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Graphene: Synthesis, Characterization, Properties and Applications in the Energy Sector
Executive summary
This dissertation explores the synthesis, characterization, properties and application of graphene in the energy sector. It introduces graphene asa amember of carbon and details how it is synthesized from graphite. The dissertation looks at nanomechanism of graphene which details the properties that enhances it to be good appliance in energy sector. This dissertation gives an overview and introduction of graphene which is an interesting material for one to study. The paper identifies is a detailed one as it identifies all the mentioned sysnthesis, characterization, properties of graphene. The dissertation looks at examples of some perfomed experiments that help to derive the synthesis of graphene. The paper explores all relation represented by equations that lead to understanding deep components that make up graphene and how they help in realization of its properties. Finally after understanding the electrical and mechanical properties of graphene it details some of it application and it generalizes to application in energy sector.
Declarations and Statements
Declaration
I hereby declare that this work has not been presented for any degree and is not being submitted concurrently in candidature for any degree.
Signed………………………………………………… Date………
STATEMENT 1
this paper represents the results from my own independent investigation/work unless where otherwise stated. A bibliography has been appended for sourced information.
Signed …………………………………………………………………….Date …………………………………………..…
STATEMENT 2
I have given the consent for my dissertation, when accepted it can be available for inter-library loan and for photocopying. The summary and the title can be made obtainable to outside organizations.
Signed ………………………………………………….….Date…………………………………………….
Table of Contents
Executive summary. 2
Declarations and Statements3
List of tables. 7
List of Figures. 8
Abbreviation. 10
Preface. 11
Acknowledgements12
Definitions. 13
CHAPTER 1: INTRODUCTION.. 14
1.1 Introduction. 14
1.2 Graphene and its history. 15
1.3 Multilayer Epitaxial Graphene (MEG)16
1.4 Thesis Outline. 18
1.5 Back Ground. 18
1.5.1 3D Materials and their Electrical Properties. 18
1.5.2 Two Dimensional Electron Systems. 20
1.5.3 Quantum Dots. 23
1.6 Conclusion. 24
CHAPTER 2: THE STUDY OF NANOMECHANICS. 25
2.1 Introduction. 25
2.2 Materials Mechanical Properties. 25
2.3 Anisotropic Materials. 26
2.4 Bulge Test27
2.5 Conclusions. 30
CHAPTER 3 NANOMECHAMICS OF GRAPHENE. 31
3.1 Introduction. 31
3.2 Comparison of Carbon and Silicon. 31
3.3 Carbon and its forms. 33
3.3.1 Diamond. 35
3.3.2 Fullerenes. 36
3.3.3 Graphene and Graphite. 37
3.4 Graphene Fabrication. 38
3.5 Properties of Graphene. 41
3.5.1 Fundamental Characteristics of graphene. 41
3.5.2 Electronic Propertiesof graphene. 42
3.5.3 Mechanical Strength of graphene. 43
3.5.4 Optical Properties of graphene. 43
3.5.5 Electrical Properties of Graphene. 44
3.6 Mechanical Properties of Graphite and Graphene. 46
3.6.1Mechanical properties of graphite. 46
3.6.2 Graphene’s Mechanical properties. 48
3.7 Conclusion. 49
CHAPTER 4: DETAILED CALCULATION OF MATERIALS PROPERTIES. 50
4.1 Introduction. 50
4.2 Device Fabrication. 50
4.3 Data Analysis. 51
4.4 Coulomb Blockade. 53
4.5 Magnetic Field Dependence. 55
4.6 Conclusions. 56
CHAPTER 5: GRAPHENE CHARACTERIZATION.. 57
5.1 Introduction. 57
5.2. Characterization of graphene using the JPK nanowizard 3AFM system.. 57
5.2.1 Using QITM for the measurement of graphene. 58
5.2.2 Graphene measurement using the AC mode. 59
5.3 Measuring the conductivity of graphene. 60
5.4 Device Fabrication. 61
5.5. Device Characterization – AFM and Raman. 62
5.6. Conclusion. 64
CHAPTER 6: APPLICATIONS OF GRAPHENE. 65
6.1 Introduction. 65
6.2 Biological Engineering. 65
6.3 Optical Electronics. 66
6.4 Ultrafiltration. 66
6.5 Composite Materials. 67
6.6 Application of Graphene in the Energy Sector67
6.6.1 Photovoltaic Cells. 68
6.6.2 Energy Storage. 69
6.6.3. Further applications of grapheme in energy sector71
6.7: Conclusion. 79
CHAPTER 7: CONCLUSIONS. 80
References. 82
List of tables
Table 2.1: Young’s Modulus of various materials – Adapted from [41]25
List of Figures
Figure 1.1: First example of an array of functioning epitaxial graphene field effect transistors patterned on both the carbon terminated faces of 4H SiC and silicon, figure adapted from [37]16
Figure 1.2: Single layer graphene figure adapted from [37]17
Figure 1.3: Sample Graphite structure compared to the C-Face MEG structure of multilayer graphene figure adapted from [37]17
Figure 1.4: a) A silicon MOSFET where a metal gate is used to pull charges towards the Silicon/Silicon Oxide interface where the two-Dimensional Electon Gas (2DEG)is formed. Image adapted from [14]. b) A modulation doped GaAs/AlGa As heterojunction. Figure adapted from [15]. The 2DEG forms at the interface where charges introduced by silicon. 21
Figure 1.5: Progress made in improving the mobility of GaAs/AlGaAs heterojuntions. The solid black square (■) is the current mobility record for graphene on silicon oxide. Figure adapted from [29]23
Figure 1.6: a) Schematic of a quantum dot connected to a source, drain, and gate electrode. b) (upper) Schematicof a quantum dot defined on an AlGaAs/GaAs heterostructure using gatedefined depletion regions. (lower) Scanning electron microscope image of a single (left) and double (right) quantum dot. The white dot defines the region of electron confinement in the dot and the white arrows denote the conducting path of the electrons. The ohmic contacts to the dotare shown by black crosses. c) (upper) Energy levels in a quantum dot during coulomb blockade (left) and during conduction. Figures adapted from [37].24
Figure 2.1: Schematic of Bulge Test, Figures adapted from [41]29
Figure 3.1 : (a) Intel’s 45 nm transistor which uses a Hafniun based dielectric. (b) A wafer of the 45 nm transistors photographed with a dime. The processors of a dual core chip are made up of 410 million transistors, and for the quad chore chip it has 820 million. Figure taken from intel.com/pressroom/kits/45nm/photos.htm.. 33
Figure 3.2: Various Forms of Carbon a) diamond lattice image taken from http://mrsec.wisc.edu b) hope diamond image taken from Smitsonian c) Lab grown diamond image taken from Apollo Diamond Inc. d) Graphite lattice Image taken from http://www.scifun.ed.ac.uk e) pencil graphite Image taken from xara.com f) Graphite image taken from United States Geological Survey g) single layer of graphene image taken from ewels.info.com h) single walled carbon. 34 Figure 3.3: Graphene Fabrication, Figure taken from Berger et al. [4]……………………………………………………40
Figure 3.4: it shows a graph resistivity of a single layer of graphene against the gate voltage. The second graph shows the Quantum Hall Effect in single layer graphene. Figures taken from Novoselov, Geim, et al [59][60].45
Figure 4.1: shows the ratio at room temperature 2-point resistance plotted against the resistant us the room temperature 2-point resistance for all the devices. Figure adapted from [23]52
Figure 4.2: Longitudinal and Hall resistance measured as a function of magnetic field at 100 mK for the 5 nm thick graphite dot shown in the insets. Figure adapted from [23].54
Figure 5.1: The image of graphene flakes when dipped in mica substrate and measurement are taken. Image taken from [22]59
Figure 5.2: This is measurement of graphene flakes using the AC mode surface made up of silicon. Image taken from [32]59
Figure 5.3: Example of graphene scans which shows overlapping graphene layers. Image taken from [27]60 Figure 5.4: (A) Schematic of a suspended graphene resonator. (B) An optical image of a double layer graphene sheet (C) Raman signal from a scan on the graphene piece (D) An optical image of few (~4) layer graphene suspended over a trench and contacting a gold electrode. E) A scanning electron microscope image of a few (~ 2) layer graphene resonator. Image taken from [27][30][31]……………….63
Figure 6.1: How to create 3D graphene: combine lithium oxide with carbon monoxide, forming lithium carbonate (Li2CO3) and the honeycomb graphene. Figure adapted from http://www.kurzweilai.net/images/3D-graphene.jpg. 69
Figure 6.2: A better way to build a lithium ion battery. Figure adopted from [76]70 Figure 6.3: Silicon-graphene battery triples lithium ion battery densities. Figure adopted from [77]….71
Figure 6.4: Seven-atom rings (in red) at the transition from graphene to nanotube make this new hybrid material a seamless conductor. Figure from [55]72
Figure 6.5: Flexible organic solar cells equipped with graphene electrodes. Figure from[56]73
Figure 6.6: Yu-Ming Lin on High-Performance Graphene Transistors. Figure from [44]74
Figure 6.7: High-performance graphene transistors made using sticky tape. Figure from [44].75
Figure 6.8:Sample mobile screen made from graphene. Figure from[58]76
Figure 6.9: An OLED display . Figure from [58]76
Figure 6.10: Graphene utra capacitors. Figure from [60].78 Figure 6.11: Flexible chemical sensor made with carbon nanotubes could help detect traces of toxins and explosives in water. Courtesy of Mark Roberts. Figure from. http://phys.org/news173035243.html#jCp…………………………………………………………………………………..79
Abbreviation
QHA-Quality Hall Effect
MEG- Multilayer Epitaxial Graphene
2DEG-Two Dimensional Electron Gas
MOSFET- Metal Oxide Semiconductor Field Effect Transistor
CVD- Chemical Vapor Deposition
MBE -Molecular Beam Epitaxy
NEMS-Nanoelectromechanical System
LED- Light Emitting Diode
LCD- Liquid-Crystal Display
Preface
Graphene can be termed as one of the latest element discoveries which shows interesting electronic properties-with the potential to surpass the materials used in the current electronic applications. The main aim of this dissertation is to ascertain the characteristics, properties and how they can be used in the energy sector. Since graphene has not started being used to the applications that it is thought to depend on it, all the information in this dissertation is based on literature combining the properties and the various ways in which graphene can be applied in the Energy factor. Although the energy sector has its developments and has been successful, graphene promises to bring some improvements which are outlined here according to empirical results found from tests carried out on graphene. This is meant to form a one stop reference of the application for the use of graphene in the Energy sector.
Acknowledgements
The success of this dissertation can be attributed to combined efforts from various individuals and groups who have supported me dearly. The first important influence came from my project supervisor who has great professional influence on the development of the scientific project. The supervisor pushed me to develop my weakness and exploit my strengths. Through his guidance on the project, it was possible for me to successfully discover and explore all most parts of the project.
Many thanks to my family members who gave me both financial support and love at all time. They also offered emotional support whenever it was necessary. I would also like to appreciate my friends for their many ideas and emotional support towards this project.
Definitions
Graphene: it can be referred as the carbon atoms that are packed into two dimensional lattice and form a flat monolayer.
Graphite: this is an allotrope of carbon and it is the most stable carbon form. It can easily conduct electricity.
Coulomb: this is the derived SI unit of electric charge; it is the charge that is transported by constant current of one ampere in one second.
Nano mechanics: it is nanoscience branch that study fundamentals of mechanical properties I physical system.
Saturation fluence: A point at which an increase in the intensity of light causes a decrease in absorption of white light.
Youngs modulus; it is the measurement of elastic material stiffness and a quantity that is used to characterise material.
CHAPTER 1: INTRODUCTION
1.1 Introduction
Graphene is a new material with properties which promise to surpass properties of existing materials. This is a two dimensional element with remarkable mechanical and electrical properties. Consequently, Graphene can be used in a large number of applications, in primis, in the electronic and the energy sectors. Technology is quite exciting, for incase of any discovery fr instance of a new component or material it brings with it or it is associated with some development like exciting and fruitful periods of both technological and scientific and research. The new material such as graphene brings new opportunities which can be ventured in the quest to improve the current state of the applications in which it can be applied. In addition, the old materials had their own challenges and this means graphene cannot miss on the lookout for problems before it can be applied to the applications. The era of solving problems of the old materials arrive while new challenges arrive in the same effect. The recent discovery of graphene and the center of our research is an atomically thin layers of graphite, that has been discovered brought such a period [29]. Graphene is the reality of a long dream to isolate a single two dimensional atomic layers of atoms forming one of the thinnest materials ever experienced.
