curve is back to the initial state after stage 3, where the Vth is almost identical to its original value. (e) Band diagram of the folded heterostructure under large positive control gate field. Yellow box and blue cone represent boron nitride and graphene, respectively. The tunnelings of electrons from the top BP layer to graphene floating gate is indicated in the diagram. When applying a positive gate voltage, an upward electrical field can cause the tunneling of the electrons in the top BP layer into the graphene floating gate (Figure 4.2.9b). The electrons stored in the graphene floating gate leads to positive shift in the threshold voltage. Similarly, a large negative control gate voltage can remove the electrons from the floating gate through tunneling. Since the BP is n-type under positive gate voltage, we do not consider the minor hole tunneling from the bottom BP layer in this study. The number of electrons stored on the graphene floating gate can be estimated from the expression n = (ΔVth × CCG)/q0, deduced from charge balance equation, 187 where q0 is the elementary electron charge, ΔVth is the threshold voltage shift, CCG is the capacitance between the control gate and the floating gate, which is roughly the capacitance of 90 nm SiO2 and 40 nm PVA. For each part of the dielectric, the capacitance can be expressed as ε0εr/d, where ε0 is the vacuum permittivity, εr is the relative dielectric constant of the dielectric (2 for PVA and 3.9 for SiO2), and d is the dielectric thickness. Given a ΔV of 22 V, the calculated density of electrons tunneled into the floating gate is ∼2.8 × 10 12 cm –2 , a reasonable value considering the relatively thick boron nitride layer (~10 nm). The memory window engineering indicates 103 that the folding process can reconfigure a device with transistor behavior into a device with memory functions. In conclusion, in this work we developed a fluidic-flow assisted origami technique which can deterministically fold two-dimensional materials and their heterostructures. Molecular dynamics simulation reveals the fundamental interactions underlying the fluidic-flow assisted folding process. This technique offers the capability to obtain folded 2D materials structures and superlattices with accurately controlled twist angle and folding position. It also provides a new pathway for developing reconfigurable electronic devices and circuits through origami-based changes in the device structure. During the development of this 2D material folding technique, I tried various polymers and various substrates. Besides the method I introduced above, another useful approach is to prepattern PVA on Si/SiO2 substrate into ribbon shape by dry etching with a mask, where the spatial period is about 20 m. After patterning, Si/SiO2 is partially covered by ribbon- like PVA. Next, 2D flakes are transferred across the boundary of uncovered Si/SiO2 and PVA covered Si/SiO2. Now part of the flake is on PVA while the other part of the flake is on Si/SiO2. The last step is to flow DI water across the boundary to remove the PVA and fold the flake onto Si/SiO2 substrate. In this method, folded flakes are on Si/SiO2 substrates (just 104 like the folded exfoliated samples obtained by chance), which offers various device applications. In addition, no EBL is needed in this process. 105 5. Atomically Thin Femtojoule Memristor Aggressive scaling of the active layer thickness is critical towards reducing the operating current, voltage and energy consumption in resistive filament memristors. Previous memristor filament layers have been limited to above 3 nm due to fabrication constraints making it challenging to suppress the on-state current below 100 pA and switching voltage below 1 V. Here, we study the formation of conductive filaments in a material medium with sub-nanometer thickness, formed through oxidation of atomically-thin two-dimensional boron nitride. Filamentary switching can be accomplished with sub-picoampere current that is 2 orders of magnitude lower than the previous record. Furthermore, by confining the filament to the atomic scale, we observe current switching characteristics that are distinctively different from that in thicker medium due to profoundly different atomic kinetics. The fundamental limits for energy consumption per cycle in such a resistive switching device is also theoretically explored. Finally, a resistive memory device with 5 pA operating current and 0.6V/-0.1V SET/RESET voltage is demonstrated, showing stable switching characteristics and data retention. This ultra-low current device operating at less than 10 fJ energy per bit for SET and less than 1 fJ per bit for RESET brings us significantly closer towards realizing sub-femtojoule electronic computation. It can be attractive for applications such as a binary synapse in neuromorphic computation and in many other electronics systems that desire ultra-low power operation. 106 5.1 Introduction Resistive switching devices such as oxide based memristors 188-192 and conductive bridge random access memories (CBRAM) 193-195 utilize filamentary switching to realize low power and high speed operation. In these devices, the formation and destruction of the conductive filament enables reversible switching of device conductivity, resulting in compact two-terminal devices well suited for miniaturization and integration, and making resistive switching devices a potential candidate for applications in low-current, low power memory and neuromorphic electronics. 196-202 However, the operating current in resistive switching devices are constrained by the scaling of the medium layer thickness that dictates the dimensions and morphology of the resulting filament. 189, 203-206 The thickness of the oxide based medium layer, typically deposited by atomic layer deposition method (ALD), in existing low current memristive devices are limited to above 3 nm 207-209 and the devices typically operate at the nano-ampere current level with the lowest record being 100 pA. 210 As a result, new materials and device designs are needed for enabling an ultra-thin medium layer that is critical for reducing the filament size to the atomic scale and hence the energy required to form and rupture them. The recent emergence of two-dimensional materials has offered a new pathway for achieving a high-quality medium layer with atomic level thickness and filamentary switching 107 potential. In this work, we demonstrate the formation of a memristive switching medium layer with sub-nanometer thickness created through the oxidation of the atomically-thin two- dimensional (2D) hexagonal boron nitride. The reducting of the medium layer thickness allows the demonstration of sub-nm filamentary switching with applications for resistive memory device with sub-pA operation current. Moreover, fundamentally new atomic kinetics can arise when the medium layer thickness reduces to the atomic scale. The unique switching characteristics in this ultra-thin medium filamentary switching device is explained through Monte Carlo kinetics simulations of the filament morphology and the distinct electrostatics in the atomically-thin medium. 