INVESTIGATION OF ELECTRIC AND THERMOELECTRIC PROPERTIES OF GRAPHENE NANORIBBON ZHANG KAIWEN (M. Sc, NANJING UNIV) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF SCIENCE DEPARTMENT OF PHYSICS NATIONAL UNIVERSITY OF SINGAPORE (2012) DECLARATION I hereby declare that this thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. 1 ACKNOWLEDGEMENTS I met a lot of friends during my life of study and research in Singapore. These friends, not only accompanied me to pass through for the five years, but also helped me when I most needed. First and foremost, I would like to dedicate my deepest gratefulness to my supervisor Prof. Li Baowen. He is a rigorous physicist and talented scholar. I am very proud to be his student. What I have learned from him are not only the physics, but more importantly, the skill to deal with the real world. I‟d like to thank my supervisor Dr. Özyilmaz Barbaros who brought me to the world of graphene and guided me on experiments. He builds a lab with dedicated instruments and provides us with most convenient experimental environment. My sincere thanks to Dr. Zhang Gang and Dr Xu Xiangfan who give me their patient guidance and meticulous help. They helped me with all the background acknowledge on physics and taught me all the skills and technology on experiments. Thanks to Dr. Daniel. S. Pickard, who gives me a lot of useful advice when we work together, and Dr Manu Jaiswal for helpful discussion on my projects. Thanks to my collaborators from HIM lab, Dr.Viswanathan Vignesh, Miss Wang Yue, Miss Hao Hanfang, and Mr. Fang Chao 2 Thanks to my labmates Dr. Surajit Saha, Dr. Lee Jonghak, Dr.R.S.S. Mokkapati. Mr. Ho Yuda, Mr. Toh Chee Tat, Mr. Gavin Koon Mr. Jayakumar Balakrishnan, Dr. Ni Guangxin and his wife, Mr. Alexandre Pachoud, Mr. Hennrik Anderson. Mr. Ahmet Avsar, Mr. Orhan Kahya, Mr. Wu Jing, Mr. Huangyuan, Mr. Zhang Shujie, Mr. Ibrahim Nor, Miss Yeo Yuting, Miss Zhao Yuting, Mr. Tan, Junyou. I‟d like to thank Dr. Yang Nuo, Dr. Yao Donglai, Dr. Zhang Lifa and his wife, Dr. Chen Jie and his wife, Dr. Xie Lanfei, Dr. Ma Fusheng, Dr. Shi Lihong, Dr. Ni Xiaoxi, Mr. Liu Sha and his wife, Miss Zhu Guimei, Mr. Zhang Xun. Miss Ma Jing, Miss Liu Dan. They are not only my collegers but also close friends with so many wonderful memories during the life in Singapore. The financial support from the National University of Singapore is gratefully acknowledged. My special thanks to my husband Mr. Zhao Xiangming whose love completed and enriched my life. Last but not least, thanks to my parents. Their support and understand give me all the courage to seek improvement in life. 爸爸，妈妈，谢谢你们。 3 LIST OF PUBLICATIONS 1. K. W. Zhang, X. M. Zhao, X.F. Xu, V. Vignesh, John T.L. Thonge, V. Venkatesan, Daniel S. Pickard, B. W. Li, B. Özyilmaz, Graphene Nano-ribbon Transistors Fabricated by Helium Ion Milling, going to submit to APL, 2012 2. X. F. Xu, Y. Wang, K. W. Zhang, X. M. Zhao, S. Bae, M. Heinrich, C. T. Bui, R. G. Xie, John T. L. Thong, B. H. Hong, K. P. Loh, B. W. Li and B. Öezyilmaz, arXiv:1012.2937, Phonon Transport in Suspended Single Layer Graphene , submitted to nature material 3. K. W. Zhang, X. M. Zhao, X.F. Xu, V. Vignesh, John T.L. Thonge, V. Venkatesan, Daniel S. Pickard, B. W. Li, B. Özyilmaz, Ultranarrow Graphene Nanoribbon Fabricated by Helium Ion Milling, (poster)APS March meeting, USA, 2011 4 TABLE OF CONTENTS Chapter 1 1.1 Introduction .......................................................................... 15 Graphene: background and literature review .......................... 15 1.1.1 Graphene in carbon family .............................................. 15 1.1.2 Electronic properties of graphene.................................... 17 1.1.3 Band structure in graphene .............................................. 18 1.1.4 Band gap in graphene nanoribbon (GNR) ....................... 19 1.2 Thermoelectrical properties of graphene ................................. 21 1.2.1 Seebeck coefficient and the figure of merit ZT ............... 21 1.2.2 Thermoelectrical properties in graphene ......................... 23 1.3 Chapter 2 2.1 Objective and scope of this thesis ........................................... 24 Experimental techniques ...................................................... 26 Preparation of graphene........................................................... 26 2.1.1 Micromechanical exfoliation ........................................... 26 2.2 Experimental techniques for graphene patterning and characterization ........................................................................................ 27 2.2.1 Electron beam lithography .............................................. 27 2.2.2 Reactive Ion etching ........................................................ 30 2.2.3 Helium Ion Microscope ................................................... 31 2.2.4 Raman spectroscopy ........................................................ 32 2.2.5 Atomic force microscopy ................................................ 34 5 2.3 Experimental techniques for electrical studies ........................ 35 2.3.1 Low temperature vacuum system .................................... 35 Chapter 3 Graphene nanoribbon patterned by Helium ion Lithography ……………………………………………………………..37 3.1 Introduction ............................................................................. 37 3.2 Experimental Method .............................................................. 38 3.2.1 Graphene device fabrication ............................................ 39 3.2.2 Helium ion lithography(HIL) .......................................... 40 3.2.3 Raman spectroscopy and electrical measurement ........... 42 3.3 Experimental Result ................................................................ 42 3.3.1 HIM pattering on suspended graphene ............................ 42 3.3.2 HIM pattering on supported graphene for electrical measurement .................................................................................... 43 3.3.3 Raman spectroscopy characterization ............................. 44 3.3.4 Electrical properties characteristic .................................. 47 3.4 Chapter 4 Conclusion ............................................................................... 52 Thermal Power in Graphene nanoribbon ............................. 54 4.1 Introduction ............................................................................. 54 4.2 Sample preparation .................................................................. 55 4.2.1 Device fabrication ........................................................... 55 4.2.2 Graphene nanoribbon fabrication .................................... 57 6 4.3 Measurement and the Result ................................................... 58 4.3.1 Temperature coefficient of Resistance(TCR) for thermometers.................................................................................... 58 4.3.2 Thermal power in graphene stripe. .................................. 59 4.3.3 Thermal power in graphene nanoribbon. ........................ 61 4.4 Chapter 5 Conclusion ............................................................................... 64 Conclusion and outlook ....................................................... 66 5.1 Thesis summary ....................................................................... 66 5.2 Future work ............................................................................. 67 7 SUMMARY Graphene has been discovered in lab for only eight years. Its excellent properties make the research of this new material very important, not only for the fundamental physics but also for the application. Even more, the energy band gap opening in graphene nanoribbon (GNR) makes it a potential application material in semiconductor field. In this thesis, we developed a method to fabricate ultra-narrow GNRs which is called helium ion Lithography (HIL) using helium ion microscope (HIM). Suspended GNRs with widths down to 5nm and supported GNRs with widths down to 20nm are patterned by directly modifying graphene strips through surface sputtering by helium ions. The temperature dependent conductance measurements on supported Graphene Field Effect Transistors (GFETs) show an estimated energy gap of 13mev for 60nm wide GNR. Detailed 2D conductance measurements at low temperature reveal an enhanced characteristic energy scale for the disorder potential, which can be attributed to the damage on graphene lattice induced by helium ion bombardment and is further confirmed by Raman spectroscopy measurement. In addition, we also investigated the thermoelectric properties of GNR. GNR on Si/SiO2 substrate was fabricated by plasma etching method because of its easy and economical manipulation. Seebeck coefficient S of GNR with 8 width of ~70nm and length of 1μm was measured as a function of the back gate voltage at different ambient temperatures. At low temperatures, the Seebeck coefficient increases with increasing temperature, which can be explained by electron-hole puddles localized. However, at high temperatures, the Seebeck coefficient shows a decreasing with increasing temperature which indicates an energy gap exists. Compared with the thermoelectric properties in bulk graphene sheet, the magnitude of S is enhanced. Its optimized value occurred at 150K, which might due to the enhanced quantum confinement effect in GNR. 9 LIST OF FIGURES Figure 1.1 Graphene is the base for other dimensional graphitic materials: 0D buckyball, 1D carbon nanotube and 3D graphite (taken form reference3). ........................................................................................... 