Graphene has a very strong bond known as the carbon-carbon bond. This locks the atoms in the two dimensional material but leaves an extra electron free for electric conductivity [14] [15] [56]. A single layer of graphene that is suspended is one of the stiffest materials that are known in the world which is characterized by the high Young’s modulus of ~ 1 TPa. Graphene can be termed as an electronic material – it can therefore present electrons with a new play ground in 2, 1, and 0 dimensions. In this case the rules are changed as a result of its linear band structure. It has a low scattering which allows the Quantum Hall Effect (QHE) observation, and the graphene unique band structure that gives this old effect a new twist
1.2 Graphene and its history
The history of Graphene can be attributed to the studies that have been carried out on carbon nanotubes. This is because the nanotubes were shown to have special electronic properties which are now exhibited in graphene. However, there was a problem in the manufacture of well-controlled nanotubes that can be scaled up. Scaling up of the nanotubes [1] would mean that single-tube transistors can be transformed into large-scale integrated circuits. The impossibility of the use or scaling of the nanotubes brings a barrier in using the nantubes in serious technological applications. It was in the early 2000s that Walt de Heer discovered that Graphene would have the same properties of the nanotubes. Consequently, this was one of the major breakthroughs of the application of carbon electronics.
The simplest way of production of Graphene is by peeling it off from a piece of graphite. This is because it was discovered that graphite is just a stack of Graphene sheets put together. The simplest graphite material that can be found around is graphite pencil tip. The process of manufacturing Graphene from Graphite by peeling off is known as the Geim approach. Although the Geim approach is simple, it results into structural disorder, poor electronic properties, and defect concentrations which make it impossible for the resulting Graphene to be used in electronic applications. There have been various other approaches that can be used to produce good quality graphene – the most notable is one developed by Heer and used by Graphene works. In this method, thermal sublimation to obtain carbon interface from silicon carbide is done. The carbon rich interface is the one used to obtain Graphene sheets. Contrary to the Geim approach, this method allows for scalability and ease of fabrication necessary in an electronic material.
Figure 1.1: First example of an array of functioning epitaxial graphene field effect transistors patterned on both the carbon terminated faces of 4H SiC and silicon, figure adapted from [37]
1.3 Multilayer Epitaxial Graphene (MEG)
Multilayer epitaxial graphene is said that it can be grown on carbon-terminated SiC. The production of the multilayer Grahene occurs without affecting the properties of single layer graphene and without interfering with the scalability and fabrication into electronic applications. The mobility of MEG has empirically been proved to be the highest ever measured – over 250000 square centimeters per voltage in a second. This makes MEG a multilayer stack of effectively electronically isolated graphene [98].
Figure 1.2: Single layer graphene figure adapted from [37]
As shown in the single layer graphene, it can be seen that one atom of carbon is attached to 3 other atoms carbon. The valence of carbon is 4 and this means that one electron is free and there is mobile for electronic purposes. Contrary to graphite, the single sheet of graphene is connected by the extra bond to the fourth electron and thus there is no free electron. The figure below shows a sample of graphite structure compared to the MEG structure.
Figure 1.3: Sample Graphite structure compared to the C-Face MEG structure of multilayer graphene figure adapted from [37]
1.4 Thesis Outline
This dissertation presents an overview, and in details it shows graphene as a material which can be applied in energy sector. Generally it is intended to cover synthesis, characterization and properties of graphene which shows why it can be easily used to replace copper and aluminum in energy sector. Chapters 1-3 include an overview of the basic concepts relevant to the experimental results presented in Chapters 4-6. The results provides a basis over which graphene can be used in the energy sector which due to its impressive properties. The experimental section begins in Chapter 4 involves measurement of electrical transport of low temperature and are performed on gated, few-layer graphene quantum dots. We find that electrons in pieces of mesoscopic graphite are delocalized almost the whole piece of graphite down to low temperatures. In chapter 5 the paper looks at characterization of graphene. In details the chapter covers some of the methods that are applied in characterization of graphene plus material fabrication. The purpose of the chapter is to display characteristics of graphene and exposing its properties. In chapter 6 the paper looks at the application of graphene all sectors but generalizes with application in energy sector.
1.5 Back Ground
1.5.1 3D Materials and their Electrical Properties
Materials can be characterized by forces. For electrical materials researchers are mostly interested in the response of the electrons in the materials and atoms to the mechanical forces [1]. Fortunately, research that has been carried out has shown very promising electrical and mechanical properties of graphene.
The first of these is summed up by equation 1.1;
Ohm’s Law:
V=IR
Equation 1.1 Ohms Law
Where V refers to the difference of voltage across the conductor,
I refers to the current, where as R refers to the resistance.
The resistance can be expressed in terms of resistivity ρ as:
Equation 1.2
where L refers to material length and A refers to the cross sectional area where the current flows through. The geometry of a material does not affect its resistivity. For this reason, resistivity can be used in comparison of different materials with different geometrical specifications [99].
Ohm’s law is a general formula that is fully applicable to all 1D, 2D and 3D conductors. In a typical conductor it is clear that the charges are randomly moving and scattering and do not have a charge net movement across the material sample. Incase voltage difference, V, is applied across the conductor, this situation changes [5]. The voltage difference is realized to create an electric field, E, that gives these scattered and randomly electrons one direction net force. In this case some of the possible scattering mechanisms that are available include charge in homogeneities in the material, phonons in the material or the defects in the lattice. An equation is used to relate the drift velocity, vd, velocity where by the charges move in the direction of the applied field . And the drift velocity is related to the current density J by:
J=nevd
Equation 1.3
Where e is the electron charge and symbol n is the charge carrier density. In such a case when there is less scattering in a material, the charge carriers will travel further but the electric field is the same [4]. This ratio which is very vital quantity and applied in the characterization of scattering in conductor is defined as the mobility, µ = vd/E. And in line with this an individual can make the expression of the resistivity of a material in terms of its mobility by:
Equation 1.4: resistivity in terms of mobility
1.5.2 Two Dimensional Electron Systems
Three dimensional materials have been used for a long time. Two dimensional materials start with graphene and have their special parameter of properties. If the thickness of a conductor becomes smaller than the size of the electron wavelength than the conductor forms a two-dimensional electron gas (2DEG) and interesting quantum effects arise.
Figure 1.4: a) A silicon MOSFET where a metal gate is used to pull charges towards the Silicon/Silicon Oxide interface where the two-Dimensional Electon Gas (2DEG)is formed. Image adapted from [14]. b) A modulation doped GaAs/AlGa As heterojunction. Figure adapted from [15]. The 2DEG forms at the interface where charges introduced by silicon
The first high mobility 2DEG was formed from a Silicon metal oxide semiconductor field effect transistor (MOSFET). Technologically, the Si MOSFET is the critical component behind the transistor and modern computing revolution. A schematic of the MOSFET is shown in Fig. 1.4. A SiO2 insulating layer is grown on top of Si and an electrostatic force applied to the gate electrode is used to pull charges towards the Si/SiO2 interface [3]. The high quality interface between a Si and SiO2 can be fabricated into effective transistors and at low temperatures forms a relatively clean 2DEG which exhibits the Quantum Hall Effect (QHE). The QHE in silicon 2DEG was first demonstrated in 1980 by Klaus von Klitzing [45].
To evade the problem of scattering at a faulty semiconductor-insulator boundary, researchers at Bell Labs invented a technique called modulation doping which used Molecular Beam Epitaxy (MBE)[22]. Using MBE, a technique developed in the 1960s by Albert Cho also of Bell Labs, semiconductors can be prepared layer by layer in a nearly perfect crystalline form and a clean interface between two semiconductors is prepared. To generate a 2DEG, free charges must be created. In the MOSFET, charges are introduced through an electrostatic gate above the oxide. For the case of the GaAs/AlGaAs heterojunction, researchers at Bell Labs had the clever idea of introducing impurity atoms far enough away from the interface such that they can donate their electrons but not contribute to scattering. In this case, called modulation [6]
Figure 1.5: Progress made in improving the mobility of GaAs/AlGaAs heterojuntions. The solid black square (■) is the current mobility record for graphene on silicon oxide. Figure adapted from [29]
When Si is substituted in for Ga in the lattice it releases its extra electron. Since the conduction band of GaAs is 0.19 eV below the conduction band of AlGaAs, negative charges fall toward the GaAs side but are attracted by the positive charges that remain on the AlGaAs side [10]. This result in bands bending and confining the charge at the “perfect” AlGaAs-GaAs interface thereby forming the 2DEG. Loren Pfeiffer and collaborators at Bell Labs have spent the last 2 decades perfecting their MBE system so as to make it as clean as possible. Progress in perfecting the quality of this interface is shown in Fig. 1.5 and mobilities larger than 10 have been achieved. These samples have a ballistic mean free path of about 120 µm for an electron confined to this interface and such high quality samples have allowed for the investigation of many exotic properties of electrons in 2 dimensions.
1.5.3 Quantum Dots
A quantum dot is formed if electrons in a conductor are confined in all 3 of their dimensions – a 0 dimensional structure [2]. Typically, quantum dots are conducting island connected to a reservoir of electrons by a tunnel barrier. These are as shown in the figure below.
Figure 1.6: a) Schematic of a quantum dot connected to a source, drain, and gate electrode. b) (upper) Schematicof a quantum dot defined on an AlGaAs/GaAs heterostructure using gatedefined depletion regions. (lower) Scanning electron microscope image of a single (left) and double (right) quantum dot. The white dot defines the region of electron confinement in the dot and the white arrows denote the conducting path of the electrons. The ohmic contacts to the dotare shown by black crosses. c) (upper) Energy levels in a quantum dot during coulomb blockade (left) and during conduction. Figures adapted from [37].
1.6 Conclusion
This chapter looks at some of the intriguing effects that arise when electrons in a conductor are confined to nanoscale dimensions. Consequently, chapter looks at mescoscopic graphene electronic devices where electrons are confined in 2 and 0 dimensions in Graphene.
CHAPTER 2: THE STUDY OF NANOMECHANICS
2.1 Introduction
Nanomechanics refer to the branch of nanoscience which studies the fundamental properties of physical systems or materials at the nanometer scale. Some of the mechanical properties studied include elastic properties, thermal properties and kinetic properties [8][9]. This section discusses mechanical properties of materials using the Hooke’s law and looks at various Young’s modulus for different materials. For single layered materials such as graphene, anisotropy is considered while the bulge test is used for measurement for thin films, the in-plane mechanical properties which includes as the residual stress, Young’s modulus and Poisson’s ratio.
2.2 Materials Mechanical Properties
The mechanical equivalent to the Ohm’s law is the Hooke’s law. For a material in one dimension it is expressed as:
Equation 2.1: Hooke’s law
where E is the Young’s modulus, the stress σ is the force per unit area, and ε is strain. This assumes an isotropic system where there is no preferred crystal orientation. In many bulk solids, this is a valid assumption considering that single crystals tend to be separated into grains of random orientation. When taken as a whole the elastic constants average to some bulk value [89]. Table 2.1 shows the typical Young’s modulus for various materials [21].
Table 2.1: Young’s Modulus of various materials – Adapted from [41]
|
Material
|
Young’s Modulus(E) in GPa
|
|
Rubber
|
0.01 – 0.1
|
|
PTFE
|
0.5
|
|
Nylon
|
3-7
|
|
Oak Wood
|
11
|
|
High-Strength concrete
|
30
|
|
Glass
|
65-90
|
|
Titanium (Ti)
|
105-120
|
|
Copper (Cu)
|
110-130
|
|
Silicon (S)
|
150
|
|
Wrought iron and steel
|
190-210
|
|
Tungsten 
|
400 – 410
|
|
Silicon Carbide (SiC)
|
450
|
|
Diamond
|
1050 – 1200
|
|
Single Walled carbon nanotube
|
1000
|
|
Graphite/Graphene (within the plane)
|
1000
|
Incase of an applied strain most materials contract in the direction perpendicular to this strain. The ratio of the strains in these 2 directions defines a quantity known as Poisson’s ratio:
Equation 2.2: Poisson’s ratio
2.3 Anisotropic Materials
It is not always possible to assume a material is isotropic. This thesis is primarily concerned with single crystals and layered materials for which anisotropy is an important consideration. The second rank tensors are the Strain and Stress and so relating stress to strain requires a fourth rank tensor which has 81 components [23]. For real materials in equilibrium, there are no net forces and torques so the stress-strain relation is vastly simplified to the following 6 x 6 symmetric matrix [78]:
Equation 2.3
where τ is the shear stress and γ is the shear strain. For a cubic crystal such as silicon symmetry allows this equation to be further simplified to:
Equation 2.4
where the elastic constants for silicon are C11= 166 GPa, C12 = 64 GPa, and C44= 80 GPa (Senturia 2001) [22]. Graphite is a special case where the elastic constants along the plane are vastly different than those between the sheets.