5.2 Sample preparation and characterization To create the atomically-thin switching medium, few layer hexagonal boron nitride (h- BN) flakes were first exfoliated onto Si/SiO2 substrates with 285 nm SiO2 via a standard mechanical exfoliation method. The layer thicknesses were initially estimated by optical contrast and further confirmed by Atomic Force Microscopy (AFM). We conducted Raman spectroscopy on all the few-layer h-BN samples. A characteristic Raman peak near 1367 cm - 1 is observed in all samples, which corresponds to an E2g phonon vibration mode (Figure 5.2.1a). The few-layer samples were subsequently oxidized via an ultra-low power oxygen plasma treatment, which can oxidize h-BN flakes up to a few nanometers in depth without 108 damaging the flake morphology (see method part). AFM topographic images were taken to verify the flakes are atomically smooth after oxygen plasma treatment and have approximately the same thickness as the sample before the treatment. Raman measurements showed that the h-BN Raman peak completely vanished after the oxygen plasma treatment, which suggests the full amorphization of h-BN. Atomic resolution scanning transmission electron microscopy (STEM) reveals that pristine h-BN thin films have crystallized “honeycomb” lattice structure and hexagonal fast Fourier transform (FFT) patterns, while oxidized h-BN flakes are amorphous and have no periodic FFT structures (Figure 5.2.1b). Furthermore, electron energy loss spectroscopy (EELS) and elemental quantification identified that the oxidized few-layer hBN sample contains boron, nitrogen, and oxygen, among which oxygen dominates (Figure 5.2.1c). Therefore, we use BNOx to denote the partially oxidized boron oxide material in the following text. 109 Figure 5.2.1 a) Raman spectra of a bilayer h ‐BN flake, before (red) and after (blue) oxygen plasma treatment. b) High ‐resolution STEM images show the crystalline lattice of h ‐BN before the oxygen plasma treatment (left panel), and the sample becomes amorphous after the treatment (right panel). The scale bar is 2 nm. The insets of left panel are the electron diffraction pattern of the crystalline h ‐BN, where crystal planes and interplanar spacing are indicated by Miller indices. c) EELS spectrum of a BNOx flake. The element atom ratio confirmed the abundance of oxygen in the sample after the oxygen plasma treatment. 110 Each BNOx flake was transferred from the substrate onto a few-layer graphene flake which serves as a thin, smooth and conformal bottom electrode (BE) of the memristor structure. 40 nm silver was subsequently deposited as the top electrode (TE), capped with another 40 nm gold to facilitate electrical probing (Figure 5.2.2a). Multiple devices were fabricated with BNOx layer thickness ranging from 0.9 nm to 2.3 nm, corresponding from an original bilayer to 5-layer h-BN. The left panel of Figure 5.2.2b is the AFM image of a 0.9 nm BNOx flake stacked on a 5-layer graphene BE and the corresponding AFM height profile, and the right panel is a cross section TEM image of a device structure fabricated with this BNOx sample. We can clearly see a ~0.9 nm amorphous BNOx layer sandwiched between the graphene BE and the Ag TE. 111 Figure 5.2.2 a) The schematic of an atomically thin memristive device. A 0.9 nm thick BNOx is sandwiched between the multilayer graphene bottom electrode and the Ag top electrode. b) The lower left panel is the AFM image of a BNOx stacked on a five ‐layer graphene, of which the height profile is shown at the upper left panel. The right panel is the cross ‐ sectional STEM image of a device made from the sample in the left panel. The layered structure of five ‐layer graphene and the amorphous morphology of BNOx can be clearly observed. 5.3 Thickness Dependent Ultra-low Power Filamentary Switching and Modeling We conducted DC measurements on samples with 0.9 nm, 1.3 nm, and 1.8 nm BNOx medium layer thickness under current compliance of 5 pA, 90 pA, and 500 pA, respectively. The current compliance we applied for each thickness are the lowest currents that can stably run DC cycles while avoiding filament overgrowth. All the devices exhibit typical bipolar 112 resistive switch behavior with hysteresis loop in the I-V curves (Figure 5.3.1). By applying a positive/negative voltage from BE to TE, a conductive filament of Ag atoms can be formed/ruptured, resulting in the switching to low/high resistance state of the device. Once the positive voltage applied is larger than a critical voltage, i.e. the SET voltage, the Ag cations electrically connect the BE and TE, resulting in an abrupt jump of current and therefore turning on the device. The migration of Ag cations occurs at a lower bias than any considerable tunneling current appears, and hence dominates the conductance between the BE and TE. After a device is set, it will remain at the low resistance state (LRS) for hours without bias, until a negative voltage is applied to reset the device to a high resistance state (HRS). In previously reported resistive memory devices, the reset process is believed to form a depletion gap in the filament that electrically disconnects the TE and BE, while the set process re-connects the gap and therefore turns the device on. Several experiments have measured the filament depletion gap length to be ~6 nm, 211-213 while a lower limit of 2-3 nm gap size was predicted via theoretical analysis. 214 The filament, which is longer than the gap distance, is generated with a significant larger voltage than used for the set voltage. In contrast, the thickness of all our switching layers are smaller than the length of conventional filament gap, and therefore no forming state is needed. The on/off ratio of our devices ranges from 100 to 1000, and this asymmetrical on-state current, which had enlarged the memory window and reduced the current level for rupturing the filament, is a signature of conductive 113 bridge memristors. 