16 Figure 1.2 The atoms arrangement of graphene22 ........................................ 18 Figure 1.3 The band structure of (a) single layer graphene (b) bilayer graphene33 ............................................................................................ 19 Figure 1.4 The diagram of the Seebeck coefficient of a material (Picture taken from wikipedia) .......................................................................... 21 Figure 1.5 The diagram of thermoelectrical (a) generator and (b) cooler (Picture taken from wikipedia) ............................................................ 22 Figure 2.1 Exfoliated single layer graphene on 300nm SiO2 substrate ....... 27 Figure 2.2 The process flow of standard E-beam lithography ..................... 28 Figure 2.3 Photograph and schematic of our scanning electron microscope (Nova NanoSEM 230). ......................................................................... 29 Figure 2.4(a) EBL pattern of alignment mark, 4 marks indicated by the red circle (b) EBL pattern of Hall bar electrode (c) EBL pattern of two terminal device (d) EBL pattern of 4 terminal device. ........................ 30 Figure 2.5 The operation diagram of Helium Ion Microscpope. (Picture taken from wikipedia) .......................................................................... 32 Figure 2.6 The Energy level diagram showing the states involved in Raman signal. (Picture taken from wikipedia) .................................... 33 Figure 2.7 Typical Raman spectrum of single layer graphene ..................... 34 Figure 2.8 Block diagram of atomic force microscope (Picture taken from wikipedia) ............................................................................................ 35 Figure 2.9 Picture of low temperature system, the inset shows the details inside the probe .................................................................................... 36 Figure 3.1 Optical image of supported graphene with electrode defined by standard E-beam lithography ............................................................... 39 Figure 3.2 Direct exfoliating of graphene on pre-patterned SiO2 substrate. 10 The scale bar is 10 μm ......................................................................... 40 Figure 3.3 Demonstration of Helium ion lithography on supported graphene stripe. .................................................................................... 41 Figure 3.4(a) HIM-image on suspended GNRs with width of 20nm and 10nm respectively. Scale bar: 500nm (b) HIM-image of a suspended graphene nanoribbon with varying widths fabricated by helium-ion milling. Scale bar: 100nm. ................................................................... 43 Figure 3.5 Zoom in AFM image of the 60nm wide nanoribbon. Scale bar: 200nm. ................................................................................................. 44 Figure 3.6 (a) Raman map of integrated 2D-line intensity for helium-ion milled graphene ribbon. The white dash line emphasizes the cutting trace (b) Raman map of integrated G-line intensity (c) Raman map of integrated D-line intensity. ................................................................... 45 Figure 3.7 Raman spectrum for Location A(Loc A)marked by Blue cross in Fig. 3.6a and Location B(Loc B)marked by black cross in Fig. 3.6a. The scale bars for all images are 700nm. ............................................. 46 Figure 3.8 The conductance of GNR vs. back-gate for different temperatures from T = 6.5 K to 400 K ................................................. 48 Figure 3.9 Minimum conductance of GNR with W=60nm and L=250nm at, Gmin vs. 1/T with fits to NNH (red curve) and VRH (blue curve). Black dots denote experimental data ................................................... 49 Figure 3.10 Conductance vs. back-gate voltage at different source-drain bias at T=4.3 K. .................................................................................... 50 Figure 3.112D plot of Conductance of graphene nanoribbon with width of 60nm as a function of Vsd and Vbg at T=4.3 K. .................................... 51 Figure 4.1 Optical image of thermal power device, 1 is heater, 2 and 3 is thermometers........................................................................................ 57 Figure 4.2 Etching process for graphene nanoribbon. 1) PMMA is spin coated on top of graphene sheet; 2) etching pattern is exposure to electron beam in SEM chamber; 3) after development, cross section picture shows over dose of etching. 4) exposed part of graphene is etched by O2 plasma............................................................................. 58 Figure 4.3 Seebeck coefficient (S) of graphene with width of 5um and length of 7um as a function of backgate Vbg at temperature 15k, 50k, 11 100k, 130k,170k, 210k, 250k and290k. ............................................... 60 Figure 4.4 Seebeck Coefficient of graphene stripe at fixed backgate Vbg = 1v( Red triangle) and -50V(blue dot)................................................... 61 Figure 4.5Resistance of GNR as a function of back gate voltage V𝑏𝑔 at different temperatures 10k, 50k, 195k, 250k, and 300k. Inset is the optical picture of the device and AFM picture of the GNR. The scale bar is 500nm ......................................................................................... 62 Figure 4.6 Seebeck coefficient S of GNR (W=70nm, L=1μm) as a function of back gate Vbg at different temperatures 15k, 50k, 200k, 250k, and 300k...................................................................................................... 63 Figure 4.7 Seebeck Coefficient of graphene stripe at fixed backgate Vbg~3v( Red triangle) and 40V(blue dot) ............................................ 64 12 LIST OF ABBREVIATIONS Si Silicon 2D Two Dimensional SLG Single Layer Graphene BLG Bilayer Graphene ExG Exfoliated Graphene GNR Graphene Nano-ribbon GFET Graphene Field Effect Transistor GNR-FET Graphene Nanoribbon Field Effect Transistor SiO2 Silicon Dioxide STM Scan Tunneling Microscope CVD Chemical Vapor Deposition EBL E-Beam Lithography SEM Scanning Electron Microscope PMMA Poly(methyl methacrylate) NPGS Nanometer Pattern Generation System Cr Chromium Au Gold RIE Reactive Ion Etching K Kelvin 13 T Tesla EF Fermi Level SMU Source Measurement Unit DOS Density of States Al Aluminum HIM Helium Ion Microscope HIL Helium Ion Lithography AFM Atomic Force Microscopy EMF Electromotive Force 14 Chapter 1 Introduction Graphene, which is only one-atom thick, is now considered to be the world‟s thinnest material1. This strictly two-dimensional (2D) material was thought to be not stable and could not exist in nature. Once it was discovered in the lab, it has attracted tremendous interest and is believed to be a wonderful material for next generation electronics. This flat monolayer of carbon atoms, tightly packed into two dimensional honeycomb lattice, is the basic building block for graphitic materials of all other dimensionalities. The discovery of graphene opens a new research era for material science and its application. 1.1 Graphene: background and literature review 1.1.1 Graphene in carbon family As the thinnest known material in the universe, graphene has attracted the most enthusiasm and attention in the world. This novel material was experimentally founded by Geim‟s group using mechanically exfoliation method with scotch tape in 20041, 2. This truly two dimensional material acts as the „building block‟ of other carbon family members, shown in Fig 1.13: it can be wrapped into zero dimensional buckminsterfullerene(C 60); it can also be rolled up into widely used one dimensional carbon nanotubes, which have been extensively investigated for device applications in the last two decades4; the three-dimensional graphite in pencils can also be realized by simply stacking graphene sheets5. 15 Figure 1.1 Graphene is the base for other dimensional graphitic materials: 0D buckyball, 1D carbon nanotube and 3D graphite (taken form reference3). All of these carbon materials have been used in many applications much earlier before graphene emerged, yet many of their electronic and magnetic properties originate from the properties of graphene. Indeed, graphene has been theoretically studied to describe other carbon-based materials for around sixty years before it became a reality6, 7. Two dimensional crystals were believed to be thermodynamically unstable and unable to exist in nature8, 9, while numerous attempts at obtaining two dimensional crystals were failed10. The reason that people believed it only exists theoretically is that the thermal fluctuation in 2D crystal causes the lattice dislocations or defects at finite temperature to destabilize the crystal structure.3, 6, 7, 11 However, half a century later, Geim and his colleague cleaved the one-atom-thickness layer from bulk graphite by mechanically exfoliation2. This relatively simple technique involves repeated peeling off three-dimensional graphite, since graphene layers are only weakly coupled. 