2.4 Bulge Test
The bulge test is a method commonly and widely used to measure the thin films, in-plane mechanical properties like the Young’s modulus, the residual stress, and finally the Poisson’s ratio [93]. In the simplest implementation, a pressure difference is applied across a clamped circular film with a radius of curvature Rand the maximum deflection, z, at the top of the film is measured. The pressure difference, ∆P, applies a well defined and uniform force across the membrane of thickness, which is balanced by the induced biaxial stress, σ, in the membrane [20]:
Equation 2.5
Equation 2.6
For the case of small deflection where (z<<a), the Pythagorean Theorem can be used to express the radius of curvature in terms of the radius of the base, a, as:
Equation 2.7
Figure 2.1: Schematic of Bulge Test, Figures adapted from [41]
2.5 Conclusions
This chapter looks at the nanomechanics which are termed as the branch of nanoscience leading to study of properties of materials. The chapter studies the mechanical properties like elastic properties, thermal properties and kinetic properties of graphene. It looks at the mechanical properties of materials using the Hooke’s law and looks at various Young’s modulus for various materials. The next chapter looks at graphene which is the theme of the paper.
CHAPTER 3 NANOMECHAMICS OF GRAPHENE
3.1 Introduction
Graphene can be defined as a carbon allotrope that has a reigning optimism for the use of the material in real life applications such as electronics. There are various definitions given for graphene depending on the time of development of the definition and the review of the progress in the development of the allotrope [25]. One of the definitions of graphene in the present time defines it as a monolayer of carbon atoms that is flat and packed into lattices that are two dimensional. This means that graphenein simple is a building block of graphite. Graphite is three dimensional in its organic structure while graphene is two dimensional. It is postulated that graphene are two dimensional sheets which are put together in a stack to form graphite. Other definitions of graphene have pointed to it as a single carbon layer which can be referred to as the last member of naphthalene, anthracene, and coronene. It is imperative to define the meaning of two dimensional crystals before looking at earlier work on graphene. Atoms are building blocks of elements – a single atom is two dimensional because it can be accessed from all directions. This chapter compares materials related to graphene such as carbon, silicon, and outlines the various carbons – graphene forms. The chapter also discusses the fabrication of graphene and points out the various properties of graphene [30].
3.2 Comparison of Carbon and Silicon
Most of the important applications make use of silicon nanotechnology. Modern computing revolution thrives on silicon-based transistors. It is imperative to note that the use of silicon has been improving over the time while the transistors size has decreased with time. This allows a single chip to hold more transistors and hence increases the level of complexity of the chip designs. Powerful computers use complex algorithms and therefore require complex transistor combinations [26]. The rate of reduction of the size of transistor follows Moore’s law that explains the transistors number that a chip can hold doubles at a rate of once every 2 years. The decrease of the size of a transistor is phenomenal and has an economic reason ~ $1 trillion. The driving force computer market is the worldwide market demanding efficient, user-friendly, and affordable computers. There are also physical reasons as to why the reduction of the size of resistors is important – the ability of engineer and scientists to design and fabricate silicon into computer circuitry which are smaller and more efficient. This means the design of solution to more complex real life problems that can be solved electronically [28].
A good example of the current nanotechnology application is the Intel processor which has a channel length of 45nm. The interest in nanotechnology extends to the mechanical realm pointing to MEMS technology [44]. MEMS are finding and used as applications in different types of products. Silicon fabrication equipment and processes are always available as a result of the microelectronics boom resulting to silicon as a natural choice for MEMS. The question remains as to whether silicon is the best choice for application of the MEMS. Carbon has been pointed out as another alternative which can be used in MEMS technology. Carbon forms several distinct structures with superior electrical, thermal, and mechanical properties as compared to silicon.
Figure 3.1 : (a) Intel’s 45 nm transistor which uses a Hafniun based dielectric. (b) A wafer of the 45 nm transistors photographed with a dime. The processors of a dual core chip are made up of 410 million transistors, and for the quad chore chip it has 820 million. Figure taken from intel.com/pressroom/kits/45nm/photos.htm
3.3 Carbon and its forms
The discussion that compares silicon to carbon can first look as carbon and silicon in the periodic table. Carbon sits directly above silicon meaning that the two elements have 4 valence electrons each. But, the 4 valence electrons in carbon have similar or equal energies that make up the wave function mixing which facilitate hybridization. For example in carbon, these valence electrons results to orbital’s like 2px, 2s, 2pz and 2py while the 2 inner shell electrons belong to a spherical symmetric 1s orbital . The 1s orbital is bound tightly and has energy far from the carbon’s Fermi energy [28]. Due to these facts the graphite solid state property is contributed by the electrons in the 2s and 2p orbitals only.
Figure 3.2: Various Forms of Carbon a) diamond lattice image taken from http://mrsec.wisc.edu b) hope diamond image taken from Smitsonian c) Lab grown diamond image taken from Apollo Diamond Inc. d) Graphite lattice Image taken from http://www.scifun.ed.ac.uk e) pencil graphite Image taken from xara.com f) Graphite image taken from United States Geological Survey g) single layer of graphene image taken from ewels.info.com h) single walled carbon
3.3.1 Diamond
The diamond is a carbon that is three dimensional. It is sp3 bonded; forming 4 covalent strong bonds which bonds to other carbon atoms that neighbors them resulting to a atomic structure that is face-centered cubic [19]. Duiamond is said to have a high and remarkable thermal conductivity and young,s modulus simply because it is made up carbon-carbon covalent bonds which is said to be one of the world strongest bond. In the case of undoped diamond it has a insulator of a wide band gap (~5.5 eV) and without free electrons [17].
Diamond which is in many cases advertised cleverly for instance the “Diamonds are forever” and it has physical properties that are exceptional results to be the second famous and demanded metal after gem. It has wide application and the first and most recognized is when it is cut and polished to make beautiful jewelry pieces [15]. Hope Diamond makes the most famous and beautiful of these. To all of the crystals that are used to make jewelry which are either of the large or high quality, they come from a mined diamond. The smaller defective crystals are applied as reinforcement in tool bits that makes use of the superior hardness for cutting applications. There are few mines of diamond in the world and they control the supply of the material hence resulting to high process and maintenance of demand for them [18].
Diamond property of being a material with a very high thermal conductivity helps greatly in its application. This property makes it one of the most useful material in microelectronic but this is limited with the problem of heat dissipation which is a limiting factor in this application [12]. In addition to this the other problems that are associated and in order to solve this incidence the researchers and scientist have embarked on the growth of large wafers of diamond. There are a number of methods that are applied to do so, like, chemical vapor deposition (CVD) method. It is an interesting method that uses the carbon which contains gases like ethylene and methane to deposit solid carbon. In order to produce limited sized diamond which is defect free, the engineers and scientists ensures there is a controlled growing condition. By controlling the growth conditions, it is possible to produce defect free diamonds of limited size [11]. An example of a high quality diamond grown by this technique is shown in Fig. 3.2. This technique iss applied in the production of jewelry in the current world but the researchers are still active to scale the technology and produce wafer size diamond. The growth, wafer sized diamond growth, is the only technology that can help in production of diamonds that can cause impact in its current industrial use as it is applied in machining industry.
3.3.2 Fullerenes
Carbon exist in different forms, the most exotic one is the fullureness which are of low dimensional form. It is made up of carbon nanotubes, derivative which is 1 dimensional and 0 dimensional C60 molecule. Graphen is a graphite single layer and it is a carbon nanotube that is single walled, that is rolled inside a cylindrical tube of a diameter of ~ 1 nm [13]. Carbon nanotubes have similar mechanical properties to those of diamond and behave as metals or semiconductors. In the late 1990s and early 2000 the scientific headline was dominated by the study of carbon nanotubes and diamond as they had attracted the attention of researchers. It can be deduced that with this kind of research interest towards the carbon nanotube it led to the resurgent of the graphene interest [14]. Graphene was seen to be an important material that can be applied in both electrical and mechanical fields.
This interest in nanotubes was partly responsible for the resurgent interest in graphene as a potentially important and interesting material for electrical and mechanical applications.
3.3.3 Graphene and Graphite
Graphene and Graphite are that makes up the lead off a pencil and they are the hybridized carbon forms of two dimension (sp2) [40]. A stack of sheets of graphene which are held together by van der Waals forces and separation of 0.3nm forms graphite which is a layered material [44]. These sheets can easily and randomly slide over one another as a result of weak interaction that exists between the sheets. This property is very important, for it is the reason behind the lubricating property of graphite and the writhing ability of a pencil, but, so far the layers interaction has not yet been understood. For many years people have believed that the frictional forces are considerably reduced by the presence of water [74] [64]. Behold this some believes that the frictional effect that is very important is the registry of the lattice that is between the material layers. The property of super lubricity is as a result of the said registry mismatch and in this case the there is considerable reduction of the frictional forces [31]. In order to clearly elucidate the believed mechanisms, scientist makes use of mechanical experiments that are based on limited numbers of graphene layers [100].
A graphene that is of 2 Dimension sheet is a hexagonal structure in which all the atoms forms a 3 bond to all the atoms that are near it (10). This type of graphen is said to be a product of 3 of the valence electron and it referred as the σ bonds which orient towards their neighboring atoms. Graphen and diamond have both similar thermal and mechanical properties for the covalent carbon-carbon bonds that form graphene are similar to those that make the diamond structure. Because, the material is made up of 4 valence electrons, only three are used in covalent bonds but the fourth does not participate [42]. It forms a conducting π band for it appears bin a state of 2pz that is always perpendicular oriented to the graphite sheet. A combination of the graphene peculiar band structure, a semi conductor with a band gap of zero and two bands that are linearly dispersing and touching the initial corner of the Brillouin zone are the major reason behind the carbon nanotube electronic conductivity [94]. In study it has been difficult for a number of years passed to separate and isolating the graphene single layers. With this difficulty graphene has remained without being experimented until recently but bulk graphite has been a victim of study.
3.4 Graphene Fabrication
In graphene fabrication the major and widely applied method is exfoliation. This method traces its history for its foundation is on a technique of using graphite pencil for writing which has been there for centuries. Detailed explanation is that when one writes with a graphite pencil many sheets of graphene are created and spread over the paper used [38]. But the main hindrance in this method is that it cannot be controlled and hence results to sheets which are of different thickness. And as a result of this, incase one want to make studies on a single layered sheet he has to locate it. This issue is compared to an individual trying to locate a needle at a stack of hay. This problem did not stay for long for Andre Geim’s group in Manchester tried and solved it [29]. The method that was used to solve this involved; pressing or rubbing of graphite crystal that is fleshly cleaved gently flakes of oxidized silicon wafer graphene that has a certain thickness of oxide. The layers of single atoms are clearly visible using an optical microscope which is a result of effects of thin film interference [29] [43]. This technique solves the issue of the hard process that was applied initially to find the single graphene sheet, but it also hinders fabrication scheme to devices especially when applied in research. This thesis makes use of suspended graphene sheets, te process wil approximately use -1 hour to find out a -1-5 nm suspended graphene devices which in other words it will take as long as weeks to find out appropriate single suspended layer [45].
For a period of past time researchers have made a number of attempts to make improvement on exfoliation technique yield and quality. Some of the methods that have been used include the stamping method. This method for the transfer of the graphene flakes makes use of silicon pillars. The second method electrostatic voltage assisted exfoliation which make use of the electrostatic forces to control and separate graphene from the initial bulk crystals [54] [80]. Time remain as the only determining factor on whether the recorded improvements will count in the improvement of exfoliation..