193, 210 All these devices can reliably operate for at least hundreds of set/reset cycles in the ambient environment. -0.5 0.0 0.5 1.0 10f 100f 1p 10p 100p 1n t=1.8 nm t=1.3 nm t=0.9 nm I DS (A) V DS (V) Figure 5.3.1 Thickness ‐dependent ultralow power filamentary switching. a) The set–reset I–V characteristics of devices with 0.9, 1.3, and 1.8 nm BNOx layer thicknesses measured under current compliances of 5, 90, and 500, pA, respectively. The characteristics of the BNOx resistive switching devices depends significantly on the thickness of the BNOx layer. Devices with a thinner BNOx layer can be reliably operated under lower current and voltage in both “set” and “reset” processes. Furthermore, when the voltage increases at the positive side, the current for the 0.9 and 1.3 nm samples show no notable increase until the abrupt jump occurs, while the current for the 1.8 nm sample increased gradually with increased voltage before the voltage reached the threshold to set the device, which is similar to conventional resistive switching devices. To understand the unique 114 thickness dependent properties of this switching characteristic, we carried out kinetic Monte Carlo (KMC) simulations. The KMC simulations describe cationic generation, hopping and reduction behaviors at a microscopic level, which provides qualitative understanding of the electrical characteristics in these aggressively scaled memristive devices. A conductive filament is most likely to form in a region with abundant interstitial sites for metal atoms, where a rectangular grid of the sites can be used to approximate the amorphous structure for studying the filament formation. Figure 5.3.2 shows the filament morphology for different switching layer thicknesses, tOX, in which the blue dots denote oxide sites, yellow dots denote active electrode atoms or cations and gray dots denote inert electrode atoms. It shows that an extremely thin filament down to a single atomistic chain can be formed between the electrodes for the case of two layers of oxide sites (tOX = 0.9 nm). For comparison, in the case of 10 layers of oxide sites (tOX = 4.5 nm), because the filament grows in both the lateral and vertical directions before a percolative filament path can be formed, the filament expands much wider than a single atomistic chain in its lateral dimensions. Hence, the percolative filament path formed through a thicker oxide in the SET process would typically have a wider diameter. 115 Figure 5.3.2 KMC simulations of the filament formation process in mediums with 4.5, 2.25, and 0.9 nm oxide sites. The filament in the 4.5 nm medium is wider because it grows both vertically and laterally, while the simulation on 0.9 nm switching medium shows the possibility of forming a single atomic chain filament. The applied bias for the 4.5 and 0.9 nm structure is 3.15 and 0.63 V , respectively. In addition, an enhanced positive feedback process facilitates the thin filament formation in the device for the case of tOX ≈ 0.9 nm. For a resistive switching device with BNOx thickness tOX and an applied voltage of V0, the electric field increases from to if a cation (yellow dot) reaches the bottom electrode through hopping as shown in Figure 5.3.3. Here, a0 ≈ 0.45 nm is the grid spacing, which is treated as an approximate value for layer spacing in layered materials. For tOX ≈ 0.9 nm and V0 ≈ 630 mV , the vertical electric field approximately increases from ≈0.7 to 1.4 V nm −1 after the first cation hops into the switching medium, which results in an exponential increase in the local hopping rate and hence facilitates the subsequent vertical filament formation. In comparison, for tOX ≈ 2.3 nm and V0 ≈ 1.6V , the vertical electric field approximately increases from ≈0.7 to 0.86 V nm −1 after a cation hops into the switching medium during the initial filament formation stage. The change is much less significant compared with the vertical electrical field enhancement in 116 the 0.9 nm switching layer case. The enhancement of the vertical growth rate, which has an exponential dependence on the vertical electric field, thereby, is much smaller. The larger increase in the vertical electric field in devices with ultrathin BNOx layer leads to more pronounced positive feedback process of vertical filament growth, which enhances the formation of a narrow atomistic filament chain. Figure 5.3.3 Electrical potential profile during the filament growth in the 0.9 nm switching medium, as shown in the left panel. The applied voltage is 0.63 V . The right panel demonstrates the local electrical field enhancement induced by a hoping of Ag cation, which is a situation depicted in the left panel. Furthermore, through KMC simulation, we found that the intrinsic set time reduces as the BNOx layer thickness decreases since it is easier to form a percolative path in a thinner BNOX layer. Figure 5.3.4 plots the normalized set time as a function of the BNOx layer thickness for different values of the parameter β in Eq. (1). Here β denotes the efficiency at which the electric field assists in lowering the hopping/oxidation barrier height. Hence, a 117 larger β results in lower set time. The corresponding set voltages and current compliance are 0.6, 0.9, 1.2, 1.6V and 5, 90, 500, 2000 pA respectively, to be consistent with experimental data, which give approximately constant electric field for different experimental samples. For certain β value, the set time increases as the BNOx layer thickness increases. The reason is that a thinner BNOX layer is easier to form a percolative path. In addition, the current compliance for the 2.3 nm device is much larger than that of the 0.9 nm device. The filament formation is associated with ionic transport and charge transfer. A metal atom ionized and transported from the top to the bottom electrode costs an energy of 𝑧𝑞 𝑉 0 , where 𝑧 is the cation charge in the unit of elementary electron charge 𝑞 , and 𝑉 0 is the applied voltage. The ultimate limit of the energy consumption for a filament formation process with M metal atoms is 𝐸 𝑚𝑖𝑛 = 𝑀𝑧𝑞 𝑉 0 . For a thinner BNOx device, the set voltage is lower and the extremely short and atomically thin filament reduces M. The ultimate limit of the energy consumption reduces significantly. The constant t0 is a prefactor of the set time, 118 which is inversely proportional to the rate constants and exponentially dependent on the barrier heights of all processes described in the MC simulation as indicated by Eq. (1). Figure 5.3.4 Normalized set time vs. BNOx thickness for different unitless parameter β. The current compliance are 5, 90, 500, 2000 pA respectively. Despite the uncertainties of the rate constants and barrier heights, the qualitative scaling behaviors of the set time remain the same. In addition, the number of hopping cations required to electrically connect the BE and TE becomes considerably smaller when the switching medium thickness scales down since not only the filament becomes shorter, but the lateral dimensions of the filament also become smaller. Hence, the atomically thin memristive device is expected to have a faster intrinsic operation speed than the memristors with thicker switching medium. 