16 Taking advantage of the same method, the team has also managed to obtain free-standing two dimensional crystals of other materials such as single-layer boron nitride12. Afterwards, numerous research groups from all around world investigated this new born material13-18. The excellent properties making graphene one of the hottest topics in physics in recent years and a graphene “gold rush” has started since then. 1.1.2 Electronic properties of graphene Carbon-based systems show an unlimited number of different structures with variety of physical properties4, 19. Among systems with only carbon atoms, graphene plays an important role since it is the basis for understanding of the electronic properties in other allotropes. The discovery of both single layer graphene (SLG) and bilayer graphene (BLG) has revolutionized the physics of low dimensional systems and led to novel nanoscale device applications2, 20, 21. Within the last eight years, it helped create one of the most successful interdisciplinary research efforts driven by graphene‟s outstanding electronic, chemical, optical, and mechanical properties. 17 Figure 1.2 The atoms arrangement of graphene22 Graphene is composed of carbon atoms arranged on a honeycomb structure, and can also be thought of benzene rings stripped out from their hydrogen atoms23, which are shown in Fig 1.2. Every carbon atom has three nearest neighbors with an interatomic distance of 1.42 angstrom. Each atom has one s and three p orbitals, among which, only the perpendicular p orbital contributes to conductivity and hybridizes to form valence and conduction bands. Because the two sublattices give different contributions in the electronic structure, a pseudo-spin24 is defined for the relative contribution of the A and B sublattices, which consequently introduces chirality to graphene21, 25 . 1.1.3 Band structure in graphene The primary shape of graphene band structure consists of two conical valleys that touch each other at the symmetry point in the Brillouin zone, which 18 is called Dirac point. As shown in Fig. 1.3A, the energy spectrum varies linearly with the magnitude of momentum away from the Dirac point3. From a purely basic science point of view, the massless, chiral, Dirac-like electronic spectrum of single layer graphene with two linear energy bands touching each other at a single point is the fundamental basis for the observation of many exotic phenomena. The energy spectrum of bilayer graphene is quite different from single layer. Although it only adds one additional layer, the entirely quantum phenomena changed based on the massive nature of bilayer‟s chiral Dirac fermions26-32. By broking the sublattice symmetry, the spectrum is made of four massive Dirac bands (two conduction bands, two valence bands) and has hyperbolic dispersion relation. In this situation, the band gap opens29, as shown in Fig. 1.3B. Figure 1.3 The band structure of (a) single layer graphene (b) bilayer graphene33 1.1.4 Band gap in graphene nanoribbon (GNR) The band gap opening in bilayer graphene makes it a potential material in 19 semiconductor field27, 34, 35. In spite of broking A-B symmetry in bi-layer graphene, quantum confinement induced by cleaving graphene to quasi one-dimensional GNR36-40, is considered as another widely used way to create energy band gap in graphene based devices. Theoretical works using Zone-folding approximation41, π-orbitial tight-binding models42, 43 and first principle calculations44, 45 predict the band gap Eg of a GNR scaling as Eg = α/W with the GNR width W, where α ranges between 0.2-1.5, depending on the model and the crystallographic orientation46. However, these theoretical estimates can neither explain the experimentally observed energy gaps of etched nanoribbons of widths beyond 20 nm, which turn out to be larger than predicted, nor explain the large number of resonances found inside the gap39, 47, 48. On the other hand, numerous methods are invented to fabricate GNR, including plasma etching48, 49 , atomic force microscopy anodic oxidation50, scanning tunneling microscopy lithography51, as well as chemical methods including chemical derived techniques52-54 and anisotropic etching55. However, these processes presently lack control over the width, orientation and layer number of graphene. Recently, Helium-ion lithography (HIL) shows powerful ability for patterning GNR because of its high resolution56, 57 . Suspended GNR with width of 10nm was achieved by this method57, while there is lack of study on the GNR‟s properties. In my thesis, GNR fabricated by HIL will be studied. 20 1.2 Thermoelectrical properties of graphene 1.2.1 Seebeck coefficient and the figure of merit ZT The energy loss in industry is a great waste. Approximately 90 per cent of the world‟s power is generated by heat engines that use fossil fuel combustion as a heat source. The heat engine typically operates at 30-40 per cent efficiency. As a result, roughly 15 terawatts of heat is lost to the environment58. Thermoelectric device could potentially convert part of this low-grade waste heat to useful electricity. The thermopower or Seebeck coefficient, represented by S, of a material measures the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material as shown in Fig. 1.4. S=− ∆𝑉 ∆𝑇 Figure 1.4 The diagram of the Seebeck coefficient of a material (Picture taken from wikipedia) At the atomic scale, the applied temperature gradient causes charged carriers in the material to diffuse from the hot side to the cold side. Based on 21 this mechanism, thermoelectric cooler or generator is built, as shown in Fig. 1.5. Carriers flow through the n-type element, crosses a metallic interconnect, and passes into the p-type element. If a power source is provided, the thermoelectric device acts as a cooler. Electrons in the n-type element move opposite the direction of current and holes in the p-type element will move in the direction of current, both removing heat from one side of the device. When a heat source is provided, the thermoelectric device works as a power generator. Figure 1.5 The diagram of thermoelectrical (a) generator and (b) cooler (Picture taken from wikipedia) For a material to be a good thermoelectric cooler or generator, it must have a high thermoelectric figure of merit, ZT. The figure of merit is defined by: ZT = S^2 ∗ σ/к Where S is the Seebeck coefficient, σ is the electrical conductivity, and к is the thermal conductivity. It has been challenging to increase ZT>1, since the parameters of ZT are generally interdependent58-60. Increasing the thermoelectric power S for a material also leads to a simultaneous decrease in 22 the electrical conductivity. Also, an increase in the electric conductivity leads to a comparable increase in the electronic contribution to the thermal conductivity. Thus, bulk materials have a limited ZT. The highest ZT for bulk material report to date is about 2.4 in Be2Se361-63. However, recent studies have suggested that the value of ZT may become significantly higher by incorporating nanostructures into bulk materials or use low dimensional structures. The use of low-dimensional systems for thermoelectric application is mainly due to: a) enhance the density of states near E , leading to an enhancement of the Seebeck coefficient; b) decrease of phonon conductivity by increasing the boundary scattering. 1.2.2 Thermoelectrical properties in graphene Graphene, which is a 2D material, can provide such quantum confinement effect for the application on thermoelectric material. Large thermopower has been discovered experimentally in single layer graphene64. Unfortunately, due to the large thermal conductivity in graphene15, 65-67 , figure of merit in graphene is much smaller than 1, which prevents the graphene from heat engineering application. On the other hand, Theoretical works have proved that thermopower can be significantly enhanced in functional graphene material, such as GNR68-71, graphane68, 72, 73 (Hydrogenated graphene), due to band gap opening. Although this enhancement has not been observed in 23 gapped dual gate bilayer graphene due to charge puddles near the CNP74, the optimized value occurs at 100 Kevin provides an opportunity for low-T thermoelectric application. As a result, experiment work is also needed to investigate the thermoelectric properties in gapped GNR. 1.3 Objective and scope of this thesis In the first part of this thesis, the main focus is to pattern graphene sheet in to quasi-one dimensional graphene nanoribbon with the help of helium ion beam sputtering. Band structure is modified after the ion beam cutting and the energy gap opens. The effect of helium ion bombardment to graphene is analyzed. The second part investigates the thermoelectrical properties changes in graphene nanoribbon compared to graphene sheets. The thesis is organized as follows: Chapter 2 introduces the methods of preparing graphene samples and an overview on experimental techniques used in this thesis. Experimental results are presented in Chapter 3 and Chapter 4. In chapter 3, we introduce the method of preparing graphene nanoribbon from graphene sheet both on suspended substrate and supported substrate. We show that the width of the GNR in this method can be narrowed down to 5nm on suspended samples and 20nm on supported ones. Electrical properties characterization of the supported GNR with width of 60nm shows the energy band gap opening in later part of this chapter. In chapter 4, we study the thermoelectric properties of graphene based devices. First, we study the 24 thermoelectrical properties in graphene sheet. Then, we investigate the thermopower in GNR. We find that the enhancement of thermal power may due to the opening of a band gap in GNR. Moreover, the temperature behavior of GNR‟s thermopower at low temperature region deviates from that of gapped semiconductor materials. This could be explained by the electron hole puddles in GNR. The conclusion and outlook will be presented in chapter 5. 