Figure 3.3: Graphene Fabrication, Figure taken from Berger et al. [4]
Secondly, the other techniques used in graphene fabrication is the dispersion of graphene from a solution forms
From research carried out it is the most applied techniques in the growth of graphene for mass production in the current world. It is a simple method as it only involves heating of a SiC wafer which yields a partially graphitized upper [37]. However, it is very difficult and challenging to control the sizes of grain and the number of layers with this technique hence limiting mobilities that has been achieved with this type of graphene [46]. Furthermore, it becomes a problem to isolate the single sheets and hence lithography is a necessity in order to pattern the electrostatic gates that are on tope of the graphene. Use of grown graphene to come up with suspended mechanical structures is a process that has not yet been demonstrated. The only routes that have been applied for the growth of graphene include the chemical vapor deposition (CVD) and molecular beam epitaxy (MBE) [36]. CVD is the method that is preferably used for the successful growth of both carbon nanotubes and diamond and the MBE method is preferably for high quality GaAs/AlGaAs heterostructures. Globally, most of the experimental research groups currently depend on the exfoliation as the major method.
3.5 Properties of Graphene
3.5.1 Fundamental Characteristics of graphene
There was no empirical evidence that two dimensional compounds before 2004 when isolation of graphene was done. Theoreticians believe that two dimensional compounds could not exist because of thermal instability if such compounds were found [4]. Soon as graphene was isolated it became crystal clear that isolation of two dimensional compounds was possible only that it was to take time before scientists figured out the process of isolation that could result in a compound like graphene. The sheets of graphene were studied and found out that the sheets had slight rippling in the compound which modifies the material’s structure. However, there more research have been carried out on the compound suggesting that the carbon bonds in the graphene sheets are small and strong and can therefore not be destabilized thermally [35].
3.5.2 Electronic Propertiesof graphene
Graphene has a very high electrical conductivity because the holes and electrons are both used as charge carriers. The number of electrons in carbon atoms is 6. This means that the inner layer of carbon atom has 2 electrons while the outer layer has four electrons as carbon is in group IV of the periodic table. As with other elements, the bond within the carbon atom happens with the four outermost electrons [47]. On the other hand, graphene’s atoms are bonded on a plane that is two dimensional to 3 other atoms of carbon. The bonding of the three outermost electrons means that one electron is left to freely for electronic conduction. Since the plane is two dimensional and graphene is the thinnest of carbon elements, it shows that the electrons for conductivity can be accessible from both surfaces of the plane. The free electrons in graphene also help in the bonding of graphene because of its orbitals overlap [48].
Research on graphene has shown that the effective mass of holes and electrons is zero at the Dirac point [6]. It is imperative to note that the result of the study is due to energy movement in the element which is linear at low energies. The electrons and holes whose effective mass add to zero at the Dirac point are known as graphinos. The Dirac points is used to refer to the six corners, that of the Brillouin zone in graphene . At the Dirac points, electron conductivity is very low. This means that doping is required so that it can boost electrical conductivity of graphene, which is more than that of copper at room temperature. The free electron in the graphene sheet is very mobile. Theoretically, the limits are measured at 200000cm2V-1S-1. The latest empirical results have shown the mobility at 15000cm2V-1S-1. The lack of mass in the free electrons in graphene makes them as mobile as photons and travel longer distances without scattering [11]. Often, graphene is used along other substrates such as Silicon. The substrates can limit ballistic transport distances.
3.5.3 Mechanical Strength of graphene
Inherent strength makes graphene stand-out of many available elements. The length of carbon bonds between its atoms is about 0.142 nm which makes it one of the strongest materials to be discovered. It has a tensile strength of 130000 megapascals (MPa) which can be compared to the previously strongest element A36 structural steel, which has a tensile strength of 400 megapascals. Other elements are less strong because structural steel was rated as the strongest element ever discovered. Consequently, it can be said that graphene is extraordinarily strong since it is the only two dimensional element [14] with only three electrons in the carbon atoms bonding to three other atoms. In addition, graphene is very light with an empirical mass of 0.77mgs/m2.
Various electrical conducting materials are less elastic. With high conductivity, lighter mass, and high tensile strength, graphene is also elastic. This means that after strain, graphene has the capability of retaining its size. A practical to obtain graphene’s elasticity was carried out in 2007. The results showed that graphene’s spring constant range between one and five Newton per meter and has a Young’s modulus of 0.5 TPa. However, there are limited techniques of producing unflawed graphene [49]. These techniques are improving day by day to make graphene less costly and reducing the complexity in the production procedures.
3.5.4 Optical Properties of graphene
In addition to the aforementioned properties, graphene has an ability to absorb light – white light. It is amazing how the one thick atom sheet can possibly absorb 2.3% of white light. The electronic properties play a major role in this optical property. Since there are various techniques of graphene production, there are different sizes and fineness of the graphene produced by a certain technique. It is imperative to note that fine structured graphene absorbs more light than less fine graphene [27]. Consequently, the level of absorption can be attributed to graphene’s fine structure constant. Moreover, the thicker the element, the greater is the absorption of white light in graphene [34]. For instance, the addition of another layer of graphene adds the percentage absorption by a value of approximately 2.3% of the white light. Although there is an increase in absorption, whenever the thickness of graphene sheets is increased, saturation fluence is reached [29]. This a point at which an increase in the intensity of light causes a decrease in absorption of white light.
As a result of the mentioned characteristics that are quite impressive, it is clear that when the optical intensity reaches the threshold, which is the saturation fluence, there is saturable absorption and incase of light that is very intense, and absorption is reduced. This characteristic is very important especially when considering the mode of locking in the fibre lasers. Thefull-band mode locking is achievable when using an erbium-doped dissipative soliton fibre laser that is capable to obtain the wavelength tuning as large as 30 nm due to the property of graphene of wavelength-insensitive ultrafast saturable absorption [30]
3.5.5 Electrical Properties of Graphene
As graphene attracts research, the major experiments are focused towards its lectronic properties. The most notable feature about the early work on graphene transistors was the ability to continuously tune the charge carriers from holes to electrons. An example of the gate dependence in single layer graphene is shown in Fig. 3.3. This effect is most pronounced in the thinnest samples whereas samples from multiple layers show much weaker gate dependence due to screening of the electric field by the other layers [31].
There are some conditions when the graphene exceptional mobility enhances quantum Hall Effect observation of the holes and electrons and they include both the low temperatures and high magnetic fields [29] [33]. The graphene quantum Hall Effect of graphene shows a certain difference from the conventional quantum Hall effect in that plateaus as a resulst of its band structure that is unique and it occur at half integers of 4e2 /h instead of the typical 4e2 /h.
For more practical applications most the scientist makes use of the strong gate dependence of graphene and they apply it in either for sensing purposes or transistor applications. Unfortunately, graphene has a very small resistivity changes for it has no band gap. Therefore, as a result of a graphene transistor own nature it can only be limited by a low on/off ratio [79]. However the only solution of this mentioned limitation is to ensure the graphene is carved into small ribbons. THe opening of the band gap is realized when the ribbon is shrinked and charge carrier momentum in the transverse direction ends up being quantized [32].
Figure 3.4: it shows a graph resistivity of a single layer of graphene against the gate voltage. The second graph shows the Quantum Hall Effect in single layer graphene. Figures taken from Novoselov, Geim, et al [59][60].
As a result of this the band gap and the width of the ribbon are proportional. With the carbon nanotube the effect seems to be pronounced as its like exaggerated, the band gap and its diameter are proportional. The researcher cannot fail to mention that observation of band gap in graphene opening has only been recorded in wide ribbon devices and the lithographically patterned from large graphene flakes [63] and in narrow chemically synthesized graphene ribbons [65].
3.6 Mechanical Properties of Graphite and Graphene
3.6.1Mechanical properties of graphite
Graphite is unique in that the elastic constants in the direction perpendicular are vastly different than the elastic constants along the basal plane. This was known for quite some time and was experimentally measured during the 1960s and 1970s. Due to the resurgent interest in graphene and few layer graphene structures, it is worthwhile to revisit this history of graphite. A detailed discussion of the mechanical properties of graphite is given in [31].
The following set of six equations can be used to describe the stress and strain of a hexagonal lattice such as graphite where the x and y axis are along the basal plane [44].
Equation 3.1: six equations for stress description
where C is the elastic modulus. Both C and S can be experimentally measured using different techniques. Acoustic wave propagation or ultrasonic testing gives C while flexural vibrations and static stress-strain curves are determined by S. It is therefore useful to have equations that relate the two constants [50].
The first careful attempts to determine the mechanical elastic constants measured the resonance frequency of cantilevers of natural graphite flakes. Cantilevers with length, L= 0.4 cm – 1.0 cm and thicknesses t = of 0.01 cm – 0.05 cm were cut from natural graphite flakes. For vibrations dominated by shear, the resonance frequency is determined solely by the shear modulus G:
By examining the length dependence, Baker and Kelly determined that vibrations in as-received graphite samples were dominated by shear with a modulus, G = 0.1 GPa while irradiated crystals were dominated by bending with E= 0.6 TPa [70]. This value of G is considerably lower than the value determined by specific heat data and attributed to dislocations in the basal plane which reduce the “true” value of G in the non-irradiated samples. A more thorough study was conducted by a group at Union Carbide [7]. Utilizing static test, ultrasonic pulses and sonic resonance methods, the elastic constants were determined to be:
The spread in values of C44 is due to irradiated and non-irradiated samples exposed to fast neutrons with irradiated samples giving the higher value. This is consistent with what was observed in the above resonance frequency measurements where irradiation increased C44 by reducing basal plane dislocations. This higher value is believed to be the “true” value as it also matches specific heat data [69].
The Poisson’s ratio along the basal plane of graphite is defined as υ= -S12/ S11. The Union Carbide group experimentally measured the ratio C12/C11= 0.17. They then used the above expression which relates C and S to assume that C12/C11 must be less than or equal to υ. From this, they get a Poisson’s ratio along the basal plane of graphite to be υ= 0.16 ± 0.06.
The experimental graphene mechanical properties, have not be explored at a high rate and the time is ripe to go back and look at some of old assumptions about bulk graphite for the determination of how the elastic constants scale down to the atomic thicknesses. By working with single atomic layers or few atomic layers some of the uncertainties involved in working with large single crystals such as dislocations and defects are avoided [51].
3.6.2 Graphene’s Mechanical properties
Graphene is a monolayer of covalent bonded carbon atoms that represents a two dimensional material that haves the unique transport and mechanical properties. These properties are desired in different and wide areas of application [68]. Graphene in particular shows an outstanding electron transport properties due to the presence of charge carrier that behaves like mass less particles and its 2D hexagonal crystal structure. Graphene is defined by a specified and extreme high in plane stiffness-Young Modulus- and its superior strength. It is due to mechanical properties that it has the utmost importance for its application for they are highly needed. For instance it gives graphene capability to be exploited as super strong structural material [79].
The pristine graphene structure represents the 2D plane sheet that is covalently bonded carbon that forms the ideal hexagonal crystal lattice. In most cases the graphene specimens exists either in free standing layers or monolayer’s that are attached to substrates made of another material. The term “free standing graphene” is used to mean the graphene sheet is sufficiently isolated from all parts of its environments. Generally the mechanical properties of a crystalline solid of a graphene are controlled by its characteristics of its pristine crystal lattice and the structural defects. Structural defect includes the grain boundaries and the dislocations. For example, the atom- atom interactions in the ideal, defect free crystal lattice as well as the elastic properties of the solid [53].
3.7 Conclusion
This chapter has introduced graphene which is the theme of the research paper. Graphene is said to be an allotrope of carbon. It details its formation and how the covalent bond is bonded to make this strong material. The chapter looks also at both mechanical and electrical properties of graphene and the reason behind these properties. Like introduced in previous chapter it involves the nanomechanics of graphene as a material under investigation in this research paper.