119 5.4 Device Characteristics of a 0.9 nm BNOx Memristive Device Figure 5.4.1 shows the characteristics of a resistive switch memory device with 0.9 nm BNOx layer. Figure 5.4.1a shows the set and reset I-V curves of the device with 0.9 pA, 5 pA, and 9 pA current compliance. The high resistance state (HRS) current level is fluctuating around 10-100 fA, without any evidence of gradually increase until the abrupt rise in the current occurs. The 10 -100 fA current level is dominated by the equipment noise. The device can be written and erased at sub-pA current level with a distinct difference of on/off current (ratio ~10-100). The energy consumption for the programming (SET) and erasing (RESET) operations are estimated to be less than 10 fJ and 1 fJ, respectively, when we applied a 10 ms voltage pulse to execute these operations. The energy level above could be overestimated since the device is expected to operate well with even shorter time though our current measurement system was limited to provide 10 ms pulses. The set voltages under different current compliance are reliably near 0.6-0.7 V , which is consistent with the aforementioned Ag cation migration mechanism. Figure 5.4.1b shows the data retention of the memory device with a 0.9 nm BNOx switching layer, measured at 85 ℃. The device resistance at the low resistance state (LRS) was measured after the device was switched on under 5 pA current compliance, and HRS resistance was measured after the device was switched off. The data was read at 0.18 V without applying current compliance, with a total measurement time of 4 hours. The device shows excellent data retention, suggesting that the Ag filament is robust 120 even for the operation at low power and elevated temperature. Figure 5.4.1c shows HRS and LRS current levels obtained during 100 continuous set-reset DC cycles, with a reading voltage of 0.15 V and current compliance of 5 pA. The set voltages statistics for the 100 cycles exhibit a normal distribution centered at 0.63 V and a standard deviation of 0.088 V (Figure 5.4.1d), indicating that the filament formation process is highly reproducible and consistent, even operated at ultra-low power. The device has a record low operation current that is about two orders of magnitude lower than previously reported. 210 Such a device is attractive for applications in memristive computational device ssuch as binary synapses for neuromorphic computing. 121 Figure 5.4.1 Characteristics of a device with 0.9 nm BNOx. a) Set–reset I–V characteristics of a device with 0.9 nm BNOx switching layer subject to different current compliances of 0.9, 5, and 9 pA. b) Data retention measured at 85 °C. Both HRS and LRS resistances were measured with a 0.18 V read voltage. c) The current read at 0.15 V over 100 continuous switching cycles. d) The statistical distribution of the set voltage for 100 switching cycles and the Gaussian fit curve. The set voltages exhibit a normal distribution centered at 0.63 V , with a standard deviation of 0.088 V . In summary, the resistive switching of conductive filaments in a sub-nanometer thickness material medium is studied for the first time. The atomically-thin switching medium layer is formed through a unique process involving the oxidation of two-dimensional hexagonal 122 boron nitride. It is observed that the confinement of the filament to atomic-scale thickness results in distinct atomic kinetics for the filament formation. The resulting resistive memristor device can operate at sub-picoampere on-state current, less than 1 V operating voltage, and energy consumption per bit of less than 10 fJ for SET and less than 1 fJ for RESET. The device brings us one step closer towards realizing memristive electronic computation at the energy level of sub-femtojoule per bit, which are necessary for many emerging applications that desire ultra-low power operation, such as binary synapse in neuromorphic computation systems. 5.5 Efficient Learning with Ultra-low Power Compound Synaptic Devices In this section, we designed compound synaptic devices based on ultrathin BNOx binary synapses and demonstrated their efficiency programming through simulations. Figure 5.5.1 shows that the current of an experimentally demonstrated 0.9 nm BNOx memristor can be potentiated and depressed abruptly with positive/negative voltage pulses. The post- synaptic current can be well-maintained over 100s without notable decay. Therefore, the BNOx memristor can be programmed into binary states and served as a binary synapse. Comparing to conventional synaptic devices, the BNOx binary synapse consumes record-low power (~fJ level) and has long term memory effect, making it favorable for neuromorphic applications. 123 Figure 5.5.1 0.9 nm BNOx memristor operated as an ultra-low power binary synapse a) a 0.9 nm BNOx memristor set with a 0.6 V , 10 ms pulse. (b) the same device reset by a -0.45 V , 10 ms pulse. To increase information storage capability, we simulated the performance of 16-state compound synapse formed by connecting 15 BNOx binary synapses together. The compound synapse was randomly programmed to different synaptic weights, under 4 bit resolution. We calculated the distribution of synaptic weights using 512 (16×32 network) BNOx compound synapses and 5% variation in I-V model parameters. Figure 5.5.2a shows the synaptic weight at each level, indicated by current. The compound synapse matrix can be operated at pA level, whereas conventional memristors typically work at A current range. In addition, since the overlap between the states is small, the compound synapse matrix can be highly accurate. 124 Figure 5.5.2. a) Simulated distribution of synaptic weights of a 16×12 network composed of compound BNOx synapse made of 15 BNOx memristors. b) Power and accuracy tradeoff in synaptic learning using BNOx compound synapse. Dots with different colors indicate different programming resolution In Figure 5.5.2b, we modeled the power consumption and accuracy tradeoff in synaptic weight programming with different bit states. An increased programming resolution results in elevated power usage and improved accuracy. In conclusion, the BNOx compound synapse derives its advantages from the ultralow power consumption of individual BNOx synaptic device due to its ultimately thin geometry giving rise to pA level operating current. It can offer clear benefits over conventional synapses in terms of accuracy and power efficiency. The compound synapses could be promising for applications in synaptic learning network, low-power memory-centric computing, and neuromorphic computation in general. 