25 Chapter 2 Experimental techniques 2.1 Preparation of graphene 2.1.1 Micromechanical exfoliation In 2004, graphene was first experimentally discovered by Geim‟s group using micro-mechanical exfoliation method. This method is simple and convenient, but it provides high quality and enough sample sizes for academic research. The details of the method are as following: A small high quality graphite piece is selected as the seed. Two clean pieces of scotch tapes are used to stick the two faces of the graphite piece, and then separated gently. This is called one step of exfoliation. The initial graphite piece will become two parts sticking on each tape, in which one part is selected as the seed for next exfoliation. The exfoliation is repeated until a fairly thin and more or less transparent graphite piece can be found on one tape. Then this tape is carefully transferred onto a 300 nm SiO2 wafer. After transferring, graphene can be observed on 300nm SiO2 surface under optical microscope. The exfoliation method relies on two factors: first, the arrangement of carbon atoms in graphite forms layer structure. Each carbon atom is bonded to three other atoms inside a layer; however, each layer is only weakly coupled by Van der Waals force. As a result, graphite is easily been separated into pieces during exfoliation. Second, graphene has a relatively high optical contrast on 26 300nm SiO2 substrate which makes the location of graphene piece on substrate become possible, as shown in Fig. 2.1. Figure 2.1 Exfoliated single layer graphene on 300nm SiO2 substrate 2.2 Experimental techniques for graphene patterning and characterization 2.2.1 Electron beam lithography Electron beam lithography is a lithography technique that uses a focused electron beam in a patterned fashion on a resist layer to selectively either remove or retain exposed area. Among the various lithography techniques, the EBL enable the fabrication scale down to around 10nm, which is much higher than photolithography or ion beam lithography. This advantage makes the EBL the key technique in the nano-fabrication area. EBL is also the main lithography method used in this thesis. The details of the EBL process are described as following: First, a thin layer of resist is spin-coated onto a targeted substrate, which is SiO2 in our case. A specific designed pattern is generated using the Nanometer Pattern Generation 27 System (NPGS). The pattern can be alignment mark, etch mask, hall bar electrode or any other specific shape. This pattern is then incorporated into the SEM by the NPGS software. The area of the resist which is exposed to the beam with a specific time will become more soluble in the developing process, due to the reduced molecule weight of the resist. As a result, the design pattern will be generated on the resist after developing process. The process flow is shown in Fig. 2.2. Figure 2.2 The process flow of standard E-beam lithography In this thesis, the lithography process is performed using the FEI Nova NanoSEM 230 Scanning Electron Microscope, as shown in Fig. 2.3. 30KV was selected for the beam voltage to get high resolution. PMMA A4 is selected as the polymer resist for the EBL. The developer is a mixed solution of MIBK and IPA with the ratio of 1:1. 28 Figure 2.3 Photograph and schematic of our scanning electron microscope (Nova NanoSEM 230). There are three main types of patterns we generated by the EBL. First is the alignment mark, which serves as a function of alignment for the next step EBL. The graphene flake recognized under optical microscope and located with respect to the corner of the wafer. The x and y axis of the graphene flake determined by this method is not accurate enough to be directly patterned by SEM. As a result, a more detailed and nanometer scale alignment mark is exposed and developed first to surely cover the graphene flake, as shown in Fig. 2.4a. This alignment mark which can be observed in SEM provides nanometer scale accuracy for the following EBL process. The second type of pattern is the etch mask which serves a function of defining the graphene‟s geometry. The shapes of exfoliated graphene are usually random, which are not suitable for the electrical measurement. The unwanted area of the graphene flake is exposed by the EBL process while the other part is covered with the PMMA resist. Then, the unwanted area is removed by the reactive ion etching described in the following section while the 29 other part is protected by the resist. The third type of pattern is the designed metal electrodes, such as hall bar, two terminal device, four terminal device and thermal power measurement device, as shown in Fig. 2.4 (b-d). After the designed area is exposed, the wafer was thermally evaporated with metal contacts, which is chromium and gold in our case. After evaporation, the whole device is dipped into acetone for a few hours to remove the left PMMA resist, and to lift-off the unwanted metal on top of PMMA resist. As a result, a metal electrode is formed for the following electrical measurement. Figure 2.4(a) EBL pattern of alignment mark, 4 marks indicated by the red circle.scale bar:50 μm (b) EBL pattern of Hall bar electrode, scale bar: 20 μm(c) EBL pattern of two terminal device. Scale bar: 50μm (d) EBL pattern of 4 terminal device. Scale bar:5 0μm 2.2.2 Reactive Ion etching Reactive ion etching is an etching technique used in many micro 30 fabrication processes. Chemically reactive plasma is generated by an RF source under low pressure: electromagnetic field generated by the RF source will stripe the electron of gas atoms and produce positive ions. The electrons striped by the electromagnetic force will build up a potential drop, which is usually several hundred volts, across the targeted substrate and the top plate. This potential difference will drive the positive ions onto the targeted substrate and remove the material with both chemical reaction and physical bombard. In our experiment, oxygen is used as the source gas for etching graphene, since the oxygen ions are easily reacted with carbon atoms. The RF power is usually selected to be 20W, which will generate an etching speed of around 20 layers per minute. 2.2.3 Helium Ion Microscope Helium ion microscope is the new member of the microscope family based on a scanning helium ion beam. It has some unique properties compare with electron beam and focused ion beam: first, the helium ions have much smaller de Broglie wavelength (small diffraction effect) than electrons, which leading to a much higher resolution (around 0.25 nm) than SEM; second, it has a much lower sputtering effect than the focused ion beam due to the relative light mass of helium ions. The small diffraction effect combined with high resolution make it an ideal tool for direct cutting and patterning of ultra-thin materials. 31 In addition to the high spatial resolution, the shallow escape depth (~1nm) of the He ions excited secondary electrons provide images with good surface contrast. Furthermore, the electron flood gun removes the charging effect on the sample, which makes the HIM able to image non-conducting samples. The operation diagram is shown in Fig. 2.5a. The helium ions are generated around the sharp tip (around 1 to 3 atoms) and accelerated down a column with a series of alignment, focus, and scanning elements, that landing on the sample with a diameter of around 0.75 nm. The numbers of secondary electrons detected by the ET detector determine the gray scale of each image point. Figure 2.5 The operation diagram of Helium Ion Microscpope. (Picture taken from wikipedia) 2.2.4 Raman spectroscopy Raman spectroscopy is a spectroscopic tool which is usually to detect the vibrational, rotational or other low frequency modes in different material. It relies on the inelastic scattering of sample molecules with photons which 32 usually come from the incident laser. The incident photons interact with the molecule vibrations, phonons and other excitations in the system, which provide red or blue shift of incident photons‟ frequency, as shown in Fig. 2.6. The Rayleigh scattering signal, in which the frequency doesn‟t change, is filtered out by the analyzer, while the rest of the two scattering signals are collected. Figure 2.6 The Energy level diagram showing the states involved in Raman signal. (Picture taken from wikipedia) Raman spectroscopy is widely used in graphene community to determine the graphene parameters, such as number of graphene layers, strain in graphene, graphene quality, as well as graphene temperature. Fig. 2.7 is the typical Raman signal of a graphene piece lie on top of SiO2 substrate. There are three typical peaks in the graphene‟s Raman spectrum, the D band, G band and 2D band. The D band appears due to the lattice defect or molecule absorbers, the G band indicates the vibrational state of graphene‟s sp2 bonding, while the 2D band shows the stacking of graphene layers. 33 Figure 2.7 Typical Raman spectrum of single layer graphene. A lot of experiments were done to study the Raman signal response of graphene under difference conditions. Ferrari, et al, demonstrated that the G band intensity and 2D band FWHM will increase while the layer of graphene increases75. The difference of the signals is quite obvious that it makes Raman spectroscopy an ideal method to determine the layer of graphene. Raman spectrum is also used to study the hydrogenation of graphene and its reverse effect68. The emerging of the D band after the hydrogenation of graphene indicates the attachment of hydrogen atoms on the graphene lattice, while the decrease of D band intensity shows successfully recover of hydrogenated graphene back into pristine graphene. Mohiuddin, et al, show that while the strain in graphene lattice changes, the frequency of G band will shift left or right76. Balandin, et al, show that while the temperature of graphene changes, the frequency of 2D band will change accordingly15. 