CHAPTER 4: DETAILED CALCULATION OF MATERIALS PROPERTIES
4.1 Introduction
Graphene can be used in the production of quantum dots for instance the nanometer-thick graphene sheets, micron scale on an insulating substrate which has a patterned metallic contact. Although they have already been constructed, GaAs heterostructures [47], and small metal grains [67] have been employed in the production. Carbon nanotubes [13] [54] [62], single molecules [88], and many other materials have also been used to construct quantum dots [8]. Graphite has a carbon layered structure and has electronic spectrum which is unusual, this results in making it promising for the studies of quantum dot. All the devices that are characterized by low resistance contacts literally enhances determination of the material basic transport parameters of the material, but those materials with high contact resistances like Rc ≥ h/2e2 = 13 kΩ are deduced to be in Coulomb blockade regime [66]. In this state there is possibility of measuring both the electron addition and excitation spectrum. This chapter details the quantum dot device fabrication with how the results could be analyzed. The analysis shows that at room temperatures the devices that have low contact resistances results in maintain their small resistance incase of low temperatures [65]. The four-probe measurements generally are made for the extraction of longitudinal resistivity and the Hall of the graphite. The Coulomb blockade oscillations at low temperatures are shown by those that at room temperature have high contact resistances.
4.2 Device Fabrication
The devices are fabricated as follows. It involves a number of steps as follows. The first involves the sonication of Natural graphite flakes (Asbury Carbons Grade 3061) in dichlorobenzene solution for time approximately to be 5 minutes. Secondly, placing of a drop of the solution onto a degenerately doped Si wafer with a 200 nm thermally grown oxide is done. The rinsing of the chip is done with isopropyl alcohol and there after dried by use of nitrogen. The result is a dispersion of graphite pieces that range in thickness from several hundred nanometers to as small as a few nanometers [55]. When it comes to wire up of the graphite pieces we makes use two separate methods. The first one is the “designed electrode” method, and in it ,an AFM is employed for location of thin pieces with respect to predefined alignment marks and then electron beam lithography is used to define multiple (two to six) electrodes to the piece. Evaporation of 50 nm of Pd is done after lithography, hence followed by lift off. The product is the quasi-2D graphite quantum dots which have typical lateral dimensions of approximately 1 µm and their thickness varies from a few to tens of nanometers [78].
4.3 Data Analysis
In order to make analysis of the results, we make the simplifying assumption that that helps to derive the facts. This is assumed as; the entire graphite piece is a uniform conductor with a single density and in-plane mobility. This is appropriate if the electrodes make contact to all the graphene layers and the doping in the crystal is uniform. (Neither of these assumptions has been independently verified). From the standard equation for the Hall resistance RH= B/ne, the slope of the line in Fig. 4.1 corresponds to a density of 9.2 x 1012cm-2. The sign of the Hall voltage indicates that the dominant charge carriers are holes [56]. Assuming that all sheets are contacted and the charge is relatively uniformly distributed among the sheets, we approximate a density of n1= 2 x 10 for a single graphene sheet in the 18 nm thick device and n1= 6 x 10 for the 5nm tall device.
Figure 4.1: shows the ratio at room temperature 2-point resistance plotted against the resistant us the room temperature 2-point resistance for all the devices. Figure adapted from [23]
This density is larger than what has previously been found in bulk graphite samples [23] [91] and indicates a significant amount of hole doping in this device. The origin of this doping is unknown. The inferring of the resistance per square, R is done after accounting for effect brought by the geometrical factors, of the entire sample and the resistance per square of a single graphene layer, R1. For the 5 nm thick device at 100 mK, we have R = 3.4 kΩ and R1 = 51 kΩ. With the equation µ= 1/neR , the mobility of µ= 200 cm [76]
For the purpose of varying the carrier density, which is within the graphite quantum dot, the gate is used. The assumption is that, the gate capacitance parallel to that of the plate capacitor; Cg= εoεA/d, where d= 200 nm is the SiO2 thickness, εo is the free space permittivity, ε is the SiO2 dielectric constant, and A is the area of the device. The result of this is the capacitance per area of C’g =1.8* 10-8 F/cm2 which means that 10 V that is applied to the back gate will cause a density change of 1 x 1012 holes/cm2. This can be termed as a very small fraction of the totals density even though the sample studied is thin. Nevertheless,it is observed in many samples that are carried ut at room temperature consistency with small decrease in conductance, with the depletion of holes by the gate. At low temperatures, reproductive fluctuation is responsible of obscuring any of the mentioned changes in the conductance as a function of Vg [57].
4.4 Coulomb Blockade
All the devices that shows at low temperature Coulomb blockade have a room temperature 2-point and a resistances that is greater than 20 kΩ(closed dots) .
Figure 4.2: Longitudinal and Hall resistance measured as a function of magnetic field at 100 mK for the 5 nm thick graphite dot shown in the insets. Figure adapted from [23].
The random electrode method is used to derive data and information from a fabricated device. At T = 100 mK, with the gate voltage that of ∆Vg = 1.5 mV, the conductance exhibits defined clear definition of Coulomb blockade oscillations with a certain period. A plot of dI/dV sd vs Vg and Vs. The maximum voltage which the system can hold and still be in the blockade regime is ∆Vs.= 0.06 MV [58].
A sample device that is made by the designed electrode method is described. The thickness of the device is 6 nm, which is equal to 18 sheets. The determined period of the Coulomb blockade oscillations is ∆Vg= 11 mV that goes to as maximum blockade voltage that of ∆Vsd= 0.3 mV. A third device, which is the other device fabricated by the random electrode method as the following descriptions; It has 5 nm height and shows ∆Vg = 1.3 mV Coulomb oscillations with a period in gate voltage . The Coulomb blockade depends on the semi-classical theory for the description of results [2]. The following equation is used to calculate the Coulomb oscillations period in gate voltage;
∆Vg= e/Cg,
Equation 4.1
and using the equation 13 for Cg, it is now possible to make the approximate the area of the graphite quantum dot. Take for instance the ∆Vg = 11 mV device, A = 0.08 µm2 is the expected and likely area of the dot. The measured total area of the graphite piece shown is 0.12 µm2 while the area between the electrodes is 0.05 µm2. This is used to demonstrate that, the whole piece of graphite is serving as a single quantum dot and it could be extended beyond the electrodes [59]. For the device, ∆Vg = 1.3 mV is the measured gate voltage period that can be equated to a quantum dot with A = 0.70 µm2. 0.45 µm2 is the area between the electrodes and it is used to mean that the dot extends into the graphite piece that lies below the electrodes.
4.5 Magnetic Field Dependence
In this section the observation and examination of the magnetic field dependence in Coulomb blocklade oscillations was examined. This involved a closed dot at B = 0 T which is made up of defined oscillations. An increase on the magnetic field causes evolving of the peaks in a complicated fashion [75]. The oscillations no longer go to zero and it is the most notable, which means that the dot becomes more open. The open dot indicates fluctuations that are clear in the peak positions and it is the function of magnetic field. Similar transitions from closed to more open dots together with the peak positions changes as a function of field, is showed by other devices. Currently it is not clear the origin of these effects [64].
4.6 Conclusions
In conclusion, the white rectangular outlines are used to show the electrode size and the position that were evaporated on the device. The 0.12 µm2 is the total area of the graphite piece and both the 0.013 µm2 and 0.015 µm2 are the area under the source and drain electrodes respectively. The 0.05 µm2 is therea of the piece of graphite that is between the drain electrodes and the source. Lines traces are the one that shows the 6 nm height of the graphite [74].
In the case of the closed dots/tunnel contacts, the observation was made of the Coulomb charging phenomena, the inferred the gate and the source-drain capacitances. Those who will indulge in future studies can make investigation of the nature and role of interlayer that couples between the sheets; explore the single particle energy level spectrum, and the effects of a magnetic field. It can be deduced that studies on devices with a variety of thicknesses that have improved control over the contacts are the one that can possibly address these issues. It should be noted that graphene’s massless band dispersion relation results in a different density of states which gives ∆E ~ vfh/2Dfor a square dot of length D where vf~ 106m/s is the Fermi velocity [63]. For example, the quantum dot has D~ 200 nm which gives ∆E ~ 10 meV. This is about 30x the charging energy. Recent work by Andre Geim’s group explored this regime for graphene quantum dots with D< 100 nm fabricated from single layers of graphene [65].
CHAPTER 5: GRAPHENE CHARACTERIZATION
5.1 Introduction
Thisn chapter looks at graphene characterization. Graphene characterization can be carried out in a number of ways but this chapter will employ the two major methods that people mostly depend on. It is a process that took long for scientist to come up with means and ways of carrying out. But at last a method that relied on the nanowizard was discovered taking the process to a higher stand [27]. It is the process of producing the 2D crystal structures which wad done through exfoliating the graphite mechanically using the adhesive tape. After exfoliation the single layer sheets were made and transferred for electrical investigation to an oxidized silicon substrate. It is a process that was carried out in large scale project for the production of the application, foundation for future innovation and the fostering of scientific advances [33].
5.2. Characterization of graphene using the JPK nanowizard 3AFM system
One thing about graphene is that it can be produced using the micromechanical cleavage which some time in history of graphene it was used to provide samples for research. When one intend to produce graphene for commercial purposed, it can be done using the liquid phase exfoliation and it depends on graphite oxide to complete the process. This is not the only method but a second one involves the epitaxial growth on silicon carbide or it can make use of another material. In addition another method will involve anodic bonding, chemical vapor deposition, chemical synthesis and the photoexfoliation [44]. AFM is termed as the best method that one can depend on in graphene characterization because of its high spatial resolution and various ways that enhances probing different physical properties [55]. The image height in the system gives an overview of the graphene layer and its substrate that underlies. When one combines the graphene with Raman spectroscopy it enhances differentiation between different numbers of graphene layers.
5.2.1 Using QITM for the measurement of graphene
The newest method of measurements is the quantitative imaging mode that’s combined the simultaneous and continuous quantitative data acquisition with the superior imaging quality. By using scan an entire force curve is recorded at all points of pixels which can be used for analysis in order to investigate several material properties [44]. The real enacted force is contained in both the vertical and lateral direction that allows sensitive imaging on the loosely attached soft and brittle samples.
.
Figure 5.1: The image of graphene flakes when dipped in mica substrate and measurement are taken. Image taken from [22]
The above figure 5.1 shows graphene flakes on substrate of silicon with overlaps and the folds. In the figure the adhesion image is used to show the increased contrast within the specified area. The bottom of the figure the image is decreased in stiffness as per the wrinkled portion of the flakes which is seen at the darker part.
5.2.2 Graphene measurement using the AC mode
Figure 5.2: This is measurement of graphene flakes using the AC mode surface made up of silicon. Image taken from [32]
According to the above figure 5.2 a number of graphene flakes are distributed accros a silicon surface [10]. These flakes are multilayered graphene sheets that appear to be very flat. At the higher edges, the higher stricter are due to folds and wrinkles on the material. Some of the flakes are clearly resolved on their height as a result off the phase contrast images so as to determine the exact numbers of the layers stacked and the optical advances method are include in the process.
5.3 Measuring the conductivity of graphene
Graphene is an interesting material which has properties that are god at catching individual eyes. It is a material with very high conductivity as a result of delocalized electrons that exist between layers. Single graphene layers in other words tries to show a certain property that isolate behavior along the direction perpendicularly [5]. For instance the figure 5.3 below shows those images which were recorded when the system was at conventional mode.
Figure 5.3: Example of graphene scans which shows overlapping graphene layers. Image taken from [27]
Reducing the size of electromechanical devices offers a great potential in terms of applications that will shape the future. The small electromechanical devices in this discipline include valves, nanoscale resonators and switches. Their potential in current and future applications is based on their abilities such as information processing, molecular manipulation and sensing. The smaller the electromechanical device, the more mobile it can be. However, it is imperative to note that the functionality and efficiency of the devices must not be compromised for size. The prototypical nanoelectromechanical system (NEMS) is a nanoscale resonator, it is the beam of material that vibrates in response to an applied external force [20] [62]. The highest limit would be a resonator is one atom thick, which is limited by the fact that puts severe constraints on the material. It should be robust, stiff, and stable as a single layer of atoms. Graphene could be used in such application but has yet been implemented.
Graphite is built up of grapheme sheets inform of staked layers with separation distance of 0.3nm. The grapheme sheets (staked layers) are then held together by weak van der Walls forces [44]. Along its basal plane, it is characterized by high thermal conductivity, stiffness and high strength. Additionally, it is possible to exfoliate the graphite into an insulating substrate. As a result, a micron-sized graphene sheets are formed with its thickness down to a single atomic layer [29] [14] [15] [99].
Resulting from these findings, the current study is mainly focused on the electronic characteristics of grapheme sheets. The study explores on a technique of suspending multilayer and also single grapheme sheets over trenches with the final aim of mechanically actuating them. In addition, the research expounds on the mechanical properties of grapheme resonators, particularly on their spring constant, resonance frequency, quality factor and built in tension [73].