125 6. BNOX Memristor Based Boltzmann Machine A Boltzmann machine whose effective “temperature” can be dynamically “cooled” provides a stochastic neural network realization of simulated annealing, which is an important metaheuristic for solving combinatorial or global optimization problems with broad applications in machine learning and operations research. However, the hardware realization of the Boltzmann stochastic element with “cooling” capability has never been achieved within an individual semiconductor device. In this section I will demonstrate a new memristive device concept based on two-dimensional material heterostructures that enables this critical stochastic element in a Boltzmann machine. The dynamic cooling effect in simulated annealing can be emulated in this multi-terminal memristive device through electrostatic bias with sigmoidal thresholding distributions. We show that a machine- learning-based method is efficient for device-circuit co-design of the Boltzmann machine based on the stochastic memristor devices in simulated annealing. The experimental demonstrations of the tunable stochastic memristors combined with the machine-learning- based device-circuit co-optimization approach for stochastic-memristor-based neural- network circuits chart a pathway for the efficient hardware realization of stochastic neural networks with applications in a broad range of electronics and computing disciplines. This work is a collaboration with Prof. Jing Guo’s group at UFL. 126 6.1 Introduction The similarities between statistical mechanics and combinatorial optimization fields, as described by Kirkpatrick et al, 215-216 has stimulated extensive interest and progresses in developing algorithms and methods based on simulated annealing (SA) for solving optimization problems. These methods and algorithms have found extensive applications in a variety of important problems such as computer-aided circuit design, 217 power systems, 218- 219 fingerprint matching, 220 scheduling 221-222 and routing. 223-224 Artificial neural networks (ANNs) have been widely adopted to solve a broad range of problems including optimization, voice recognition, computer vision, and electronic design automation. 225-228 A hardware accelerator based on an ANN for the SA algorithms can significantly improve the computational efficiency for solving the combinatorial optimization problems. The Boltzmann machine (BM), whose dynamics is similar to the thermodynamics of a natural physical system, is especially suitable for performing the SA algorithms for optimization. 229 One major challenge, however, is an efficient hardware realization of the stochastic artificial neurons in the BM. To perform the simulated annealing tasks, a combinatorial optimization problem can be mapped to an imaginary physical system, whose energy is described by the cost function of the optimization problem. The effective “temperature” needs to be cooled down in the “annealing” process, which requires that the “temperature” of the stochastic neuron to be tunable. A transistor-circuit-based approach is inefficient in implementing a 127 stochastic artificial neuron. Although memristors have been explored for efficient hardware implementation of the ANN structures, 196, 230-236 the following issues need to be addressed. First, the artificial neuron implemented by a memristor needs to be stochastic and shows Boltzmann-like statistics. Second, the effective “temperature” of the stochastic memristor needs to be dynamically tunable. Here we show that by exploiting the unique material properties of the two-dimensional material system, a tunable stochastic memristor following Boltzmann statistics can be realized as the neuronal element in the BM for SA. 6.2 BNOx-WSe2 Device for Generating Dynamically Tunable Sigmoidal Distributions Figure 6.2.1a shows the schematic of the heterojunction device structure. This vertical memristor is constructed on 285 nm Si/SiO2 (285 nm) substrate with 4 nm oxidized boron nitride, i.e. BNOx, as the resistive switching medium. 237 The top electrode consists of silver while the bottom of the BNOx layer forms van der Waals interface with multi-layer WSe2. Figure 6.2.1b shows a cross-sectional scanning transmission electron microscopy (STEM) image of the memristor and an electron energy loss spectroscopy (EELS) mapping of the material composition, which clearly reveals the device structure consisting of the crystalline layered WSe2 and amorphous BNOx. The silver metal layer serves as an active electrode, which ionizes upon the application of electrical bias and drifts through the BNOx layer. The 128 silver ions are reduced to silver atoms as they receive electrons from the bottom electrode to form a silver filament inside the BNOx layer, which switches the device from the high resistance state to the low resistance state. The multi-layer WSe2 under the BNOx serves not only as an inert electrode connected to the external bias, but also as a gate-tunable series resistor that can vary the potential distributions between the WSe2 and BNOx layers. The external bias voltage, i.e. Vbias as indicated in Figure 6.2.1a, includes the potential change across both the WSe2 layer and the BNOx filamentary medium. Since the resistance of the WSe2 layer can be modulated over six orders of magnitude through electrostatic gating, the gate bias can hence significantly tune the effective potential drop across the BNOx layer for a given Vbias. In a typical device, the WSe2 reaches its minimum conductance at -18 V back- gate voltage. Figure 6.2.1c shows several cycles of the typical set-reset hysteresis loops of the memristor under a back-gate voltage of 50 V . The set voltage is around ~0.9 V under this bias condition and stochastically varies over different switching cycles. After the device is switched on, it spontaneously returns to the off-state once Vbias becomes smaller than ~ 0.3 V , indicating that the state of the device is volatile. This state volatility is a desirable feature of stochastic sampling devices. Unlike the memristors designed for data storage applications, filament volatility is a preferable characteristic in these devices since faster stochastic sampling and simpler peripheral circuitry can be enabled if the device spontaneously resets to the high resistance state after each sampling event. Such features can be obtained in this device at relatively small current compliance (~50 pA). The low compliance current limits 129 the size of the conductive filament formed during the sampling to reduce its stability. Figure 6.2.1d shows the dynamic measurement on the device showing the set and reset time-scale of the device at Vg = 50 V . A bias voltage of 1.8 V is applied for 45 ms to set the device, followed by a 0.15 V pulse train to read the memristor state at 7.5 ms time intervals. 