2.2.5 Atomic force microscopy 34 Atomic force microscope is a high resolution scanning probe microscopy, which relies on the interaction between the tip and the surface of the sample. Piezoelectric parts are used to precisely manipulate the tip in x and y directions in nano-scale range. A laser combined with a photo detector is used to determine the z position of the tip as shown in Fig. 2.8. The resolution of AFM in z direction can reach to orders of fractions of a nanometer. Figure 2.8 Block diagram of atomic force microscope (Picture taken from wikipedia) Due to AFM‟s high resolution in z axis, it is mainly used to determine the thickness and surface morphology of graphene. Moreover, the tapping mode of AFM provides a nondestructive method compared to other microscope such as SEM or HIM. 2.3 Experimental techniques for electrical studies 2.3.1 Low temperature vacuum system 35 The electrical measurements in this thesis are mainly conducted in the low temperature vacuum system from Cryogenic Pte Ltd, as shown in Fig. 2.9. After the wafer is bonded on the delicated LCC package, the package is loaded into the probe of the system with wires conducted out to the SMU and lock-in measurement units. The chamber of the wafer in the probe can be pump to a vacuum level of 1e-4 mbar. The cooling power of the system comes from the Pulse Tube with a compressor of 100W. The temperature of the system is controlled by a Lakeshore 340 temperature controller. Figure 2.9 Picture of low temperature system, the inset shows the details inside the probe 36 Chapter 3 Graphene nanoribbon patterned by Helium ion Lithography 3.1 Introduction Graphene, a two dimensional atomic-thin layer of hexagonally arranged carbon atoms, is widely considered to be a promising candidate for future nano-electronics due to its high mobility1, 14, 77, stability33 and high thermal conductivity15. Charge transport of graphene is totally different from conventional semiconductor materials due to its linear energy dispersion relation33. This unique structure is the key for the superior properties of graphene. However, lacking an energy band gap in graphene‟s band structure limits its application in semiconductor industry: graphene based field-effect transistors (FETs) show a limited current on-off ratios due to the absence of band gap.49 A number of approaches have been proposed to induce a band-gap. A non-zero band gap can be induced in graphene by breaking the inversion symmetry of the AB-stack in bi- or trilayer graphene28, 78-80 , but it is very difficult to control the exact number of layers during fabrication. Alternatively, quasi-one-dimensional confinement of the carriers in graphene nanoribbons induces an energy gap in the single-particle spectrum39, 48, 49 . Lithographic etching is reported as the earliest and most convenient method to produce GNRs from graphene sheet. However, standard e-beam lithography gives only access 37 to 20 nm and above size range, and only with specialized processing81. Several alternative methods have been developed to produce GNRs, including chemical sonication of exfoliated graphite54, controlled nano-cutting with metal particles82, etching with physical masks (e.g. nanowires)83, or unzipping of multi-wall carbon nanotubes53, 84 . However, these processes presently lack control over the width, orientation and layer number of graphene. Recently, a high on/off ratio (which can exceed 104 at room temperature) is achieved in suspended GNRs even with 150nm in width16, representing a significant breakthrough in the field of graphene-based electronics. According to the quantum confinement effect, an even higher on-off ratio could be expected for narrower GNR. However, most current lithography methods are based on resist (such as PMMA) patterning, which is not suitable for suspended devices49, 81. Recently, Helium-ion lithography (HIL) shows powerful ability for patterning GNR because of its high resolution and resist-free characteristics56, 57. Suspended GNR with width of 10nm was achieved by this method, while there is lack of study on the GNR‟s properties. In this thesis, we demonstrate the capability of HIL to fabricate the ultra-narrow suspended and supported graphene nano-ribbon. And the electronic transport of supported GNR fabricated by HIM is studied. 3.2 Experimental Method 38 3.2.1 Graphene device fabrication Supported graphene was exfoliated from natural graphite, and transferred to 300nm SiO2/Si substrate. Standard E-beam lithography is used to predefine the graphene stripe and metal contact as shown in Fig. 3.1. The graphene stripes have around 200nm in width and 1μm in length. The short width and length is to facilitate the following Helium ion pattering process. Figure 3.1 Optical image of supported graphene with electrode defined by standard E-beam lithography Suspended graphene sheet was fabricated by direct exfoliation from graphite on pre-patterned SiO2 substrate, as shown in Fig. 3.2. The diameter of pre-patterned hole is around 3 μm and the depth is 300nm. After exfoliation, the device was annealed at 300 degree in Ar/H2 environment for 3 hours in order to remove the glue residue. 39 Figure 3.2 Direct exfoliating of graphene on pre-patterned SiO2 substrate. The scale bar is 10 μm 3.2.2 Helium ion lithography(HIL) Helium ion lithography is carried out using Helium Ion Microscope (Zeiss Orion system), operated at ~43kV acceleration voltage with a beam current of 0.6pA. The ion-beam control uses a modified Nanometer Pattern Generation System (NPGS, Nabity). The HIL process is demonstrated as in Fig. 3.3. A focused ion beam is designed to scan a double U shape on the graphene stripe, which result in a narrow graphene nanoribbon in the centre. The graphene area which is exposed to the ion beam is removed by the ion bombard. 40 Figure 3.3 Demonstration of Helium ion lithography on supported graphene stripe. The fabrication of these GNRs using HIL requires an ultra-clean sample surface. There are two reasons for this: first, the surface impurities will block the helium ion beam from cutting the graphene, which will result in inconsistent edges of GNR while cutting; second, the surface impurities tend to scatter the helium ions, which will damage the bulk GNR. To obtain a clean surface in our samples, we perform a three step annealing process: First, graphene flakes are annealed at 3000C under Argon-Hydrogen environment (5% H2) to remove exfoliation related glue residues. Subsequent to metal electrode deposition, the graphene is annealed again at 2500C under same conditions. In the final step, the sample is mounted on a heating stage located in the HIM chamber. This allows for in-situ annealing under vacuum conditions to remove organic contaminants prior to helium-ion patterning. Simultaneously, with the vacuum annealing, an UV exposure is also used to 41 clean the graphene surface from amorphous-carbon related contaminants. 3.2.3 Raman spectroscopy and electrical measurement The graphene is characterized by the Raman spectroscopy before and after cutting. The Raman spectroscopy used in this thesis is WITec CRM200 Raman system with 532nm excitation laser. The power is blow 0.3mW to avoid damage to the graphene sheet and the laser spot diameter is around 400nm. The conductance measurements on our GNR field-effect transistors (GNR-FETs) were carried out using the standard combination of Keithley 6221 current source and Keithley 2182A nano-voltmeter. A current-reversal technique is used to cancel the effects of thermal electromotive force (EMF) in the voltage test lead connections. 3.3 Experimental Result 3.3.1 HIM pattering on suspended graphene Fig. 3.4a shows a HIM image of GNRs with width of 10nm and 20nm, which are suspended on the substrate with pre-etched holes. Fig. 3.4b shows a suspended GNR, the width of which varies from 5nm, 10nm to 20nm in a staircase-like pattern (dark area is the cutting trace). This demonstrates that HIM is able to consistently pattern the suspended graphene sheet into minimum 5nm ribbon. 42 Figure 3.4(a) HIM-image on suspended GNRs with width of 20nm and 10nm respectively. Scale bar: 500nm (b) HIM-image of a suspended graphene nanoribbon with varying widths fabricated by helium-ion milling. Scale bar: 100nm. 3.3.2 HIM pattering on supported graphene for electrical measurement We also fabricate supported GNR devices for the properties study. Fig. 3.5 shows the AFM image of 60nm wide supported GNR. We fabricated dozens (>30) of supported GNRs device with width ranging from 20nm to 100nm using above procedure. 43 Figure 3.5 Zoom in AFM image of the 60nm wide nanoribbon. Scale bar: 200nm. 3.3.3 Raman spectroscopy characterization We first examine the influence of helium-ion sputtering on the graphene surface by Raman spectroscopy. The 2D Raman maps of intensity of G-band, second-order Raman band and D-band are plotted in Fig. 3.6 (a-c). Brighter colour shows higher intensity. In Fig. 3.6a, the white dashed line indicates the cutting trace and the source (drain) area is marked with S(D). The height of the D peak in Fig. 3.6c indicates the disorder induced during fabrication. 