FERROELECTRIC GATING OF GRAPHENE By Guangxin Ni SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY AT NATIONAL UNIVERSITY OF SINGAPORE UNIVERSITY ADDRESS JUNE 2012 c Copyright by Guangxin Ni, 2012 ⃝ NATIONAL UNIVERSITY OF SINGAPORE DEPARTMENT OF PHYSICS The undersigned hereby certify that they have read and recommend to the Faculty of Science for acceptance a thesis entitled “Ferroelectric gating of graphene” by Guangxin Ni in partial fulfillment of the requirements for the degree of Doctor of Philosophy. Dated: June 2012 External Examiner: Research Supervisor: ¨ Barbaros Ozyilmaz Examing Committee: ii NATIONAL UNIVERSITY OF SINGAPORE Date: June 2012 Author: Guangxin Ni Title: Ferroelectric gating of graphene Department: Physics Degree: Ph.D. Convocation: July Year: 2013 Permission is herewith granted to National University of Singapore to circulate and to have copied for non-commercial purposes, at its discretion, the above title upon the request of individuals or institutions. Signature of Author THE AUTHOR RESERVES OTHER PUBLICATION RIGHTS, AND NEITHER THE THESIS NOR EXTENSIVE EXTRACTS FROM IT MAY BE PRINTED OR OTHERWISE REPRODUCED WITHOUT THE AUTHOR’S WRITTEN PERMISSION. THE AUTHOR ATTESTS THAT PERMISSION HAS BEEN OBTAINED FOR THE USE OF ANY COPYRIGHTED MATERIAL APPEARING IN THIS THESIS (OTHER THAN BRIEF EXCERPTS REQUIRING ONLY PROPER ACKNOWLEDGEMENT IN SCHOLARLY WRITING) AND THAT ALL SUCH USE IS CLEARLY ACKNOWLEDGED. iii To my family. iv Table of Contents Table of Contents v Acknowledgements viii Abstract x Introduction 1.1 From carbon to graphene . . . . . . . . . . . . . . . . . . . . 1.2 The electronic field effect in graphene . . . . . . . . . . . . . 1.3 Large-scale graphene synthesis and its potential applications 1.4 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Structure of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 11 Background of graphene and ferroelectric 2.1 Band structure of graphene . . . . . . . . 2.2 Electronic properties of graphene . . . . . 2.3 Optical properties of graphene . . . . . . . 2.4 Ferroelectric dielectrics and applications . . . . . . . . . . . . . . . . . . . . . 12 12 15 17 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fabrication and experimental setups 25 3.1 Graphene fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1.1 Mechanical exfoliated graphene . . . . . . . . . . . . . . . . . 26 3.1.2 Chemical vapor deposition of graphene . . . . . . . . . . . . . 28 3.2 Fabrication of graphene field effect transistor GFET . . . . . . . . . . 30 3.2.1 GFET devices using mechanically exfoliated graphene . . . . . 30 3.2.2 GFET devices made out of chemical vapor deposition graphene 31 3.3 Ferroelectric dielectric preparation and characterization . . . . . . . . 32 3.4 Transport measurements and experimental set-ups . . . . . . . . . . . 35 v Ferroelectric gated graphene field effect transistors (GFeFETs) as non-volatile memory devices 4.1 Introduction and background . . . . . . . . . . . . . . . . . . . . . . 4.2 P(VDF-TrFE) gated GFeFET non-volatile memory . . . . . . . . . . 4.2.1 Asymmetric bit writing using ferroelectric gating . . . . . . . 4.2.2 Symmetric bit writing using ferroelectric gating and back ground doping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Understanding of ferroelectric gating . . . . . . . . . . . . . . 4.3 Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . Quasi-periodic nanoripples in graphene grown by deposition and its impact on charge transport 5.1 Introduction and background . . . . . . . . . . . . . 5.2 Sample fabrications . . . . . . . . . . . . . . . . . . . 5.3 Results and discussions . . . . . . . . . . . . . . . . . 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . Large-scale CVD graphene at high non-volatile using ferroelectric polymer gating 6.1 Introduction . . . . . . . . . . . . . . . . . . . . 6.2 Sample fabrications . . . . . . . . . . . . . . . . 6.3 Results and discussions . . . . . . . . . . . . . . 6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . 38 39 41 42 48 57 59 chemical vapor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 62 64 65 73 . . . . electrostatic doping . . . . . . . . . . . . . . . . . . . . Wafer scale graphene ferroelectric hybrid devices for electronics 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Results and Discussions . . . . . . . . . . . . . . . . . . 7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 75 78 80 89 . . . . low voltage . . . . . . . . . . . . . . . . . . . . . 90 91 92 99 Ongoing experiments 100 8.1 Non-volatile p-n junctions . . . . . . . . . . . . . . . . . . . . . . . . 