10 set- read cycles were shown in Figure 6.2.1c. The device always spontaneously self-reset within 7.5 ms, and hence can generate successive sampling without any intentional reset operation. Figure 6.2.1 (a) Schematic of the hybrid memristive device structure with the BNOx filament switching layer forming van der Waals interface with the multi-layer WSe2. The top electrode is formed with Ag metal. (b) The cross-sectional STEM image reveals that the device consists of crystalline layered WSe2 and amorphous BNOx. The EELS mapping indicates the material composition in each layer. The scale bars are 10 nm. (c) Three consecutive set-reset switching loops of the device at 50 V gate voltage. d) The dynamic time domain measurement of the 130 memristor switching at Vg = 50 V . In each switching cycle, a 1.8 V , 45 ms voltage pulse was applied between the TE and BE to set the device, followed by a pulse train of 0.15 V amplitude to read the memristor state at 7.5 ms time intervals. Ten set-read cycles were shown. The device always spontaneously self-reset within 7.5 ms. The pink squares are the current level measured during the application of the set pulse. The green circles indicate the current level measured with the read pulse. The set voltage pulse train is shown as the red line with the voltage scale on the right axis. Figure 6.2.2a shows the statistics of the set voltage extracted from 30 set-reset cycles, which follows a Gaussian distribution with a mean value of 0.93 V and a standard derivation of 0.18 V . To understand the stochastic characteristics, a three-dimensional (3D) kinetic Monte Carlo (KMC) method is used to simulate the filament formation and SET process of the memristor device. The KMC simulation describes the hopping events stochastically by an exponential probability distribution. The agreement between the experiment and simulation indicates that the distribution of the SET voltage is physically due to the stochastic hopping properties of the ions in the filament formation process. 238 The stochastic ionic movement that dictates the filament formation process in this device provides a platform for realizing exponential class sigmoidal distribution function. Here, we define PSET (t < t0, Vbias) as the probability that the device will set within time t 0 for a given external voltage bias across the memristive device. Figure 6.2.2b shows the experimentally measured distribution of PSET (t < t0, Vbias) as a function of the SET voltage shifted with respect to V0 at three different gate biases: -10 V , 20 V , and 50 V , respectively. V0 is the 50% 131 probability bias voltage point, i.e. PSET (t < t0, Vbias = V0) = 0.5. In each test, a voltage Vbias is applied between the Ag electrode and WSe2 for t0=300 ms. For each gate bias, this procedure is repeated 50 times at each value of the Vbias to obtain the set probability. Measurements at different Vbias conditions leads to Figure 6.2.2b, which shows the set probability as a function of Vbias shifted with respect to V0. For Vbias significantly lower than V0, the probability of setting the device within a certain time (t0 = 300 ms) approaches zero while for Vbias sufficiently higher than V0, this probability is close to unity. In the intermediate region of the probability distribution, a sigmoidal transition region exists where the probability increases as Vbias increases. Furthermore, the gate modulated tunable Fermi level and charge density in the WSe2 layer allows the dynamic tuning of the transition region to spread in such distribution functions. At voltage biases where the WSe2 layer becomes more resistive (e.g. Vg= -10 V), the effective portion of the voltage drop across the memristive switching medium becomes smaller. Hence the bias voltage will be less effective in modifying the probability distribution, resulting in the probability transition occurring within a wider spread of the bias voltage. On the other hand, a WSe2 layer with higher conductance (e.g. Vg= 50 V) as tuned by the gate bias tends to decrease the spread of the sigmoidal transition region of the distribution. Based on the Markovian dynamics approximation, which is valid when the thermal equilibration rate is much larger than the ion hopping rate, the SET probability within t<t0 can be expressed in an exponential form, P≈ 1 − 𝑒 −𝛾 𝑡 0 , where is a parameter proportional to the average hopping rate. In the hopping transport regime, the average rate is 132 exponentially sensitive to the applied bias 𝑉 𝑏𝑖𝑎𝑠 , 𝛾 ≈ 𝛼 𝑒 (𝛽 𝑉 𝑏𝑖𝑎𝑠 ) ,, which results in a double exponential form for the probability, 𝑃 (𝑉 𝑏𝑖𝑎𝑠 ) ≈ 1 − 𝑒 −𝛼 𝑡 0 e (𝛽 𝑉 𝑏𝑖𝑎𝑠 ) , 𝛼 and 𝛽 are constants that are only dependent on the material properties and device structures. This double exponential function asymptotically approaches and can be further simplified to a distribution function that resembles Fermi-Dirac distribution, which is used to describe the experimentally obtained distribution probability as a function of Vbias, 𝑃 (𝑉 𝑏𝑖𝑎𝑠 ) ≈ 1 1+exp(− 𝑉 𝑏𝑖𝑎𝑠 −𝑉 0 𝑇 V ) = 𝑆 ( 𝑉 𝑏𝑖𝑎𝑠 −𝑉 0 𝑇 𝑉 ) = 1 − 𝑓 0 ( 𝑉 𝑏𝑖𝑎𝑠 −𝑉 0 𝑇 𝑉 ) , (1) where V0 is the voltage at which there is 50% probability to set the memristor within 300 ms, and 𝑇 V is a characteristic scale in the unit of voltage resembling the temperature effect in Fermi-Dirac distribution, termed as the effective “temperature”. Here S is the sigmoid function, sometimes also called the logistic function, and 𝑓 0 is the Fermi-Dirac distribution function. Based on the values of V0 and 𝑇 V extracted from the experimental data and the analytical fit, V0 increases as the WSe2 layer becomes more resistive, which is consistent with our previous discussion. In addition, 𝑇 V also increases with increasing resistance in the WSe2 layer. Figure 6.2.2b clearly demonstrates the sampling of an exponential class sigmoidal function with tunable spread of the transition region, reminiscent of the Fermi- Dirac distribution in statistical physics. 133 Figure 6.2.2 (a) The statistics of set voltages extracted from 30 set-reset cycles, under Vg = 50 V . A Gaussian fit of the data is plotted as the orange curve. (b) The probability that the device will set within time t0=300 ms as a function of the bias voltage Vbias shifted with respect to V0 for Vg= -10 V , 20 V , and 50 V . The experimental data is shown as the dots. The dashed lines show the analytical fit with the sigmoid function eq. (1). 6.3 A Boltzmann Machine Based on the Stochastic Memristor To understand the dependence of the effective “temperature” on the applied gate voltage, a behavioral model as shown in the inset of Figure 6.3.1a is developed. The device is modeled 134 as a memristor in serial combination with a WSe2 layer modulated by the gate electric field. The gate voltage modulates the resistance of the WSe2 layer as, 𝑅 FET (𝑉 g ) = 𝑍 (𝑉 g −𝑉 T ) , (2) where Z is a constant independent of the gate voltage, 𝑉 g is the gate voltage, and 𝑉 T is the threshold voltage. The voltage on the intrinsic memristor is a fraction of the applied voltage through a voltage divider relation. As a result, the effective “temperature” can be expressed as, 𝑇 V (𝑉 𝑔 ) = 𝑇 V0 〈𝑅 M 〉+𝑅 FET 〈𝑅 M 〉 = 𝑇 𝑉 0 [1 + 𝑍 ′ (𝑉 g −𝑉 T ) ], (3) where 𝑇 V0 is an effective “temperature” constant, 〈𝑅 M 〉 is the average resistance of the intrinsic memristor, and 𝑍 ′ = Z/〈𝑅 M 〉. As shown in Figure 6.3.1a, the model describes the modulation of the effective “temperature” by the gate voltage as observed in the experiment. The design of a “cooling” procedure in