44 Figure 3.6 (a) Raman map of integrated 2D-line intensity for helium-ion milled graphene ribbon. The white dash line emphasizes the cutting trace (b) Raman map of integrated G-line intensity (c) Raman map of integrated D-line intensity. We select two locations: location A(Loc A) is located in the centre of the GNR and location B(Loc B) is located adjacent to the GNR. These two locations are marked in Fig. 3.6a and the respective Raman spectrum (blue and 45 black curves respectively) is shown in Fig. 3.7. Raman spectrum for the individual curves is normalized to its respective G peak intensity for easy comparison. The Raman spectrum at Loc A (blue curve) exhibits two new sharp features appearing at 1356cm-1 (D-band) and 1626cm-1 (D‟-band), as a consequence of increased disorder. The ID/IG intensity ratio between the disorder-induced D-band and the characteristic pristine graphene G-band is as high as 2.1. The FWHM of second-order Raman band at 2705cm-1 broadens to 47cm-1. Figure 3.7 Raman spectrum for Location A(Loc A)marked by Blue cross in Fig. 3.6a and Location B(Loc B)marked by black cross in Fig. 3.6a. The scale bars for all images are 700nm. Far away from the cutting line, which is the location B, the Raman spectrum shows features similar to pristine graphene. The D peak intensity is much smaller than the D peak intensity in Location A. This demonstrates that 46 the graphene damage is only located along the cutting line. The further away of the cutting line, the less the damage. Yet the result qualitatively showed that there is a higher defect density in the 0.4 micron spot measured on the ribbon than far away from the ribbon. However, the ion bombardment and back-scattering effects do introduce additional disorder. To get further insight into the characteristics in our samples, charge transport was investigated down to low temperatures in helium-ion patterned supported GNRs. 3.3.4 Electrical properties characteristic The electrical transport measurement of GNR was done from 4.2K to 400K at vacuum condition. Before measurements, the samples are in-situ annealed at 400 K under high vacuum conditions to remove loosely attached ad-atoms and water absorbents. The GNR with width range from 60nm to 100nm were measured. We selected a typical device with width of 60nm discussed as following: The conductance of a 60 nm patterned GNR-FET is plotted as a function of back-gate voltage at different temperatures in the inset of Fig. 3.8. The conductance of GNR shows a bipolar feature similar to pristine graphene. At the charge neutrality point (Vg ~ 30 V), the conductance reaches minimum at all the temperature ranges. While the temperature drops, the conductance of GNR 47 drops at all temperature range, which is different from that in pristine single layer graphene. This phenomenon indicates that the GNR is defective85. At low temperatures, the strong insulating behavior around the charge neutrality point indicates the formation of a transport band gap81. Figure 3.8 The conductance of GNR vs. back-gate for different temperatures from T = 6.5 K to 400 K The plot of minimum conductance as a function of temperature is shown in Fig. 3.9. At high temperature range, the transport can be described within the thermal-activation theory, Gmin ~ exp( Ea / 2kBT ) , where the activation energy Ea  13meV is obtained by a linear fit to the Arrhenius plot. This value of the gap is somewhat larger than the case for other lithographically formed nanoribbon with the same width described in literature and can be better compared with the gaps for ~ 40 nm pristine GNRs, reported previously39, 86. This indicates the possibility that the effective ribbon width for our device is smaller than the geometrical value because of the strongly defected edge of the ribbon. 48 At low temperatures, the conductance deviates from the linear behavior of thermal activation. Similar to the plasma-etched nanoribbons, the behavior in this regime is consistent with the variable range hopping (VRH) mechanism, where G min 1/ (1 D ) ~ exp( T / T0 ) . Here, T0 indicates the characteristic temperature scale for the localized states, and D is the dimension of the VRH. The best fit to the data at low temperatures is attained with D=2, indicating a two dimensional VRH. Figure 3.9 Minimum conductance of GNR with W=60nm and L=250nm at, Gmin vs. 1/T with fits to NNH (red curve) and VRH (blue curve). Black dots denote experimental data We also study the transport gap for the defective nano-ribbon by measuring the conductance of the GNR at temperature of 4.3 K with varying global gate and source-drain bias. Fig. 3.10 shows the conductance of GNR on the same device discussed in the previous section. The conductance of graphene nanoribbon is suppressed in a large back-gate range near the charge neutrality 49 point at low bias. Using the method as described in references39 , we obtained the estimate of the back-gate width of conductance suppression, V bg ~ 50V , by extrapolating the slope of the smoothed dG/dVg in the on-state regions to zero. This back-gate conductance gap represents a disorder energy-scale rather than a transport-gap energy-scale. Although previous experiments suggest that these two energy scales are linearly dependent for GNRs of varying width39, the constant of proportionality represents the level of disorder in the system. In the present case, the large voltage-span for back-gate suppression reflects the enhanced disorder potential rather than an increase in the transport gap. This is consistent with the observations made from Raman spectroscopy that helium-ion milling of GNRs results in additional damage to the graphene lattice from the back-scattered Helium ions. Figure 3.10 Conductance vs. back-gate voltage at different source-drain bias at T=4.3 K. 50 In addition to suppression of conductance at small bias, the 2D conductance plots also reveal a series of resonances which are characteristic of GNRs. These peaks indicate the resonant conduction paths through localized states inside the transport gap, which is in agreement with other experimental works for disordered GNR86. At larger source-drain bias, the suppressed region becomes smaller. At the source-drain bias around 50mV, the conductance of the ribbon is fully activated. Figure 3.11 2D plot of Conductance of graphene nanoribbon with width of 60nm as a function of Vsd and Vbg at T=4.3 K. A more detailed 2D map of conductance as a function of global gate and source-drain bias is plot as shown in Fig. 3.11. We obtained the energy scale eVsd of ~ 50 meV for this device. This value of the energy scale in the bias direction is surprisingly close to the value of intrinsic band-gap of a 60 nm GNR 51 due to quantum confinement (Eg ~ 60 meV), following theoretical estimates that also include electron-electron interactions87, 88 . However, this must be interpreted in light of the strong disorder potential seen from the back-gate dependence. In plasma-etched GNRs, the transport-gap obtained from the 2D conductance plots can be related to the energy of the smallest charged-puddle along the length of the GNR86. The charging energy of this island is typically governed by the width of the GNR. In case of helium-ion milled GNRs, the additional lattice damage produces new localized states near the neutrality point of the energy spectrum. The formation of these mid-gap states is already known for the case of bulk graphene due to lattice damage or attachment of ad-atoms68, 89 . Therefore, an accurate description of the transport-gap for our system needs a more detailed analysis to account for this additional disorder within the charged graphene islands. 3.4 Conclusion In summary, we successfully fabricated suspended and supported graphene nanoribbons using helium ion lithography. Suspended GNRs were patterned to widths down to 5nm, while the smallest width for supported GNR was 20 nm. In addition, supported GNR-FETs with width of 60nm were fabricated and characterized for transport properties. The disordered energy-scale is strongly enhanced in our system as suggested by the large back-gate voltage-span of 52 conductance suppression. This behaviour can be explained by the large disorder induced by the back-scattering of helium ions, which is further confirmed by Raman mapping. 53 Chapter 4 Thermal Power in Graphene nanoribbon 4.1 Introduction Thermoelectric properties (TEP) of graphene have been investigated both theoretically69, 72, 90-93 and experimentally64, 74, 94, 95 . Kim et al.64 discussed temperature and carrier density dependence of the thermal power in graphene experimentally in 2009 and found that the linearity of thermopower in temperatures at fixed doping level can be explained by Mott relation fitting96. This suggests a diffusive thermopower in graphene. The maximum value of thermopower or Seebeck coefficient is around 80μv/K , appeared near the central neutrality point. Near zero carrier concentration, the observed result of S explicitly departures from the formula ∝ 1/√𝑛 given by Boltzmann theory with 𝑛 as the number density of the charge carriers. Hwang et al. have proposed the electron-hole-puddle model to explain the experimental observed transport at very low doping. By this model, local carrier density is finite and total transport coefficients are given by the averages of the semi classical Boltzmann results in the puddles. In addition, TEP of high mobility graphene also been experimentally investigated by Wu et al..94 The Failure of the Mott relation could indicate importance of the electron-electron interaction in high mobility samples near CNP. Different from single layer, the energy band gap opens in a bilayer 54 graphene would lead to an enhancement in thermopower. This has been predicted theoretically97. Experiment work has done by Chen et al.98 on a dual gated bilayer graphene and showed that, inside the gap regime, temperature linearity will be broken and the optimized value of S achieves at around 100K. The phenomena in bilayer graphene from band gap opening could occur in gaped GNR or functional graphene device with the same reason. Theoretical work predicts a significant enhancement of Seebeck coefficient in ultra-narrower GNR69, 71 and graphane72. The decrease of thermal conductivity and increase of thermoelectrical power factor make graphene a possible candidate for energy engineering. In our work, we measured the TEP in graphene nanoribbons. Our samples were prepared using electron beam lithography combined with plasma etching. The enhancement of the magnitude of Seebeck coefficient with width of 80nm compared to two-dimensional graphene stripe indicated that the gap opening in this particular GNR device do affected the thermal power signal. Moreover, the change of thermopower as a function of temperature is nonlinearity. 