100 8.2 Optical transmittance of strained or gated graphene . . . . . . . . . . 106 Summary, conclusion and outlook 9.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Unsolved questions . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Can we reach the VHS regime? . . . . . . . . . . . . . . . 9.2.2 Can we completely remove the quasi-periodic nanoripples? vi . . . . . . . . 109 109 111 111 113 9.2.3 Can we achieve less than 100 Ω/✷ sheet resistance in CVD graphene? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Future outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Gate-tunable graphene-ferroelectric photonics . . . . . . . . . 9.3.2 Piezoelectric effect induced electrical nanogenerator . . . . . . 9.3.3 Ultrahigh doping of graphene using single crystal ferroelectric thin film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 116 116 117 118 Bibliography 119 Publications 141 Patents 143 vii Acknowledgements Over my four-year Ph.D time, I would like to express my deep thanks to my advisor, ¨ Prof. Barbaros Ozyilmaz. He is both knowledgeable and insightful, and has pointed me in the right direction many times; I cannot imagine having had a better advisor. I enjoyed learning from him, and I appreciated his encouragement and support of new ideas. His sense of what is genuinely of scientific value and his intuition for good and clean experiments has had a strong impact on me. Last but not least, his great passion has motivated me during the past four years and will continue to keep me moving in the future. I would also like to express my appreciation to Dr. Zheng Yi, from whom I learnt most of my knowledge of electronic transport measurements and data analysis skills. His strict attitude on experiments and his flexibility in addressing challenges influenced me deeply. He gave insightful guidance for my projects and experiments, and for what i am very grateful. I would like to thank Prof. Yao Kui, who is an expert in ferroelectric material. He gave me much insightful guidance about ferroelectrics. I would like to thank Prof. Christian Kurtsiefer, who is the most knowledgeable person I know on optics and is capable of building dedicated instruments by himself. He is always very patient with even my most detailed questions and always gives me very useful guidance and help. I would like to thank Dr. Chin-Yaw Tan and Dr. Shuting Chen for their help with the ferroelectric polymer thin films in time of great need. I would like to thank Dr. TROADEC, Cedric, who helped me with the synthesis of a shield mask to greatly speed up my research. I would like to thank Dr. Ao-Chen, Hongzhi Yang, Dr. Manu Jaiswal, Dr. Xiangfan Xu, Minggang Zeng, Lanfei Xie, Jayakumar Balakrishnan, Xiangming Zhao, Kaiwen Zhang, Cheetat Toh, Dr. Qiaoliang Bao Dr. Chen Yu and Yufeng Song (from NTU) for their help. I also wish to thank the following for their guidance and help: Prof. Guoqing Xu, viii ix Prof. Yuanping Feng, Prof. Jiansheng Wang, Prof. Jie Yan and Prof. Lin Yi . Finally, I would like to thank to my family, my parents and my wife, for their patience and absolute love. NUS, Singapore December 28, 2011 Guangxin Abstract In this dissertation, we describe experimental investigations of charge transport properties of both mechanically exfoliated and chemical vapor deposited (CVD) graphene and its potential applications using functional ferroelectric substrates. We demonstrated a non-volatile memory device in a graphene field-effect transistor structure using ferroelectric gating. Two distinct bistable resistance states were maintained by controlling the polarization of the ferroelectric thin film. Furthermore, this thesis is devoted a better understanding of CVD graphene. We elucidated a new type of quasi-periodic nanoripple arrays (NRAs) within a single graphene domain. The impact of these NRAs on charge transport of CVD graphene was also studied. Utilizing the hybrid CVD graphene and ferroelectric polymer structure, we demonstrated a novel type of flexible transparent conductors with low sheet resistance, high transparency and good mechanical flexibility. By transferring large-scale CVD graphene to wafer-size ferroelectric inorganic substrates (PZT), an array of low-voltage operation transistors and non-volatile memory devices were fabricated and investigated. x faced by the current FET devices [63]. Although graphene transistors are unlikely suitable for modern digital logic circuits due to the lack of a band gap, its ultra-fast carriers make GFET more easily usable for radio-frequency applications. Experimentally, wafer-scale graphene transistors with a cutoff frequency approaching 400 GHz have been already achieved [64]. The exploration of other potential applications of graphene is still ongoing. As ultrafast memories, graphene with potentially aggressive scaling ability and ultrafast reading speed have been achieved by our laboratory group [65, 66]. In photonics, ultrafast photodetectors and graphene-based light polarizers have been experimentally demonstrated [45]. 