SA, therefore, can be translated into the design of a series of gate voltage pulses by mapping the effective “temperature” to the gate voltage through the 𝑇 V (𝑉 g ) relation. The device demonstrated here can enable a compact, single-device implementation of the stochastic artificial neurons in a BM for SA. Figure 6.3.1b shows a schematic block diagram of a BM-based circuit, in which the weighted sum can be computed by a standard memristor crossbar array (CBA), 239-240 and the stochastic artificial neurons can be implemented by the 2D-material-based memristor devices demonstrated here. In addition, a voltage amplifier is 135 used to amplify the output of the CBA and provide the input voltage to the stochastic artificial neurons. A readout circuit block reads the state of the stochastic artificial neuron device and provides a binary voltage input to the CBA. The “cooling” procedure in SA can be achieved by designing the applied gate voltage on the stochastic artificial neuron device as described before. Figure 6.3.1 (a) Comparison between the model and experiment on the effective “temperature” of the sigmoid distribution as a function of the gate voltage. The inset shows the schematic diagram of the model. (b) Block diagram of a Boltzmann machine designed by using the stochastic memristive neurons for solving a combinatorial optimization problem. As an example of applying the BM with SA to solve combinatorial optimization problems, a school timetabling problem is solved. 241-242 The timetabling problem requires assigning resources including teachers (T), classrooms (R), and course subjects (C) to classes of students over a number of periods (P) with a combination of constraints. It can be mapped into minimizing the energy (or cost) function of an imaginary physical system, whose 136 dynamics is described by an isomorphic BM. For the school timetabling problem solved here, the timetabling information is expressed in terms of a 4 th order tensor whose entry values are represented by the neuron states. The coefficients in the expression of the cost function are mapped to the weights which could be implemented by a cross-bar array. The effects of two sources of stochasticity in the stochastic neurons - the standard deviation of V0, = std(V0) and a finite effective “temperature” TV - on the BM performance in solving a sample scheduling problem, which involves the assignment of 5 teachers and 5 classrooms to 5 courses over 5 class periods, are examined in Figure 6.3.2 (a) and (b), respectively. In Figure 6.3.2a, the cost function vs. generation is simulated for different values of at zero “temperature” TV =0, which reduces the BM to a Hopefield network with a stochastic threshold V0, whose randomness is characterized by . The results show that with close to 0, the network suffers from a problem of trapping in a local minima of the cost function. While increasing solves the problem of trapping, an excessively large perturbs the system away from minimum points. To study the impact of randomness due to the effective “temperature”, Figure 6.3.2b assumes =0 and performs a SA, which has an exponential form of the cooling procedure as, 𝑇 𝑖 = 𝑇 0 [1 − 10 −𝛼 T 𝑖 ], (4) where 𝑇 𝑖 is the temperature at the i-th generation, 𝑇 0 is the initial temperature, and 𝛼 T is a unitless exponent factor which determines the cooling rate. A larger positive value of 𝛼 T 137 corresponds to a slower cooling rate and a smaller positive value of 𝛼 T corresponds to a faster cooling rate. The BM dynamics lowers the total cost function stochastically in the SA process, which is equivalent to the search for an optimized solution stochastically. The main panel of Figure 6.3.2b shows the cost function vs. the generation number for several different values of 𝛼 T , with the cooling procedure shown in the inset. A cooling procedure that is too rapid with a small 𝛼 T = 2 can lead to trapping in a local minima, whereas a cooling procedure that is too slow with a large 𝛼 T = 4 results in excessive perturbation, both of which miss the global optimization stochastically. A careful design of the cooling procedure parameter 𝛼 T , therefore, is essential for the optimum performance of the stochastic neural-network circuit in solving the combinatorial optimization problem. Figure 6.3.2 (a) The cost vs. generation for different 𝛾 values, which are the standard deviations in the distribution of V0. The effective “temperature” is 0. (b) The cost vs. generation for different 𝛼 𝑇 values in SA, whose cooling procedures are shown in the inset, with 𝛾 = 0. 138 6.4 A Machine-learning-based Method for Device-circuit Co-design of the Boltzmann Machine To design the stochastic-memristor-based neural-network circuit, the stochastic nature at both the device and circuit levels needs to be addressed. First, because the circuit characteristics are stochastic, the design objective is in the form of the expectation. Evaluating a data point of the stochastic hardware in the design space requires averaging a sufficiently large number of samples, which can be computationally expensive. Second, the relation between the design objective function and the design space parameters is unknown and can be non-convex. Third, even with a large number of samples, statistical noise still exists in the dataset. For design optimization of the stochastic neural network, we developed a new method by combining the Markov chain Monte Carlo (MCMC) simulations of the device and circuit with Bayesian optimization (BO), and show that this new MCMC-BO approach is especially suitable and efficient to address the stochastic nature. Previous application of the traditional BO method in electronics has been limited to deterministic CMOS circuitry. 243 Stochastic neuromorphic circuits discussed here, however, have fundamentally different operation principles and requires device-circuit co-design of stochastic parameters, which can be addressed by the new MCMC method. The BO can use Gaussian process (GP) as a prior, and the new data points in addition to a small initial dataset can be obtained iteratively as the next “best” guess determined by an acquisition function. 139 The method requires only a small dataset and is accommodative to a general design objective function and statistical noise in the dataset. The results for the design optimization of the BM circuit for SA by using the MCMC- BO method are shown in Figure 6.4.1. The optimization objective function, which is defined as the expectation of the cost or energy of the BM, is obtained by using the sample average approximation. 244 To achieve statistical accuracy, it is computed as the average of 5000 generations after an initial 2000 generations of the burn-in phase, whose samples are discarded, in each MCMC simulation of the BM, and it is further averaged over 100 independent chains whose initial states are random. 