5.4 Device Fabrication
The process of fabricating suspended graphene sheets is a similar peeling process to that that has been previously reported. In this process, Kish graphite or Toshiba Ceramics, which should be freshly cleaved, is rubbed into a silicon wafer. The silicon wafer is usually made of thermally grown SiO2 of 260 – 330 nm, with 280 nm as the ideal size [29] [99]. In this instance, mechanical exfoliation of the graphene sheets is made over surface of silicon oxide that is etched into predefined trenches. The etched trenches in this case are usually of a depth between 260 and 500 nm, widths and lengths between 0.5 and 10 µm. a dry RF plasma etching technique is used to define SiO2. The process of photolithography is then used to define the electrodes, usually in the composition size of 30 nm Au and 5 nm of Cr. The graphene sheets are then suspended over nearby trenches (the small sizes) after peeling off on the edges of trenches (large sizes) and electrodes. This results into a cantilever clamped or a micron-scale doubly clamped beam to the surface of silicon oxide through the attraction of van der Waals [72].
5.5. Device Characterization – AFM and Raman
To measure the sheets’ thickness in quantitative terms on the substrate next to the trench, a non-contact mode AFM is used. This is shown in the inset. Silicon cantilevers, usually operating with a resonance frequency of 250 and 310 kHz are used to take the images of all non-contact AFM images based on a dimension 3100 and operating in ambient conditions. However, in the case of sheets that are thinner than 2-3 nm, such measurements are not reliable for determining the actual thickness [27] [30] [31]. To cater for these cases, a spatially resolved Raman Spectroscopy is used to help in the determination of number of sheet layers [27] [31] [61]. Through the aid of Renishaw InVia Raman microscope, light consisting of a wavelength of 488 nm is made to focus on the resonator. This is done through the use of a 50x objective, where each Raman trace is observed within integration time ranging between 1 to 5 seconds [71].
The sample sits on a piezoelectric stage which is scanned to take a Raman spectrum at specific points along the graphene sheet. The graphene sheet has an AFM-determined height of 0.9 nm. By comparison with previous results [27] [30] [31], the shape of the Raman peak near 2700 cm-1 suggests the sheet is two layers thick over the area lying on the SiO2substrate, while the section suspended over the trench is a single graphene layer.
Figure 5.4: (A) Schematic of a suspended graphene resonator. (B) An optical image of a double layer graphene sheet (C) Raman signal from a scan on the graphene piece (D) An optical image of few (~4) layer graphene suspended over a trench and contacting a gold electrode. E) A scanning electron microscope image of a few (~ 2) layer graphene resonator. Image taken from [27][30][31]
5.6. Conclusion
The chapter includes the characterization of graphene and details all the methods that are applicable in the process. In addition it covers material fabrication. There are a number of ways that are employed in characterization and help to show the properties of graphene. Characterization helps to show the graphene properties through exposing it using some methods.
CHAPTER 6: APPLICATIONS OF GRAPHENE
6.1 Introduction
Properties of graphene as the lightest, strongest in addition to its electrical properties make it standout as a replacement or improvement to the available materials used in various applications. This chapter discusses application of graphene is various applications such as biological engineering, composite materials, nanotechnology, and energy technology. The application of graphene in the energy sector is also discussed in detail.
6.2 Biological Engineering
Although the use of graphene in biological engineering has not yet been implemented, it is a prospect that graphene can be of vital importance to the area. Despite this, there are hurdles which must be overcome before graphene can be used in biological engineering – its compatibility in biological engineering has to be investigated. Clinical contraindications should also be investigated through clinical, safety, and regulatory trials. Often, materials are used in combination of other materials – compatibility with materials used in bioengineering should also be tested. Some of the properties of graphene for use in bioengineering include a large surface area, high electrical conductivity, strength, and thinness [87]. The properties are good for development of sensory devices to monitor DNA sequencing, glucose levels, and cholesterol levels.
6.3 Optical Electronics
Although it has not already started being used on commercial scale, the use of graphene in optical electronics can boost the efficiency and effectiveness of optical equipments. The optical properties of graphene as aforementioned can be used in the manufacture of LCD displays, touchscreens and organic LEDs [22]. This is because graphene can be able to transmit a high percentage of light and is electrically conductive. The electrical properties of graphene are very impressive – with doping, graphene is highly conductive that copper. Combined with the tensile strength of graphene, production of electronics with graphene can be highly advantageous. Moreover, graphene is very thin because it is made up of one atom thick. This makes graphene very transparent and able to transmit over 96% proven with practical results. One of the practical applications where the element can be used is the Smartphone, tablet, television, and desktop computer touchscreens. The material currently used in the manufacture of the touchscreens is indium tin oxide. Although the performance of ITO is amazing, the properties of graphene have proven to match those of ITO in the current applications. With tests and improvements on graphene, it could be able to produce even better results [79]. Some of the improvements that might add to the properties of ITO are graphene’s tensile strength and flexibility. In addition, the absorption of graphene can be improved or adjusted by the adjustment of its Fermi levels. Graphene could also be used in making e-paper which could show interactive and updatable information and flexible strong electronic devices.
6.4 Ultrafiltration
From the properties of graphene, it shows that its quality to allow water to pass through does make it less impervious to other liquids and gases. Consequently, graphene can be used in the separation of water and other fluids – this is called ultrafiltration. Other properties that support graphene for ultrafiltration include its electronic properties which could be used to measure and compare the densities, pressure, and strain of the two fluids being separated. It is also thin and can be used in applications that do not require a lot of space [83]. The current compound used in current ultrafiltration applications is aluminium oxide. Such applications where graphene can be used include body armour for military and vehicles. Graphene could also be used to measure stress levels and respond to pilots in aircraft wings.
6.5 Composite Materials
The strength and lightness of graphene can be used in development of aerospace items. There have been efforts to incorporate carbon fibre into aircrafts. Compared to carbon fibres, graphene is stronger and stiffer [79]. Steel with its strength, has been used in the development of aircrafts. Graphene is even stronger and lighter than steel. It could be used to replace steel in the production of aircrafts. Aircrafts are faced with the problem of lightning strikes while in the air. Graphene’s electrical properties are strong to be used as a coating on the surface to curb aircraft lightening problems [100].
6.6 Application of Graphene in the Energy Sector
The energy sector’s main aim is to produce energy and to store the energy for use in various applications. There are various methods through which energy is produced including hydro-electric power production, geothermal power production, solar energy harvesting and many other methods. It is imperative to note that graphene can not be used in all of these applications of energy production. With the aforementioned properties of graphene, the most suitable fit is the solar energy harvesting which is mostly used for generating energy used for emergency and for mobile devices [76]. It is also important to note that graphene can be used in building energy storage reservoirs which can be much more efficient than the existing energy storage systems.
6.6.1 Photovoltaic Cells
Photovoltaic cells are developed with the use of ITO or silicon. Properties of graphene such as low light absorption and high electron mobility mean graphene can be used in the manufacture of photovoltaic cells. Silicon cells are very expensive to produce – this confirms the reason for the high cost of solar panels and other applications of photovoltaic cells. Compared to silicon, graphene can be much cheaper. Other properties that make graphene more viable for photovoltaic cells is that it generates multiple electrons when it absorbs a photon. Consequently, a lot of energy is not lost as it happens with silicon cells which produce a photon for every electron produced. There is a property of graphene that can also improve application in photovoltaic cells – its flexibility and strain can be used in clothing so that charging pocket items could be simple while walking or exposed to the sun [84].
3-D graphene is a recent achievement meant to improve the efficiency of solar cells. 3-Dimensional graphene can be a very economical replacement for platinum commonly used in dye-sensitive solar cells. Dye-sensitive solar cells are easy to produce, flexible, and relatively efficient to convert solar energy into electricity. In the meantime, the dye-sensitive solar cells rely on the rare and expensive materials such as platinum. An ounce of platinum goes for around $1500. This means that a readily available graphene could make the production of DSSCs more economical and affordable to many users. This means that the two dimensional graphene must pass through a process that can convert it to 3D model without forming graphite. Yun Hang Hu together with his research team invented novella strategic approach so as to synthesize a unique 3D version of graphene, this graphine had a structure which was like honeycomb. Lithium oxide was used and was chemically reacted after combination with carbon which resulted to a lithium carbonate and the honeycomb graphene [87]. Lithium carbonate is very important in this reaction has it help in yielding the shape the graphene sheets and their isolation from each other thus preventing the formation of graphite. By the use of an acid, the lithium carbonate can be removed from the honeycomb graphene.
Figure 6.1: How to create 3D graphene: combine lithium oxide with carbon monoxide, forming lithium carbonate (Li2CO3) and the honeycomb graphene. Figure adapted from http://www.kurzweilai.net/images/3D-graphene.jpg
An experiment conducted by the team showed that 3-dimensional honeycomb graphene can be applied in energy conversion and storage due to properties that it showed like; high catalytic activity and excellent electrical conductivity. Another experiment was carried out and this time replacing the dye-sensitized solar cell made of platinum counter electrode with one that is made of 3-dimensional honeycomb graphene. There after the solar panels were placed on the sunshine and their output measured [71]. The results showed a conversion of solar energy at a rate of 7.8% which is almost equal to the conversion rate of conventional solar cell depending on the expensive platinum at around 8% [78]. It is also noted that there are no hurdles in the adoption of the honeycomb graphene to its application in the use in dye-sensitized solar cells.
6.6.2 Energy Storage
Elements that have been used in energy storage have similar characteristics as those of graphene – graphene surpasses some of the characteristics. When energy is not in use and it is being generated, it can be kept for future use or for use in cases of emergency. The current energy storage systems are not as efficient as required. This is why there are improvements in the storage devices to increase the volume of storage and reduce the costs of production although the solutions have been developing at a slower rate. Although the current batteries can store a lot of energy, such batteries can take a very long time to charge [86]. On the other hand, capacitors have also been used to store energy and can be charge quickly although they can only hold a small amount of energy. Graphene can be used in these development to produce super-capacitors which can be charged quickly and store a large amount of energy at the same time. Such batteries can be used in longevity with lighter weight than the available batteries [96]. They can be used in small scale applications such as Smartphone, laptops, and tablet PCs. They could also be used in large scale applications such as electrically powered vehicles.
Tests have shown that, anodes that performs better when used to make lithium ion batterisare the ones that are made with ribbons of graphene. The results for 50 charge discharge cycles published in ACS Nano journal show that the proof of concept units maintained a capacity that doubles and is greater than of graphite currently used in anodes of lithium ion battery [77]. The main application of the use of graphene ribbons in batteries is the increasing mobile world.
Figure 6.2: A better way to build a lithium ion battery. Figure adopted from [76]
The capacity of a battery is very important and the large it is, the better. The efficiency of mobile devices ends up being ½ a day useless because of the capacity of batteries. Compared with other materials used in Li batteries, graphene ribbons are better because they can withstand many charge-discharge cycles with less degradation of charge rate [85]. Lithium ions have a characteristic of expanding the material that they inhabit and these material contacts as it pulls away. On the other hand, their are some other materials that have extraordinary capacity, like silicon for lithium but break down and lose their ability to store ions. The property of dispersion of oxide nanoparticles and keeping them from fragmentation during cycling is enhanced the fact that graphene ribbon make a strong framework. With such great properties, graphene shall soon be seen to be applicable in commercial energy storage applications.
Figure 6.3: Silicon-graphene battery triples lithium ion battery densities. Figure adopted from [77]
6.6.3. Further applications of grapheme in energy sector
After several considerations by researchers and companies they have shown use of the material in several fields. This is because properties of graphene, the carbon sheet have only one atom thick.
Electrodes with very high surface area have been investigated to have very low electrical resistance. One of the applications of graphene is in the electrode that is made out of the carbon nanotube that is grown on the graphene. This was done through a series of research that was initiated by growing of graphene on the metal substrate and the later growing in the nanotube on the graphene sheet. In order to be applied in growing of electrode the graphene is said to have certain properties. This is because it has the base of each nanotube is bonded, atom to atom, to graphene sheet the nanotube graphene structure is very essential in one molecule with a very huge surface area. The seamless graphene or nanotube hybrid is the best electrode interface material that is possible for the storage of energy and electron applications [55]. They have a very large surface area that is referred as the key factor in making of energy storing capacitors. Carbon is said to be no peer has a conductive material when it is in thin and robust form for instance the form of graphene or any other type of nanotube. When the two are combined they offer a very great potential for electronic components for example the super capacitor which have a massive surface area that holds energy in a tiny package.