1.4 Motivations The goal of this dissertation is to study the electrical transport properties of graphene (both mechanically exfoliated and CVD graphene) on ferroelectric substrates and its potential applications for non-volatile memory, transparent conductors and novel types of transistors. Furthermore, we investigate the original limiting factor of CVD graphene. More specifically: • As a one atom thick single crystal, graphene’s electronic properties are closely related to the surrounding environment. Currently, most graphene research is restricted to normal Si/SiO2 substrate. Although SiO2 dielectric can provide excellent optical contrast to graphene, which was the key in discovering graphene by micromechanical exfoliation, it has several critical drawbacks, i.e., low dielectric constant (κ = 3.9), high concentration of surface impurity charges, surface 10 optical phonons, and hydrophilic surface properties. Thus, the pursuit of new dielectrics and substrates with novel functionality is of great importance, not only for fundamental studies, but also for potential applications. • Ferroelectrics are unique in having both ultrahigh dielectric constants up to a few thousand and a nonlinear, hysteretic dielectric response to an electric field. The ultrahigh κ makes ferroelectrics promising substrates for studying the charge scattering mechanism in graphene, which could be a crucial step in realizing ultrahigh mobility on substrates. Equally important, the ultrahigh κ may allow ultrahigh electrostatic doping in graphene with charge carrier density exceeding electrolyte gating and with gate tunability at cryogenic temperatures. From an application point of view, the hysteretic ferroelectric gating provides a novel functionality of non-volatile graphene-ferroelectric field effect transistors, which could be crucial for many kinds of applications such as non-volatile memory, transparent conductors, and ultrafast lasers with low-power consumption and high efficiency. • The technical breakthrough in synthesizing large-scale CVD graphene represents a milestone for graphene’s wide-range applications. Currently, grain boundaries are generally believed to be the main scattering source in CVD graphene and much effort has focused on increasing the grain size of such polycrystalline graphene to 100 µm and beyond. However, the quality of micrometer CVD graphene devices is still generally lower than that of mechanical exfoliated graphene. This indicates that there are still other unknown aspects of this new two-dimensional polycrystalline material and further exploration of CVD graphene is required. 11 1.5 Structure of this thesis This thesis is devoted to experimentally investigating the electronic transport properties of single layer graphene and its potential applications with ferroelectric substrates. The thesis is divided into three sections. The first section, from chapter to chapter 3, introduces background information of the thesis. Chapter gives an overview of graphene research. Chapter presents the theoretical background of graphene and ferroelectric material involved in this thesis. Chapter demonstrates experimental techniques and apparatuses that are used in the research. The second section, from chapter to chapter 7, is devoted to the investigation of ferroelectrically gated single layer graphene. Chapter mainly focuses on the ferroelectric polymer (P(VDF-TrFE)) gated exfoliated graphene field effect transistor for non-volatile memory applications. Chapter investigates quasi-periodic nanoripples in large-scale Cu-CVD graphene. Chapter devotes on the study of large-scale CVD graphene and P(VDF-TrFE) hybrid structure as it relates to graphene-based transparent conductors. Chapter focuses on the electrical transport studies of CVD graphene on ferroelectric inorganic Pb(Zr0.3 T i0.7 )O3 (PZT) substrates. The third section includes chapter and chapter 9. Chapter summarizes experiments which have not been completed. Chapter is devoted to the summary of this thesis and on outlook for future. Experiments results presented from Chapter to Chapter have been published. Chapter Background of graphene and ferroelectric 2.1 Band structure of