245 A multivariable design parameter space is formed by and 𝛼 T . In each BO step, a new “best” guess data point in the design space, which is determined by the acquisition function of the BO, is computed, and the hyper- parameters of the Gaussian process is learnt. Figure 6.4.1a shows the design objective function after 5 initial data points and 25 additional BO steps. The number of BO iteration steps determines the balance between the computational efficiency and accuracy, which can be examined by checking the predictive uncertainty of the GP model in BO as discussed below. As shown by the bottom panel of Figure 6.4.1a and the highlighted region in Figure 6.4.2a, a region around 3.1 < 𝛼 T < 3.4 and 0 < < 0.37, is identified as the near-optimal design region. In addition, we tested several types of acquisition functions using the BO optimization, and it is found that the identified optimum design region is insensitive to the specific choice of the acquisition function. 140 To quantify the predictive uncertainty of the GP model used in BO, the inset of Figure 6.4.1b shows the predictive uncertainty averaged over the entire design space (2 < 𝛼 T < 4 and 0 < < 1.0 V) vs. the BO iteration step number. The result shows a decrease in the average uncertainty in the first 15 steps, and it remains approximately unchanged subsequently. The main panel of Figure 6.4.2b, which resolves the predictive uncertainty in the design space with 30 data points, indicates that the predictive uncertainty is the smallest near the optimum region. As shown in Figure 6.4.2a, the efficiency of the design optimization method benefits from the strategy of sampling mostly in the near optimum region, especially in the later steps of BO. Alternatively, the optimization convergence can be checked heuristically by comparing the objective function from n BO steps with that from a larger m>n BO steps, by assessing the relative convergence 𝑒 𝑜 (𝑛 , 𝑚 ) = |𝑜 min 𝑛 − 𝑜 min 𝑚 | 𝑜 min 𝑚 ⁄ , where 𝑜 min 𝑛 is the minimum objective after n BO steps Figure 6.4.1 Design of the BM for SA by the MCMC-BO simulations with GP. (a) the average cost function vs. 𝛾 and 𝛼 𝑇 . Here, 𝛾 is the standard deviation in the distribution of V0, and 𝛼 𝑇 is the parameter in the cooling procedure. (b) Pseudo color plot of the uncertainty in the average cost as a function of both 𝛾 and 𝛼 𝑇 . The evaluated design points are shown by the 141 red crosses. The inset shows the average uncertainty vs. the BO step. (a) and (b) are after 5 initial data points and 25 additional BO iteration steps. . To confirm that the MCMC-BO method indeed identifies near optimum designs for the stochastic neural-network circuit, we selected a design in the identified optimum region with experimentally accessible device and “cooling” schedule parameters and assessed its performance in comparison to the designs outside this region. The existence of a region instead of a single point allows designing the “cooling” schedule parameter 𝛼 T in accordance to a given value. For example, for an experimental device with a variation of ≈ 0.15 V , it is identified that 𝛼 T ≈ 3.31 falls in the identified region. The cooling schedule starts from an initial effective “temperature” 𝑇 0 = 0.5 V and “cools” down with the exponential schedule, which falls in the range of the “temperature’ accessible by modulating the gate voltage of the experimental device as shown in Figure 6.3.1a. Figure 6.4.2b compares the statistical distribution of the cost function for this design with those of two other designs outside the optimum region. Not only the average cost of this design reduces compared to two other designs, but also the variance of the probability distribution decreases. As a result, for the optimum design, the probability of the cost to be smaller than C0=5.5, P(Cost<C0)>0.95, is larger, whereas for 𝛼 𝑇 = 4, 𝛾 = 0 and 𝛼 𝑇 = 2, 𝛾 = 0.8 V , the probabilities are P(Cost<C0)<0.03 and P(Cost<C0)<0.08, respectively. The design within 142 the optimum design space region shows clear performance advantage in terms of a smaller stochastic cost function. Figure 6.4.2 (a) The trace of the data points for the first 30 data points in BO, and the region with the optimum cost function is highlighted. (b) The stochastic distribution of the cost function for different stochastic design parameters. The results here experimentally demonstrate a tunable stochastic artificial neural device enabled by two-dimensional materials interfaced in a hybrid memristive device structure, which shows Fermi-Dirac-like activation behaviors that resembles statistical thermodynamic behaviors of Fermions. The device can provide a highly efficient, single-device realization of the artificial neurons in a stochastic neural-network realization of Boltzmann machine for solving combinatorial optimization problems with SA algorithms. To optimize the design of the Boltzmann machine, we further explore a machine-learning-based strategy to tackle the stochastic nature of the design problem. 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Abstract (if available)
Abstract
Since the successful isolation of graphene fourteen years ago, the family of two-dimensional (2D) materials has attracted tremendous interests in the research community. Unique and novel physical properties have been found or proposed in 2D materials, such as Dirac-Fermions, valley degree of freedom, Weyl Semimetal, and Quantum anomalous Hall Effect. In a perspective of electronic device engineering, the 2D layered material family contains conductors, semiconductors (both p-type and n-type) and insulators, which is promising for CMOS integration. Compared to traditional silicon electronics, 2D material devices are flexible, transparent, environmentally friendly, biocompatible, and in many circumstances, performs better. In addition, 2D semiconductors have a wide range of bandgaps from sub 0.1 eV to over 3 eV, enabling us to design infrared optoelectronic devices with small bandgap materials, build logic circuits with intermediate bandgap materials, and fabricate power electronics with large bandgap materials. With these advantages, it is desired to both explore the exotic fundamental properties of 2D materials and develop concept-new 2D material based electronic devices.
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Zhao, Huan
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2D layered materials: fundamental properties and device applications
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Viterbi School of Engineering
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Doctor of Philosophy
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Electrical Engineering
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09/23/2019
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2D semiconductors
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