Figure 6.4: Seven-atom rings (in red) at the transition from graphene to nanotube make this new hybrid material a seamless conductor. Figure from [55]
Graphene is applied in lower cost solar cells. Some of the researchers have carried out research and built up a solar cell that make use of graphene as an electrode while using the carbon nanotubes and buckyballs. They two are combined and they absorb light in order to generate the electrons that make a solar cell composed only of the carbon [56]. The main intention of this is elimination of need for higher cost materials and dependence on complicated manufacturing techniques that are needed for solar cells. Scientists from the University of Stanford have built a solar cell that is purely made up of carbon and it has a promising alternative to the expensive materials that are used in the photovoltaic device today [93]. According to their research, carbon is said to have the highest potential in order to deliver the high performance at a low cost [94]. This type of a solar panel that can be made at a low cost is said to be the one that can only have components made up of carbon.
Figure 6.5: Flexible organic solar cells equipped with graphene electrodes. Figure from[56]
Graphene can be applied as transistors that operate at higher frequency. It is very easy and possible to build high frequency transistors of higher speed. This is in case of which the electrons in the graphene move as compared to electrons in silicon [57]. In the same application the researchers have come out with an idea of developing the lithography techniques that can easily be used to fabricate the integrated circuits based on the graphene. Some of the scientists have come up with the world fastest graphene transistor. This was accomplished as the major milestone for the Carbon Electronics for RF Applications, as they aimed at developing the next generation communication device. In order to achieve high frequency record, it was through use of the wafer scale, epitaxially grown graphene that uses the technology that is compatible to the devices used in advanced silicon device fabrication. The major advantage of the graphene lies in the high speeds where electrons propagate and it is very essential to achieve high speed, performance next generation transistors [95]. Graphene is a single atom thick layer made of carbon atoms that are bonded in a hexagonal honey comb like arrangement. This two dimensional form of carbon posses unique optical, mechanical, thermal and electrical properties.
Figure 6.6: Yu-Ming Lin on High-Performance Graphene Transistors. Figure from [44]
Figure 6.7: High-performance graphene transistors made using sticky tape. Figure from [44].
Low cost of display screen in mobile devices applies graphene. As a result of its admirable properties, researchers have embarked on massive application of graphene. They have come up with an idea of replacing the indium based electrode of the organic light emitting diode (OLED) using the graphene [96]. These types of diodes are used in the electronic device display screen that requires low consumption of power. When one uses graphene instead of indium it reduces the costs and also eliminates the use of metals in OLED in order to come up with the devices that are easier to recycle [58].
Figure 6.8:Sample mobile screen made from graphene. Figure from[58]
Figure 6.9: An OLED display . Figure from [58]
Graphene for storing hydrogen for fuel cell powered cars. This is when the graphene is prepared in layers in order to increase the binding energy of the hydrogen to the surface in fuel tanks and hence results to higher amount of hydrogen storage and there after lighter weight fuel tanks. It has been applied in the development of the practical hydrogen fuelled cars.
Sensors to diagnose diseases; these sensors are based upon the graphene large surface area and the idea that the molecules that are sensitive to certain disease can attach to the carbon atoms of the graphene. For instance the researchers have come up with an idea that the fluorescent molecule and the strands of DNA can be combined for diagnosis of the disease [62]. A sensor is formed by attaching the fluorescent molecule to form a single strand and the attaching the DNA to the graphene. In case of an identical single strand DNA combines with the strand on the graphene a double strand DNA if formed that floats off from the graphene, increasing the fluorescence level. This method results in a sensor that can detect the same DNA for a particular disease in a sample [97].
Graphene is used in lithium_ion battery that recharge faster. These type of batteries make use of graphene on the surface of the anode. The defect in the graphene sheet that is introduced using a heat treatment provides pathway for the lithium ions for attachments to the anode sub state. The main advantage is that the time that is required to recharge a battery that uses the graphene anode is shorter than with the conventional lithium-ion-batteries [60].
Ultra capacitors with better performance than batteries; these capacitors tries to stress electron on the graphene sheet. They take advantage of the large surface of the graphene to provide increase on the electrical power that is stored within the capacitor. The ultra capacitors are said to have much electrical storage capacity as lithium ion batteries but it will be able to be recharged in single and simple minutes of tome instead of hours.
Figure 6.10: Graphene utra capacitors. Figure from [60].
Chemical sensors effective at detecting explosives: These sensors contain sheets of graphene in the form of foam which changes resistance when a low level of vapours from chemicals, such as ammonia, is present.
Figure 6.11: Flexible chemical sensor made with carbon nanotubes could help detect traces of toxins and explosives in water. Courtesy of Mark Roberts. Figure from. http://phys.org/news173035243.html#jCp
6.7: Conclusion
This chapter in details explains the applications of graphene in various sectors. It introduces some of the graphene application before streamlining the idea to the demand of the paper. Graphene has a number of mechanical properties that favor applications in electrical field and due to this it add weight to theme of the research. It details all the applications of graphene in the energy and electronic sectors like; lithium ion battery, transistors capacitors etc.
CHAPTER 7: CONCLUSIONS
This dissertation explored the electrical and mechanical properties of a new unique two dimensional atomic crystal – graphene and its potential application in the energy sector. Chapters 1-3 included an overview of the basic concepts relevant to the literature presented in Chapters 4-5. Chapter 1 deals with discussion of mechanical and electrical properties of nanoscale systems. Chapter two introduces nanoelectromechanical systems followed by chapter 3 giving a detailed discussion of mechanical and electrical properties of graphene which is the current understanding of the new material. In devices with high resistance contacts, we observed Coulomb blockade phenomena and inferred the charging energies and capacitive couplings. The experiments demonstrated that electrons in mesoscopic graphite pieces are delocalized over nearly the whole graphite piece down to low temperatures. Chapter 6 provided a detailed overview of the various applications of graphene and majorly in the energy sector. It was shown that 3D honeycomb graphene can be used to replace platinum in solar cells for efficient and economical solar harvesting applications. It was also shown that graphene nanoribbons can be used in lithium ion batteries for high performance and high capacity batteries eliminating the disadvantages of the currently used materials such as graphite and silicon.
It was demonstrated that Graphene can withstand a pressure difference greater than 1 atmosphere and such a pressure difference was used to determine the mass of the membrane and extract the elastic constants. It was found that a single sheet of graphene is impermeable to helium gas atoms and therefore free of any significant vacancy over micron size areas. Graphene represents the thinnest membrane possible, and by establishing a pressure difference across this membrane the world’s thinnest balloon was created. Graphite has been used in the manufacture of solar cells which have played a significant role in solar energy generation. Graphene can be a better replacement for such materials and can be used for creation for power storage for storing large amounts of energy and for faster charging.
References
[1] K. L. Aubin. Radio Frequency Nano/Microelectromechanical Resonators: Thermal and Nonlinear Dynamics Studies. Applied and Engineering Physics. Ithaca, NY, Cornell University: 115, 2005
[2 ] C. W. J. Beenakker, “Theory of Coulomb-Blockade Oscillations in the Conductance of a Quantum Dot.” Physical Review B 44(4), 1991, pp. 1646-1656.
[3] M. R. Begley and T. J. Mackin. “Spherical indentation of freestanding circular thin films in the membrane regime.” Journal of the Mechanics and Physics of Solids 52(9), 2004, pp. 2005-2023.
[4] C., Z. Song Berger, et al. “Electronic Confinement and Coherence in Patterned Epitaxial Graphene.” Science 312(5777), 2006, pp. 1191-1196.
[5] C., Z. M. Song Berger, et al. “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics.” Journal of Physical Chemistry B 108(52), 2004, pp. 19912-19916.
[6] P.Blake, E. W. Hill, et al. “Making graphene visible.” Applied Physics Letters 91(6), 2007, pp. 063124.
[7] O. L Blakslee, D. G. Proctor, et al. “Elastic Constants of Compression-Annealed Pyrolytic Graphite.”Journal of Applied Physics 41(8), 1970, pp. 3373-3382.
[8] M. Bockrath, D. H. Cobden, et al. “Single-electron transport in ropes of carbon nanotubes.” Science 275(5308): 1997, pp. 1922-1925.
[9] A. Bokaian, “Natural frequencies ofbeams under tensile axial loads” Journal of Sound and Vibration 142(3), 1990, pp. 481-498.
[11] K. I.Bolotin, K. J. Sikes, et al.”Ultrahigh electron mobility in suspended graphene.” Solid State Communications 146(9-10), 2008, pp. 351-355.
[12] D. Bozovic, , M. Bockrath, et al. “Plastic deformations in mechanically strained single-walled carbon nanotubes.” Physical Review B 67(3), 2003.
[13] M. R. Buitelaar, A. Bachtold, et al. “Multiwall carbon nanotubes as quantum dots.” Physical Review Letters 88(15), 2002, pp. 156801.
[14] J. S. Bunch, A. M. van der Zande, et al. “Electromechanical Resonators from Graphene Sheets.” Science 315(5811), 2007, pp. 490-493.
[15] J. S., Bunch, S. S. Verbridge, et al. “Impermeable Atomic Membranes from Graphene Sheets.” Accepted to Nano Letters, 2008.
[16] J. S., Bunch, Y. Yaish, et al. “Coulomb oscillations and Hall effect in quasi-2D graphite quantum dots.” Nano Letters 5(2), 2005, pp. 287-290.
[17] T. P. Burg and S. R. Manalis “Suspended microchannel resonators for biomolecular detection.” Applied Physics Letters 83(13), 2003, pp. 2698-2700.
[18] D. J. Campbell, and M. K. Querns “Illustrating Poisson’s Ratios with Paper Cutouts.” J. Chem. Educ. 79, 2002, pp. 76.
[19] A. N. Cleland, and M. L. Roukes “A nanometre-scale mechanical electrometer.” Nature 392(6672), 1998, pp. 160-162.
[20] H. G. Craighead “Nanoelectromechanical systems.” Science 290(5496), 2000, pp 1532-1535.
[21] M., Dienwiebel, G. S. Verhoeven, et al. “Superlubricity of Graphite.” Physical Review Letters 92(12), 2004, pp. 126101.
[22] R. Dingle, H. L. Stormer, et al. “Electron mobilities in modulation-doped semiconductor heterojunction super lattices.” Applied Physics Letters 33(7), 1978, pp. 665-667.
[23] X., Du, S.-W. Tsai, et al. “Unconventional Magnetotransport in Graphite.” arXiv:cond-mat/0404725.
[24] K. L., Ekinci, X. M. H. Huang, et al. “Ultrasensitive nanoelectromechanical mass detection.” Applied Physics Letters 84(22), 2004, pp. 4469-4471.
[25] K. L. Ekinci, and M. L. Roukes “Nanoelectromechanical systems.” Review of Scientific Instruments 76(6), 2005, pp. 061101
[26] K. L., Ekinci, Y. T. Yang, et al. “Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems.” Journal of Applied Physics 95(5), 2004, pp. 2682-2689.
[27] A. C., Ferrari, J. C. Meyer, et al. “Raman Spectrum of Graphene and Graphene Layers.” Physical Review Letters 97(18), 2006, pp. 187401.
[28] I. W.Frank, D. M. Tanenbaum, et al. Mechanical properties of suspended graphene sheets, AVS, 2007.
[29] A. K. Geim, and K. S. Novoselov “The rise of graphene.” Nat Mater 6(3), 2007, pp. 183-191.
[30] D. Graf, F. Molitor, et al. “Spatially Resolved Raman Spectroscopy of Single- and Few-Layer Graphene.” Nano Lett. 7(2), 2007, pp. 238-242.
[31] A. Gupta, G. Chen, et al. “Raman Scattering from High-Frequency Phonons in Supported n-Graphene Layer Films.” Nano Lett, 2006.
[32] M. Han, Y. , B. Ozyilmaz, et al. “Energy Band-Gap Engineering of Graphene Nanoribbons.” Physical Review Letters 98(20), 2007, pp. 206805.