graphene The exotic electronic properties of graphene are directly correlated with its band structure. In this section, a brief discussion of the energy bands is carried out within the tight binding approximation. Figure 2.1 shows the graphene honeycomb lattice structure. In one unit cell, there are two carbon atoms one from each sub-lattice A and B. Each sub-lattice can be regarded as being responsible for one branch of the energy dispersion (Fig. 2.2). The inability to transform one type of dispersion into another makes them independent of each other. The inequivalence of sub-lattice A and B is the origin of the chiral nature of graphene and the valley degeneracy. Each carbon atom has four atomic orbitals involved in bonding with the other carbon atoms in the graphene plane. The 2s, 2px and 2py orbitals hybridize to form three sp2 orbitals. This strong covalently bonded σ bonds are responsible for the robust mechanical properties of graphene. The remaining 2pz orbital yields the π bands which are perpendicular to the planar 12 13 bb a b1 γ1 Κ γ3 a1 γ2 Μ Γ Κ’ b2 a2 Figure 2.1: (a) Lattice structure of graphene, made out of two interpenetrating triangular lattices (as represented by the white and black points). (b) The dotted regime in the upper hexagonal lattice structure shows the corresponding Brillouin zone. structure. The π bands are much closer to the Fermi surface than the σ bands, thus determining the transport properties of graphene. Hence, the subsequent tightbinding approach only includes the impact of π bands. Using the tight-binding approach, the energy bands of graphene have the form of √ √ √ )cos( 3akx ) + 4cos2 ( 3akx ), (1) E(kx ,ky )=±γ + 4cos( 3aky 2 where γ = 3.0 eV is the nearest neighbor hopping energy and a = 1.42 ˚ A is the nearest neighbor distance [67]. The plus sign applies to the upper π band while the minus sign applies to the lower π ∗ band. Figure 2.2a shows the calculated full band structure of graphene under the assumption that the next nearest neighbor hopping energy γ ′ =0.2γ is negligible [6]. What makes this band structure so peculiar is that the valance band and conduction band touch each other at discrete points (Dirac points), which correspond to the corners of the first Brillouin zone. This creates a zero-gap semiconductor with linear dispersion near the Dirac points. 14 a b E k Figure 2.2: (a) The tight-binding calculated full band structure of graphene. (b) Zoom-in of the energy bands close to one of the Dirac points. Near the Dirac points, the charge carriers mimic relativistic particles, propagating through the honeycomb lattice with zero effective mass and consequently can be described by the Dirac-like Hamiltonian: H = vF ( kx ∓ iky kx ± iky ) = vF ⃗σ · ⃗k . (2) where vF is the Fermi velocity, k is the quasi-particle momentum and σ is the Pauli matrix. The corresponding eigenvectors of such Hamiltonian can be written as |k>= ⃗r √1 eik·⃗ ( ∓ie−iθk /2 eiθk /2 ) (3) The linear dispersion relationship of the quasi-particles can be obtained by substituting equation in equation 2, as ε = vF ⃗k, which has the same form as a photon. This indicates that quasi-particles in graphene are massless and moving with a velocity of vF ≈ × 108 cm/s. The important consequence of Dirac fermions is that 15 the low-energy physics in graphene is governed by the spectrum close to the K and K’ points. Many of the new and exciting properties of graphene stem from this fact. Dirac fermions behave in unusual ways compared to ordinary electrons when subject to a magnetic field or confining potentials, leading to the observation of an anomalous quantum Hall effect or the phenomena of Zitterbewegung and Klein tunneling [68]. 2.2 Electronic properties of graphene By transferring graphene (exfoliated, CVD, etc) onto a substrate such as an oxidized silicon wafer (Si/SiO2 ), the charge carrier density can be tuned from holes to electrons across the charge neutrality point by applying an external electric field. The gate voltage induces a surface charge density n = ϵ0 ϵVBG /te, where ϵ is the permittivity of SiO2 , e is the electron charge and t is the thickness of the SiO2 layer. The charge density shifts with the Fermi level position (EF ) in the band structure, as shown in Figure 2.3a. The resistivity increases rapidly as the charge decreases, finally reaching its maximum value at the Dirac point. From this curve one can extract the fieldeffect mobility µ = αe dρ −1 ( dV ) , where α = 7.2 × 1012 cm−2 for our field-effect devices with a 300 nm SiO2 layer and dρ dV is the derivative of resistivity. Alternatively, one can also deduce the carrier