4.2 Sample preparation 4.2.1 Device fabrication Graphene was mechanically exfoliated and transferred to the SiO2 substrate as described in chapter 2. Heater and thermometers are defined with standard 55 electron beam lithography (see in chapter 2), followed by Cr/Au(5/35nm) evaporation and lift off in hot acetone. Fig4.1a displays an optical image of a graphene thermopower device. For thermal power measurement, at least three electrodes, two thermometers and one heater, are needed. Electrode 1 is the heater, and Electrode 2 and 3 are two thermometers. Each of these two thermometers is connected to 4 wires, so that their resistance can be measured accurately by 4-probe measurement. Depending on the size of the graphene flakes, the distance of the thermometers can vary from 2 μm to7 μm, while the heater is fabricated as close as possible to electrode 2 to generate a temperature gradient efficiently. The distance usually varies from 700 nm to 1 μm in our devices. In order to get a uniform thermal distribution perpendicular to the channel (or along the thermometer electrodes), the length of the heater is designed larger than the thermometers. Oxygen plasma etching is used to isolate the graphene flake electrically from the heater. After wire bonding, the device is loaded in to the chamber of Vacuum system for measurement. 56 Figure 4.1 Optical image of thermal power device, 1 is heater, 2 and 3 is thermometers. 4.2.2 Graphene nanoribbon fabrication After device fabricating, graphene sheet needs to be further etched to quasi-one dimensional graphene nanoribbon. We use the plasma etching method for fabrication GNR in this experiment. This method was considered as simplest and most economical method and was widely used for fabricating GNR. The process is described in Fig 4.2. First, a layer of PMMA A5 was spin-coated on top of graphene sheet. The thickness of the PMMA layer is around 400nm and quite uniform which make sure of the stable etching result. Etching pattern is edited and designed by NPGS and Design CAD. The pattern is later exposed under SEM with critical dose of electron beam (see in Fig 4.2.2). A little bit over dose will help to get narrower graphene nanoribbon. After developed (Fig 4.2.3), the sample was transferred into the chamber of Reactive Ion Etching (RIE), and the unprotected part was etched by O2 plasma. 57 Figure 4.2 Etching process for graphene nanoribbon. 1) PMMA is spin coated on top of graphene sheet; 2) etching pattern is exposure to electron beam in SEM chamber; 3) after development, cross section picture shows over dose of etching. 4) exposed part of graphene is etched by O2 plasma. 4.3 Measurement and the Result 4.3.1 Temperature coefficient of Resistance(TCR) for thermometers Before the thermopower measurement, the Temperature coefficient of Resistance (TCR) for the two thermometers is calculated. The TCR is the relative change of the resistance R of thermometer when the temperature is changed by 1 Kelvin R(T) = R(T0 )(1 + α∆T) Where T0 is the reference temperature and ΔT is the difference between T and T0. Finally, α is the linear temperature coefficient. With this fixed α, we can calculated the temperature changes when resistance changes, vice versa. After loading the sample in to Vacuum system, the resistances of the two 58 thermometers are measured with temperature slowly decreasing from 300K to 4K. The curve slot at fixed temperature point is used as α. This figure will be recorded for calculating the temperature gradient later in thermopower measurement. 4.3.2 Thermal power in graphene stripe. We first study the thermal power in two-dimensional graphene sheet. The optical picture of the device is shown in Fig 4.1. An ac current is applied to heater 1 to generate a temperature gradient cross the graphene( or along the two thermometers 2 and 3). Potential difference is then generated because that the carriers keep moving from the hot side to the cold side. ∆V is measured across the electrode 2 and 3. With the same applied ac current on the heater, we also measure the resistance changes of the two thermometers. Combined with the TCR, temperature difference is calculated. Thus, Seebeck coefficient can be obtained by the equation: S = ∆V/∆T. In Fig 4.4, thermopower of graphene stripe with width of 5 μm and length of 7 μm is measured as a function of V𝑏𝑔 from 15K to 300K. The sign of the S, which indicates the sign of the majority charge carriers, changes from positive to negative when across the CNP. Away from CNP, the magnitude of Seebeck coefficient is slightly decreased with increasing carrier density which is manipulated by the back gate voltage Vbg. According to the Boltzmann 59 formulation64, the Seebeck efficient can be considered as the entropy transport per unit charge97. This can provide us as a qualitative understanding of the behavior of graphene thermopower‟s temperature dependence. While the Fermi level is far away from the Dirac point, the electrons are highly degenerate and only portions of T/EF transport with entropy. As a result, the Seebeck coefficient is proportional to the temperature at high carrier densities. However, close to the charge neutrality point, both electrons and holes exist in graphene due to the charge inhomogeneity in graphene surface. Contribution of Seebeck effect from both electrons and holes will cancel each other and the absolute |S| will decrease as the carrier density decrease. Since the electron-hole puddle99 exists in almost all the graphene devices near the charge neutrality, the non-degenerate limit is hard to achieve. In our experiment, the maximum S at 300K is around 53μv/K . Figure 4.3 Seebeck coefficient (S) of graphene with width of 5 μm and length of 7 μm 60 as a function of backgate Vbg at temperature 15K, 50K, 100K, 130K,170K, 210K, 250K and290K. When ambient temperature decreased, the magnitude of TEP also decreased. Linearity relationship was found in two-dimension graphene, Fig 4.4 shows that, at a fixed V𝑏𝑔 , the magnitude of S changes linearly with temperature both near the CNP as well as away from CNP. This can be explained by famous Mott‟s relation96 which is mathematically derived from Boltzmann‟s transport equations under the relaxation time or scattering rate approximation. Figure 4.4 Seebeck Coefficient of graphene stripe at fixed backgate Vbg at 1v( Red triangle) and -50V(blue dot) 4.3.3 Thermal power in graphene nanoribbon. Inset of Fig 4.5 is the optical picture of the GNR device and the AFM 61 picture showing the details of graphene nanoribbon. The width and length of the GNR is 70nm and 1μm respectively. The resistance of the sample is measured by standard lock-in method. Around the Dirac point, the resistance of the GNR shows insulating behavior at low temperatures as shown in Fig. 4.5, which is consistent with the electrical transport studies of GNR prepared by the same method. A fitting of the resistance as a function of gate voltage V𝑏𝑔 gives a mobility of 10505 cm2/vs at room temperature. Figure 4.5 Resistance of GNR as a function of back gate voltage V𝑏𝑔 at different temperatures 10K, 50K, 195K, 250K, and 300K. Inset is the optical picture of the device and AFM picture of the GNR. The scale bar is 500nm Seebeck coefficient was measured using the same method as bulk graphene. Fig. 4.7 shows the Seebeck coefficient as a function of gate voltage from 15K to 300K. The sign of the signal changes from positive to negative when across the CNP, which is the same as bulk graphene. However, there are two major 62 changes of GNR thermal power signal compared with bulk one. Figure 4.6 Seebeck coefficient S of GNR (W=70nm, L=1μm) as a function of back gate Vbg at different temperatures 15K, 50K, 200K, 250K, and 300K. First, the maximum thermal power at each temperature has a large increase compared to the bulk graphene case. At room temperature, the maximum value of Seebeck coefficient is 143 μV/K, while the maximum value reaches around 225μV/K at 150K. The opening of a small band gap in GNR might account for such enhancement. Second, the maximum thermal power for a specific temperature shows non-monotonic temperature dependence. As shown in Fig. 4.8, the maximum thermal power is plotted vs temperatures from 15K to 300K. At low temperatures, the thermal power increases with temperature increasing, while at 63 high temperature, the thermal power shows opposite trend. This anomalous trend is likely to originate from the electron-hole puddle in GNR. As is demonstrated by F. Molitor, et al86, 100, in graphene nano-ribbon fabricated by the plasma etching method, electron-holes puddles dominate the electron transport at low charge carries densities. For high temperature, the thermal power follows almost 1/T dependence of degenerate semiconductors. While at low temperature, the carriers are delocalized in puddles, the overall thermopower greatly decreased due to the cancellation from electron and holes. The lower the temperature, the localization is expected to be stronger, thus the smaller the thermopower. Figure 4.7 Seebeck Coefficient of graphene stripe at fixed backgate Vbg~3V( Red triangle) and 40V(blue dot) 4.4 Conclusion 64 In this chapter, we study the thermoelectric properties in GNR. Graphene was prepared by mechanical exfoliated method and etched to GNR by plasma etching. Seebeck coefficient in GNR with width of 70nm and length of 1μm was measured as a function of back gate with temperature range from 15K to 300K. An enhancement of thermal power is observed in GNR due to the opening of energy band gap. The maximum value of thermal power is 225μv/K and appears at 150K instead of room temperature, which also been found in dual gated bilayer graphene, indicating an opportunity of low-T thermoelectric material application. The optimization of thermal power in GNR predicts it could be a potential material in energy engineering. 