[33] R. Hanson, L. P. Kouwenhoven, et al. “Spins in few-electron quantum dots.” Reviews of Modern Physics 79(4), 2007, pp. 1217.
[34] A. Hashimoto, K. Suenaga, et al. “Direct evidence for atomic defects in graphene layers.” Nature 430(7002), 2004, pp. 870-873.
[35] T. Hertel, R. E. Walkup, et al. “Deformation of carbon nanotubes by surface van der Waals forces.” Physical Review B 58(20), 1998, pp. 13870-13873.
[36] J. Hrusak, D. K. Bohme, et al. “Ab initio MO calculation on the energy barrier for the penetration of a benzene ring by a helium atom. Model studies for the formation of endohedralHe C60 complexes by high-energy bimolecular reactions.” Chemical Physics Letters 193(1-3), 1992, pp. 97-100.
[37] Y. Huang, J. Wu, et al. “Thickness of graphene and single-wall carbon nanotubes.” Physical Review B (Condensed Matter and Materials Physics)74(24), 2006, pp. 245413-9.
[38] B., Ilic, H. G. Craighead, et al. “Attogram detection using nanoelectromechanical oscillators.” Journal of Applied Physics 95(7), 2004, pp. 3694-3703.
[39] B., Ilic, S. Krylov, et al. “Optical excitation of nanoelectromechanical oscillators.” Applied Physics Letters 86(19), 2005, pp. 193114.
[40] M., Ishigami, J. H. Chen, et al. “Atomic Structure of Graphene on SiO2.” Nano Lett. 7(6), 2007, pp. 1643-1648.
[41] S. M., Jay, A. Z. Christian, et al. “Examination of Bulge Test for Determining Residual Stress, Young’s Modulus, and Poisson’s Ratio of 3C-SiC Thin Films.” Journal of Aerospace Engineering 16(2), 2003, pp. 46-54.
[42] C., Jiang, S. Markutsya, et al. “Freely suspended nanocomposite membranes as highly sensitive sensors.” Nat Mater 3(10), 2004, 721-728.
[43] D. M.Karabacak, Resonant Operation of Nanoelectromechanial Systems in Fluidic Environments. Mechanical Engineering. Boston, MA, Boston University: 170, 2008.
[44] B. T. Kelly, Physics of graphite. London; Englewood, N.J., Applied Science. Kenny, T. (2001). “Nanometer-scale force sensing with MEMS devices.” Sensors Journal, IEEE 1(2), 1981, pp. 148-157.
[45] K. v., Klitzing, G. Dorda, et al. “New Method for High-Accuracy Determination of the Fine-StructureConstant Based on Quantized Hall Resistance.” Physical Review Letters 45(6), 1980, pp. 494.
[46] R. G. Knobel, and A. N. Cleland. “Nanometre-scale displacement sensing using a single electron transistor.” Nature 424(6946), 2003, pp. 291-293.
[47] L. P. Kouwenhoven, , C. M. Marcus, et al. Electron transport in quantum dots, 1997.
[48] Mesoscopic Electron Transport. L. L. Sohn, L. P. Kouwenhoven and G. Schoen. New York and London, Plenum, 1997, pp. 105-214.
[49] I., Kozinsky, H. W. C. Postma, et al. “Tuning nonlinearity, dynamic range, and frequency of nanomechanical resonators.” Applied Physics Letters 88(25), 2006, pp. 253101.
[50] M. D., LaHaye, O. Buu, et al. “Approaching the quantum limit of a nanomechanical resonator.” Science 304, 2004, pp. 74-77.
[51] N. V. Lavrik, and P. G. Datskos “Femtogram mass detection using photothermally actuated nanomechanical resonators.” Applied Physics Letters82(16), 2003, pp. 2697-2699.
[52] X., Li, X. Wang, et al. “Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors.” Science 319(5867), 2008, pp. 1229-1232.
[53] X. X., Li, T. Ono, et al. “Ultrathin single-crystalline-silicon cantilever resonators: Fabrication technology and significant specimen size effect on Young’s modulus.” Applied Physics Letters 83(15), 2003, pp. 3081-3083.
[54] W. J., Liang, M. P. Shores, et al. “Kondo resonance in a single-molecule transistor.” Nature 417(6890), 2002, pp. 725-729.
[55] X., Liang, Z. Fu, et al. “Graphene Transistors Fabricated via Transfer-Printing In Device Active-Areas on Large Wafer.” Nano Lett. 7(12), 2007, pp. 3840-3844.
[56] J. C., Meyer, A. K. Geim, et al. “The structure of suspended graphene sheets.” Nature 446(7131) 2007, pp. 60-63.
[57] K. E., Mueggenburg, X.-M. Lin, et al. “Elastic membranes of close-packed nanoparticle arrays.” Nat Mater 6(9), 2007, pp. 656-660.
[58] R. L. Murry, and G. E. Scuseria “Theoretical Evidence for a C60 “Window” Mechanism.” Science 263(5148), 1994, pp. 791-793.
[59] W. D. Nix, “Lecture Notes for “Mechanical Properties of Thin Films”.” Novoselov, K. S., A. K. Geim, et al. (2005). “Two-dimensional gas of massless Dirac fermions in graphene.” Nature 438(7065), 2005, pp. 197-200.
[60] K. S., Novoselov, A. K. Geim, et al. “Electric Field Effect in Atomically Thin Carbon Films.” Science 306(5696), 2004, pp. 666-669.
[61] K. S., Novoselov, D. Jiang, et al. “Two-dimensional atomic crystals.” Proceedings of the National Academy of Sciences of the United States of America 102(30), 2005, pp. 10451-10453.
[62] J. W., Park, A. N. Pasupathy, et al. “Wiring up single molecules.” Thin Solid Films 438, 2003, pp. 457-461.
[63] W. G. Perkins, and D. R. Begeal, “Diffusion and Permeation of He, Ne, Ar, Kr, and D[sub 2] through Silicon Oxide Thin Films.” The Journal of Chemical Physics 54(4), 1971, pp. 1683-1694.
[64] A. Pertsin, and M. Grunze “Water as a lubricant for graphite: A computer simulation study.” The Journal of Chemical Physics 125(11), 2006, pp. 114707.
[65] L. A., Ponomarenko, F. Schedin, et al. “Chaotic Dirac Billiard in Graphene Quantum Dots.” Science 320(5874), 2008, pp. 356-358.
[66] M. Poot, and H. S. J. van der Zant “Nanomechanical properties of few-layer graphene membranes.” Applied Physics Letters 92(6), 2008.
[67] D. C., Ralph, C. T. Black, et al. “Gate-voltage studies ofdiscrete electronic states in aluminum nanoparticles.” Physical Review Letters 78(21), pp. 1997, 4087-4090.
[68] F. Reif, Fundamentals of Statistical and Thermal Physics. New York, NY, McGraw-Hill Book Company 1965,.
[69] F., Rose, A. Debray, et al. “Suspended HOPG nanosheets for HOPG nanoresonator engineering and new carbon nanostructure synthesis.” Nanotechnology(20): 5192, 2006.
[70] R. S., Ruoff, J. Tersoff, et al. “Radial deformation of carbon nanotubes by van der Waals forces.” Nature 364(6437), pp. 1993, 514-516.
[71] G. M., Rutter, J. N. Crain, et al. “Scattering and Interference in Epitaxial Graphene.” Science 317(5835), 2007, pp. 219-222.
[72] R., Saito, G. Dresselhaus, et al. Physical Properties of Carbon Nanotubes. London, England, Imperial College Press, 1998
[73] M., Saunders, H. A. Jimenez-Vazquez, etal. “Stable Compounds of Helium and Neon: He@C60 and Ne@C60.” Science 259(5100), 1993, 1428-1430.
[74] R. H. Savage, “Graphite Lubrication.” Journal ofApplied Physics 19(1): 1-10. Sazonova, V. (2006). A Tunable Carbon Nanotube Resonator. Physics. Ithaca, Cornell University: 209, 1948.
[75] V., Sazonova, Y. Yaish, et al. “A tunable carbon nanotubeelectromechanical oscillator.” Nature 431(7006), 2004, pp. 284-287.
[76] R. J., Schoelkopf, P. Wahlgren, et al. “The Radio-Frequency Single-Electron Transistor (RF-SET): A Fast and Ultrasensitive Electrometer.” Science 280(5367), 1998, pp. 1238-1242.
[77] L., Sekaric, J. M. Parpia, et al. “Nanomechanical resonant structures in nanocrystalline diamond.” Applied Physics Letters 81(23), 2002, 4455-4457.
[78] S. D. Senturia, Microsystem Design. New York, NY, Springer Science+Business Media, LLC, 2001.
[79] Shagam, M. Y. Nanomechanical Displacement Detection Using Fiber Optic Interferometry. Mechanical Engineering. Boston, Boston University: 95, 2006.
[80] A. N., Sidorov, M. M. Yazdanpanah, et al. “Electrostatic deposition of graphene.” Nanotechnology(13): 135301, 2007.
[81] J. Singh, Physics of Semiconductors and their Heterostructures. New York, NY., McGraw-Hill, 1993.
[82] D. E. Soule, “Magnetic Field Dependence of the Hall Effect and Magnetoresistance in Graphite Single Crystals.” Physical Review 112(3), 1958, pp. 698-707.
[83] Staff. Yole Ranks Top 30 MEMS Suppliers; Sees Rapid Growth in Consumer, Medical. Semiconductor International, 2008.
[84] E., Stolyarova, K. T. Rim, et al. (). “High-resolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface.” Proceedings of the National Academy of Sciences 104(22), 2007, pp. 9209-9212.
[85] H. L. Stormer, “Nobel Lecture: The fractional quantum Hall effect.” Reviews of Modern Physics 71(4), 1999, pp. 875.
[86] C. C., Striemer, T. R. Gaborski, et al. “Charge- and size-based separation of macromolecules using ultrathin silicon membranes.” Nature 445(7129) 2007, pp. 749-753.
[87] K. Tanizawa, and K. Yamamoto “Measuring Apparatus ofMembrane Tension and Its Characteristics.” National Committee for Theoretical and Applied Mechanics, Science Council of Japan 53, 2004, pp. 75-82.
[88] S. J., Tans, M. H. Devoret, et al. “Individual single-wall carbon nanotubes as quantum wires.” Nature 386(6624), 1997, 474-477.
[89] S. Timoshenko, Theory of Elasticity. New York, McGraw-Hill Book Company, Inc. 1934
[90] S., Timoshenko, D. H. Young, et al. Vibration Problems in Engineering. New 121 York, John Wiley and Sons, Inc. 1974.
[91] T., Tokumoto, E. Jobiliong, et al. “Electric and thermoelectric transport probes of metal-insulator and two-band magnetotransport behavior in graphite.” Solid State Communications 129(9), 2004, pp. 599-604.
[92] S. S., Verbridge,J. M. Parpia, et al. “High quality factorresonance at room temperature with nanostrings under high tensile stress.” Journal of Applied Physics 99(12): 124304, 2006.
[93] J. J. Vlassak, and W. D. Nix (). “A new bulge test technique for the determination of Young’s modulus and Poisson’s ratio.” Journal of Materials Research 7(12), 1992, pp. 3242-3249.
[94] P. R. Wallace, “The Band Theory of Graphite.” Physical Review 71(9), 1947, pp. 622-634.
[95] M. Wilson, “Electrons in atomicallythin carbon sheets behave like massless particles.” Physics Today 59(1), 2006, pp. 21-23.
[96] B. I., Yakobson, C. J. Brabec, et al. “Nanomechanics of carbon tubes: Instabilities beyond linear response.” Physical Review Letters 76(14), 1996, 2511-2514.
[97] K. Y., Yasumura,T. D. Stowe, et al. “Quality factors in micron- and submicron-thick cantilevers.” Microelectromechanical Systems, Journal of9(1), 2000, pp. 117-125.
[98] Y., Zhang, J. Small, P. , et al. “Fabrication and electric-field-dependent transport measurements of mesoscopic graphite devices.” Applied Physics Letters 86(7): 0731042005,
[99] Y. B., Zhang, Y. W. Tan, et al. “Experimental observation of the quantum Hall effect and Berry’s phasein graphene.” Nature 438(7065), 2005, pp. 201-204.
[100] Q., Zheng, B. Jiang, et al. “Self-Retracting Motion of Graphite Microflakes.” Physical Review Letters 100(6): 067205, 2008.
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