mobility from the conductivity plot (Fig. 2.3b), where the minimum conductivity is defined as σmin . Note that the carrier mobility is only meaningful away from the Dirac point. Near the Dirac point, the conductivity of graphene does not go to zero in the limit of vanishing density of states but instead exhibits values close to the conductivity quantum 4e2 /h. This is is due to the presence of charge scatterers attributed to the thermally generated carriers and electrostatic charge inhomogeneity puddles 16 (a) (b) n p 5e /h Figure 2.3: (a) Typical dependence of single layer graphene resistivity on gate voltage at T=300 K; four-terminal measurements. (b) The corresponding conductivity vs. gate voltage plot. The dotted red line indicates the long-range scattering limit. which dominate electronic transport of neutral graphene [69]. Consequently, the conductivity minimum at the Dirac point is completely non-universal, and crucially controlled by the disorder in the sample [23]. At finite densities, the conductivity of graphene usually behaves sub-linearly (Fig. 2.3b). This sub-linear characteristic is generally attributed to resonant scattering due to the presence of adatoms, adsorbed hycrocarbons and vacancies in graphene [70]. At low temperatures, quantum effects, i.e., weak localization or universal conductance fluctuations, become obvious. Weak localization is a phenomena caused by the coherent backscattering of waves and therefore increases the resistance of graphene, while universal conductance fluctuations are created by summing over all possible paths through the samples. Depending on the relative magnitude of the intervalley scattering time and phase coherence time, either weak localization or weak anti-localization can be observed [71, 72] 17 Upon the application of a magnetic field, the weak localization diminishes gradually and the energy states in graphene start to form Landau levels which are fourfold degenerate. The Hall conductivity is accurately quantized as the chemical potential is changed from the hole part to the electron part of the Dirac spectrum. The observation of a quantum hall effect provides the most compelling evidence for the 2D massless Dirac nature of electrons in graphene [17]. 2.3 Optical properties of graphene Besides its extraordinary electrical properties, graphene also exhibits exotic optical behavior. Although it is only one atomic layer thick, graphene can effectively absorb 2.3 % of incident light. Owing to its unique linear energy dispersion relation, there is always an electron-hole pair in resonance for any excitation, making graphene wideband tunable. The combination of a large absorption per layer, ultrafast carrier dynamic and the Pauli exclusion principle makes graphene an ideal candidate for wide applications in optoelectronics and photonics, such as graphene-based flexible transparent conductors and broadband saturable absorbers. The first optical transparency measurements of graphene were done in 2008 by the Manchester group [14]. By placing graphene flakes onto TEM grids, the transmitted light intensity was recorded by optical spectrometry (Fig. 2.4). For monolayer graphene, it was found that its opacity is defined solely by the fine structure constant, α = e2 / c ≈ 1/137, a consequence of graphene’s unique electronic structure. By adding one more layer, the corresponding optical absorption doubles, yielding a quantized optical absorption of graphene as a function of layer number (Fig. 2.4A). 18 Figure 2.4: (A) Optical image of graphene flake on TEM grid. (B) Transmittance spectrum of monolayer graphene. Note that this figure is extracted from [14]. Under intense laser excitation, graphene exhibits broadband nonlinear optical absorption at a light intensity well below the damage threshold. This makes graphene a promising candidate for photonic applications. As a first step, graphene-based saturable absorbers have been proposed for ultrafast laser systems. Compared with state-of-the-art semiconductor saturable absorber mirrors, the graphene saturable absorber has two advantages, i.e., fast response to incident light over a wide wavelength range and simple device fabrication [73]. 