65 Chapter 5 Conclusion and outlook 5.1 Thesis summary Due to its extraordinary mobility and thermal conductivity, graphene has become one of the candidate materials for the next generation computer technology. However, the fact that graphene lacks of a band gap in its band structure limits its further application in semiconductor industry. Graphene nanoribbon pattering provides a promising method of introducing band gap in graphene‟s band structure. This thesis studied the electrical and thermoelectrical properties in graphene nanoribbon. We fabricated graphene nanoribbons with width ranging from 5nm to 100nm both for suspended or supported graphene. The suppression of G near the charge neutrality point suggests the opening of an energy gap, which makes graphene nanoribbon a potential material in semiconductor field. In the first part, we introduced the development of the helium ion lithography method on mechanically exfoliated graphene using helium ion microscope. Using this method, we successfully fabricated graphene nanoribbons on suspended and supported substrate. Suspended GNRs were patterned to widths down to 5nm, while the smallest width for supported GNR was 20 nm. In addition, supported GNR-FETs with width of 60nm and length of 250nm were fabricated and characterized for electron transport properties. The disordered energy-scale is strongly enhanced in our system as indicated by the 66 large back-gate voltage-span of conductance suppression. This behavior can be explained by the large disorder induced by the back-scattering of helium ions, which is further confirmed by Raman mapping. In the second part, thermal power of graphene nanoribbon with width of 70nm and length of 1 μm has been measured. Graphene nanoribbon was fabricated using simple and economical plasma etching method to avoid large disorder. The maximum thermopower signal is around 143 μv/K at room temperature. The enhanced signal may because of the opening of energy band gap in quasi- one dimensional GNR. Thermopower is further optimized at low temperature and the maximum value appeared at 150K in our experiment. The enhancement of thermopower in GNR together with the decreased thermal conductivity makes GNR as a potential material for energy engineering. 5.2 Future work Helium ion lithography is a powerful tool to fabricate ultra-narrow graphene nanoribbon. However, we cannot avoid the damage to graphene due to the back-scattering of ions. Further work should focus on the fabrication of suspended GNR-FETs. On one hand, back-scattering of helium ion can be significantly reduced in the absence of the substrate, which could result in a defect-free GNR. On the other hand, suspended GNR which exclude the influence of substrate could in principle reach the intrinsic properties of 67 graphene nano-ribbon, which is useful for fundamental studies in ultra-narrow GNRs and quantum dot structures. Moreover, the combination of Helium Ion microscope and NPGS software enable fabrication of arbitrary shape of graphene structures. Future works could focus on fabricating triangle shape of graphene flake for thermal rectification effect study, or graphene super-lattice for two-dimensional phononic crystal study. All these studies rely on the high-resolution and high controllability of HIL. Furthermore, the enhanced thermal power in graphene nanoribbon proved graphene a potential thermoelectrical material. However, the band gap in graphene nanoribbon with width of 70nm is not sufficient. 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Electrical properties characterization of the supported GNR with width of 60nm shows the energy band gap opening in later part of this chapter In chapter 4, we study the thermoelectric properties of graphene based devices First, we study the 24 thermoelectrical properties in graphene sheet Then, we investigate the thermopower in GNR We find that the enhancement of thermal power may due to the opening of a band... spectroscopy is widely used in graphene community to determine the graphene parameters, such as number of graphene layers, strain in graphene, graphene quality, as well as graphene temperature Fig 2.7 is the typical Raman signal of a graphene piece lie on top of SiO2 substrate There are three typical peaks in the graphene s Raman spectrum, the D band, G band and 2D band The D band appears due to the lattice... the G band indicates the vibrational state of graphene s sp2 bonding, while the 2D band shows the stacking of graphene layers 33 Figure 2.7 Typical Raman spectrum of single layer graphene A lot of experiments were done to study the Raman signal response of graphene under difference conditions Ferrari, et al, demonstrated that the G band intensity and 2D band FWHM will increase while the layer of graphene. .. nature of bilayer‟s chiral Dirac fermions26-32 By broking the sublattice symmetry, the spectrum is made of four massive Dirac bands (two conduction bands, two valence bands) and has hyperbolic dispersion relation In this situation, the band gap opens29, as shown in Fig 1.3B Figure 1.3 The band structure of (a) single layer graphene (b) bilayer graphene3 3 1.1.4 Band gap in graphene nanoribbon (GNR) The band... graphene nanoribbon with the help of helium ion beam sputtering Band structure is modified after the ion beam cutting and the energy gap opens The effect of helium ion bombardment to graphene is analyzed The second part investigates the thermoelectrical properties changes in graphene nanoribbon compared to graphene sheets The thesis is organized as follows: Chapter 2 introduces the methods of preparing graphene. .. years and a graphene “gold rush” has started since then 1.1.2 Electronic properties of graphene Carbon-based systems show an unlimited number of different structures with variety of physical properties4 , 19 Among systems with only carbon atoms, graphene plays an important role since it is the basis for understanding of the electronic properties in other allotropes The discovery of both single layer graphene. .. increases75 The difference of the signals is quite obvious that it makes Raman spectroscopy an ideal method to determine the layer of graphene Raman spectrum is also used to study the hydrogenation of graphene and its reverse effect68 The emerging of the D band after the hydrogenation of graphene indicates the attachment of hydrogen atoms on the graphene lattice, while the decrease of D band intensity shows... use of low-dimensional systems for thermoelectric application is mainly due to: a) enhance the density of states near E , leading to an enhancement of the Seebeck coefficient; b) decrease of phonon conductivity by increasing the boundary scattering 1.2.2 Thermoelectrical properties in graphene Graphene, which is a 2D material, can provide such quantum confinement effect for the application on thermoelectric. .. picture shows over dose of etching 4) exposed part of graphene is etched by O2 plasma 58 Figure 4.3 Seebeck coefficient (S) of graphene with width of 5um and length of 7um as a function of backgate Vbg at temperature 15k, 50k, 11 100k, 130k,170k, 210k, 250k and2 90k 60 Figure 4.4 Seebeck Coefficient of graphene stripe at fixed backgate Vbg = 1v( Red triangle) and -50V(blue dot) ... patterning GNR because of its high resolution56, 57 Suspended GNR with width of 10nm was achieved by this method57, while there is lack of study on the GNR‟s properties In my thesis, GNR fabricated by HIL will be studied 20 1.2 Thermoelectrical properties of graphene 1.2.1 Seebeck coefficient and the figure of merit ZT The energy loss in industry is a great waste Approximately 90 per cent of the world‟s power ... 1.1.1 Graphene in carbon family 15 1.1.2 Electronic properties of graphene 17 1.1.3 Band structure in graphene 18 1.1.4 Band gap in graphene nanoribbon (GNR) 19 1.2 Thermoelectrical... Thermoelectrical properties of graphene 21 1.2.1 Seebeck coefficient and the figure of merit ZT 21 1.2.2 Thermoelectrical properties in graphene 23 1.3 Chapter 2.1 Objective and scope of this... 3.112D plot of Conductance of graphene nanoribbon with width of 60nm as a function of Vsd and Vbg at T=4.3 K 51 Figure 4.1 Optical image of thermal power device, is heater, and is thermometers