2.4 Ferroelectric dielectrics and applications In this section, we present an introduction to ferroelectric materials with the information needed as a background for reading the subsequent chapters of this thesis. We mainly focus on the organic ferroelectric material called poly(vinylidene fluoride 19 trifluoroethylene) [P(VDF-TrFE)]. In addition, inorganic ferroelectric ceramic PZT (Pb(Zr0.3 T i0.7 )O3 ) will be introduced. We will only include here the most essential points of ferroelectrics. For more comprehensive background we refer to review articles [74, 75]. A ferroelectric is an insulating material with two or more discrete stable or metastable states of different nonzero electric polarization in the absence of an applied electric field. This can be referred to as spontaneous polarization. For a system to be considered ferroelectric, it must be possible to switch between these states with an applied electric field, which changes the relative energy of the states through the coupling of the field to the polarization. Ferroelectrics are important basic materials for technological applications such as memory devices, high frequency devices and optical devices. In many cases their nonlinear characteristics turn out to be very useful, for example in optical secondharmonic generators and other nonlinear optical devices [76]. In recent years, polymer ferroelectrics have been utilized in the broad field of fast displays in electronic equipment [77]. One of the most important characteristics of ferroelectrics is the ferroelectric hysteresis loop, in which the polarization is a double valued function of the applied electric field (Fig. 2.5). When a small electric field is applied, there is only a linear relationship between P and E, because the field is not large enough to switch any domain and the crystal will behave as a normal dielectric. As the electric field strength increases, a number of negative domains will be switched to the positive direction and the polarization will increase rapidly until all the domains are aligned. This is Polarization (µC/cm2) 20 a Ps EC -4 -8 -Pr -100 100 Electric Field (MV/m) Figure 2.5: Typical hysteresis polarization loops of ferroelectric material. The different loops are corresponding to the the polarization response at various external applied voltages. The definition of Ps , Pr , and Ec are also marked in the figure. the saturation state of a single domain. As the field strength decreases, the polarization will generally decrease. When the field is zero, some of the domains will remain aligned in the positive direction and the crystal will exhibit a remnant polarization (Pr ). This Pr can not be removed unless an applied field in the opposite direction reaches a certain value. This value of EC is called the coercive field. A further increase of the field in the negative direction will align the dipoles in the negative direction and the cycle is completed by reversing the field direction once again. Ferroelectric materials are further divided into ceramics, ceramic-compounds and organic ferroelectrics. The most commercially developed ferroelectric ceramics are based on the titanate compounds with perovskite structure, such as PbTiO3 . Such ferroelectric materials go through a phase transition from a centrosymmetric nonpolar lattice to a non-centrosymmetric polar lattice at the critical temperature. An 21 important characteristic of ferroelectric materials is the presence of domains. A domain is a microscopic region of a crystal in which the polarization is homogenous. These domains are generally not aligned, but can be aligned along a common direction by applying a perpendicular DC electric field. This procedure is called poling. The connection between ferroelectricity and organic molecules started in 1920 with the discovery of the first ferroelectric crystal, Rochelle salt, containing organic tartrate ions. Owing to their low cost, lightness, flexibility and non-toxicity, ferroelectric polymers became more and more important in the emerging field of organic electronics [77]. Ferroelectric polymers are a class of ferroelectric materials that exhibit spontaneous polarization arising from inherent dipoles present in the polymer chains. These polymeric ferroelectric materials have drawn interest recently owing to their unique properties among ferroelectric materials, i.e., relatively benign manufacturing conditions and ease of fabrication. Furthermore, the flexibility inherent to polymers allows for simple fabrication techniques, especially when integrating into complicated geometric structures. In particular, they can be easily fabricated by solvent spin casting and thickness control of solvent spin cast polymers is comparatively easier than in sol-gel or other deposition techniques currently used for ceramic ferroelectrics [75]. Polyvinylidene fluoride (PVDF) was the first ferroelectric polymer with a typical hysteresis loop and a fast switching response. It is an intermediate polymer between polyethylene (-CH2 -) and polytetrafluoroethylene (-CF2 -). By stretching the polymer to about 300 % of its original length at temperatures around 100 ◦ C, around 50 % crystalline phase can be converted predominantly from the thermodynamically stable α-phase into the β-phase in which the polymer chains exhibit the zig-zag-conformation 22 (a) F F F F C C C H F H H C H F F H C H H F F C C C H F C C H (b) F C C H H F C C F H H H F Figure 2.6: Molecule structure of PVDF and P(VDF-TrFE) are shown in (a) and (b), respectively. shown in Fig. 2.6a. The electronegativity difference between the fluorine and hydrogen substitutes located at the opposite sides of the polymer chain results in a large dipole moment perpendicular to the chain direction. Before polarization, the dipoles are randomly aligned. After the application of a high electric field in the order of 100 MV/m to a PVDF film, the sample exhibits piezoelectric properties. By substituting a hydrogen atom with a fluorine atom in one of the VDF monomers in the cell, one arrives at a material named P(VDF-TrFE) that is similar to PVDF, but with faster polarization dynamics that make it therefore better suited for many experiments (Fig. 2.6b). P(VDF-TrFE) is a semicrystalline material, where the structure and extent of crystallinity play a crucial role in the ferroelectric properties of the material. In P(VDF-TrFE) copolymers, its crystal phase is controlled by the number of fluorine atoms in the polymer chains. This is because with increasing number of fluorine atoms, the van der Waals repulsive forces within and among the chains increase and this results in an increase in the lattice energy of any α phase. Furthermore, the TrFE content also strongly influences the crystallization of P(VDF-TrFE). As the 23 TrFE content is increased, the lattice spacing of the polymer chains increases, due to the larger size of the TrFE monomer unit. Therefore, 75-25 P(VDF-TrFE) copolymers have a crystallinity of 90 % compared to only about 50 % for pure PVDF. However, any further increase in the TrFE content will decrease the crystallinity, possibly due to sterio-irregularity in the chain introduced by the TrFE. Unlike pure PVDF, the curie temperature of P(VDF-TrFE) falls below the melting point and the transition can be clearly studied. When the temperature decreases through the Curie point, the crystal undergoes a structural phase transition from a paraelectric phase to a ferroelectric phase. Generally, the ferroelectric structure of the crystal is created by a small distortion of the paraelectric structure such that the lattice symmetry in the ferroelectric phase is always lower than in the paraelectric phase. In most ferroelectrics, the temperature dependence of the dielectric constant above the Curie point (in the paraelectric phase regime) can be described by a simple law called the Curie-Weiss law: ϵ ≃ ϵ0 + C/(T-T0 ); (T>T0 ), where C is the CurieWeiss constant and T0 is the Curie-Weiss temperature. In conjunction with its easy conformability, flexibility and low cost, P(VDF-TrFE) has been studied for several sensor, actuator, and transducer applications such as artificial muscles, aquatic transducers and most recently memory devices. There have been a large number of studies geared towards implementing them as solid-state memory devices [78]. Lead zirconate titanate (PZT) has long been the leading material considered for ferroelectric memory devices owing to its large remnant polarization, fast switching speed and superior fatigue resistance. Moreover, PZT is also widely used for 24 electrical-mechanical energy conversion devices such as sensors and actuators. Recently, these devices have spread out in the computer controlled fields of robotics and mechatronics. The research and development of ferroelectric ceramics, particularly PZT ceramics, has mainly focused on their material composition in order to realize new electronic devices utilizing their piezoelectric properties. On the other hand, through the new research on DC poling field dependence of ferroelectric properties in PZT ceramics, the poling field has become an effective tool for evaluation and control of the domain structures, which fix the dielectric and ferroelectric properties of PZT ceramics. Therefore, PZT ceramics with different domain structures can be fabricated even though the ceramic compositions remain the same. These ceramics are called poling field domain controlled ceramics. It is thought that domain controlled ceramics will lead to a breakthrough in the discovery of new ferroelectric properties [78]. [...]... for carrier transport out of photovoltaic devices While 8 a b Graphene flexible displays Graphene touch panel c f Graphene photodetectors Graphene supercapacitor g Graphene polarizer e d h j i Graphene in solar cells Graphene battery Graphene in OLED Graphene transistors Graphene in biological applications Figure 1. 2: Examples of graphene potential applications ranging from graphene flexible displays... is required 11 1. 5 Structure of this thesis This thesis is devoted to experimentally investigating the electronic transport properties of single layer graphene and its potential applications with ferroelectric substrates The thesis is divided into three sections The first section, from chapter 1 to chapter 3, introduces background information of the thesis Chapter 1 gives an overview of graphene research... in CVD graphene and much effort has focused on increasing the grain size of such polycrystalline graphene to 10 0 µm and beyond However, the quality of micrometer CVD graphene devices is still generally lower than that of mechanical exfoliated graphene This indicates that there are still other unknown aspects of this new two-dimensional polycrystalline material and further exploration of CVD graphene. .. optical absorption of graphene as a function of layer number (Fig 2.4A) 18 Figure 2.4: (A) Optical image of graphene flake on TEM grid (B) Transmittance spectrum of monolayer graphene Note that this figure is extracted from [14 ] Under intense laser excitation, graphene exhibits broadband nonlinear optical absorption at a light intensity well below the damage threshold This makes graphene a promising... Chapter 9 is devoted to the summary of this thesis and on outlook for future Experiments results presented from Chapter 4 to Chapter 7 have been published Chapter 2 Background of graphene and ferroelectric 2 .1 Band structure of graphene The exotic electronic properties of graphene are directly correlated with its band structure In this section, a brief discussion of the energy bands is carried out... electron part of the Dirac spectrum The observation of a quantum hall effect provides the most compelling evidence for the 2D massless Dirac nature of electrons in graphene [17 ] 2.3 Optical properties of graphene Besides its extraordinary electrical properties, graphene also exhibits exotic optical behavior Although it is only one atomic layer thick, graphene can effectively absorb 2.3 % of incident light... integer quantum hall effect [17 ], Klein tunneling [18 ], p-n junctions [19 ], high frequency graphene transistors, nanoribbons [20], single molecular detectors [ 21] and tunable band gap in bilayer graphene [22], have been recorded Currently, there are two extremely important directions for graphene research in terms of fundamental physics studies, both of which are highly related to graphene s electric field... electric field effect [9] Graphene is found to possess many peculiar properties [11 ] It is the first truly 2D crystalline material with remarkably high crystal quality and it is representative of a whole class of 2D materials including single layers of Boron-Nitride (BN) and Molybdenum-disulphide (MoS2 ) [12 ] Its charge carriers exhibit giant intrinsic carrier mobility (1, 000,000 cm2 /Vs) [13 ] and can travel... large-scale graphene, i.e., epitaxial SiC graphene [ 51] , chemical vapor deposition (CVD) graphene [50] and chemically modified graphene [52] In the following, we briefly review these three methods for graphene synthesis before discussing its potential applications Epitaxial SiC graphene is synthesized by the desorption of silicon from SiC single crystal surfaces at high temperatures, leaving behind multilayer graphene. .. vapor deposition (CVD) method on copper turns out to be one of the most efficient and economical ways of producing graphene The advantage of the CVD method is that the growth rate of graphene is lowered by two orders of magnitude once the first layer is formed and the catalytic surface largely passivated, which yields a large-scale single layer of graphene The drawback to this method is that the nucleation . . 11 7 9.3.3 Ultrahigh doping of graphene using single crystal ferroelectric thin film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 8 Bibliography 11 9 Publications 14 1 Patents 14 3 vii Acknowledgements Over. . . . . . . . . . 9 1. 5 Structure of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Background of graphene and ferroelectric 12 2 .1 Band structure of graphene . . . . . . . . . . . . . 11 5 9.3 Future outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 6 9.3 .1 Gate-tunable graphene -ferroelectric photonics . . . . . . . . . 11 6 9.3.2 Piezoelectric