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Open ETD Ning.Pdf The Pennsylvania State University The Graduate School Department of Physics STUDY OF CHEMICAL DOPING OF GRAPHENE ON AMORPHOUS SILICA, ELECTRONIC PROPERTIES OF THE GRAPHENE-FLUORINE SUPER-LATTICE AND INTERACTIONS OF GRAPHENE WITH ATOMIC FLUORINE A Dissertation in Physics by Ning Shen 2011 Ning Shen Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 2011 The dissertation of Ning Shen was reviewed and approved* by the following: Jorge O. Sofo Associate Professor of Physics Associate Professor of Materials Science and Engineering Dissertation Advisor Chair of Committee Milton W. Cole Distinguished Professor of Physics Tom Mallouk DuPont Professor of Materials Chemistry and Physics M. C. Demirel Associate Professor of Department of Engineering Science and Mechanics Richard W. Robinett Professor of Physics Director of Graduate Studies *Signatures are on file in the Graduate School iii ABSTRACT Graphene is a novel carbon structure with excellent electronic properties. This dissertation is devoted to the exploration of two graphene related studies: the influence of an amorphous silica substrate on a graphene field effect transistor (FET) and the properties of chemically modified graphene structures with fluorination. The study of the effect of an amorphous silica substrate on a single graphene layer is interesting since a silicon wafer with thermally grown amorphous silica is commonly used as the substrate for graphene FET devices. Density functional theory (DFT) calculations show that the silica substrate induces a charge transfer to the graphene layer due to surface states of the amorphous silica. The intrinsic n-doping of the graphene is confirmed by the experimental studies of our collaborators. We further propose simple potential profile models to estimate the density of the surface states necessary to explain the magnitude of the observed Dirac Voltages in experiment. Opening a band gap in graphene is also important to its electronic applications. One possible gap-opening method is through chemical functionalization with fluorine atoms. Fluorinating certain regions of graphene can transform the carbon atoms in graphene from sp2 to sp3 hybridization, which converts highly conductive graphene into an insulator. We propose the formation of a graphene channel embedded in graphene monofluoride to confine the carriers in graphene. We have studied the electronic structures of two symmetrically orientated graphene channels with armchair or zig-zag boundaries through DFT and tight-binding (TB) calculations. The armchair channel is found to be metallic or semiconducting depending on the width of the channel. The zigzag channel is found to have dispersive edge bands which are due to the lowering of the site energy of edged carbon compared to the non-edged carbon. We further calculate the local density of states (LDOS) of the edged and non-edged carbon atoms and estimate the charge iv difference between them. Analysis of the LDOS confirms the site energy drop in the edge carbon since it has more electrons than that of the non-edged carbon atom. Atomic fluorine plasma is found to be an effective method to fluorinate graphene by experimentalists. In order to achieve a better understanding of the fluorination process of graphene and the stability of the generated fluorinated structures, we further explore the interactions between atomic fluorine atoms and graphene through DFT calculations and find the diffusion barriers for isolated fluorine ad-atoms and fluorine atom pairs on graphene. We find that the diffusion barrier of isolated fluorine ad-atom is about 0.3eV while the diffusion barrier of fluorine atom increases to about 1eV when there is another fluorine atom nearby. This indicates that diffusion becomes more difficult when fluorine atoms start assembling together which suggests the stability of the boundary of graphene and graphene monofluoride structures. v TABLE OF CONTENTS LIST OF FIGURES ................................................................................................................. vi LIST OF TABLES ……………………………………………………………………...........x ACKNOWLEDGEMENTS…………………………………………………………………...xi Chapter 1 Introduction ........................................................................................................... 1 1.1 Interesting Properties of Graphene ................................................................... 1 1.2 Organization of thesis ....................................................................................... 3 Chapter 2 Overviews of Computational Methods .................................................................. 5 2.1 Tight binding method ......................................................................................... 5 2.2 Density Functional Theory ................................................................................. 10 2.2.1 Basic Equations for Many body Nuclei and Electrons System ............... 10 2.2.2 Hohenberg-Kohn theorem ....................................................................... 12 2.2.3 Kohn-Sham Equations ............................................................................. 15 2.2.4 Common Approximations in Practical Calculations ............................... 17 Chapter 3 Effects of an Amorphous Silica Substrate on a Single Graphene Layer ................ 19 3.1 Introduction ......................................................................................................... 19 3.2 Experimental Details ........................................................................................... 20 3.2 Ab-initio Results ................................................................................................. 23 3.3 Potential Profile Model Results .......................................................................... 29 Chapter 4 Physics of a Graphene Channel Embedded in Graphite Monofluoride (CF) ......... 36 4.1 Introduction of Opening a Band Gap in Graphene ............................................. 36 4.2 Electronic Properties of the Armchair Channel .................................................. 39 4.3 Electronic Properties of Zig-zag Channel ........................................................... 45 4.4 Tight-binding model of the Dispersive Edge band of a Zig-zag Channel .......... 48 Chapter 5 Interaction of Atomic Fluorine with Graphene ..................................................... 55 5.1 Introduction ......................................................................................................... 55 5.2 Transition state theory and the nudged elastic band method .............................. 56 5.2 Binding Energy and Diffusion of a Single Fluorine Atom ................................. 63 5.3 Binding Energy and Diffusion of Paired Fluorine Atoms .................................. 70 Chapter 6 Summary and Future work ...................................................................................... 77 Bibliography..................................................................................................................... 79 vi LIST OF FIGURES Figure 2-1. The schematic graph of hexagonal graphene lattice with two sub-lattice carbon atoms: A (black color) and B(grey color).The three nearest neighbors are represented by vectors ................. 8 Figure 3-1. (a) Schematic graph of a Graphene FET device on a Si substrate with thermally grown SiO2 on top. The source and drain contacts are denoted as S and D while the back-gate is denoted as G. (b) Optical micrograph of the device fabricated with a TEM grid used as a shadow mask. Region I enclosed in a dashed line boundary represents graphene layer. Region II represents the Cr/Au contact. Region III is the Silica dielectric.28[Copyright (2011) by ACS Nano,Reprinted from Link: http://dx.doi.org/10.1021/nn800354m] ............................................................................ 21 Figure 3-2. (a) The normalized maximum values of Rds with respect to the initial value of Rds at t=0 (denoted as R0). (b) The time evolution of the Dirac Voltage for the graphene FET. The red dashed line indicates the time evolution of temperature for the FET device. The temperature is about 200ºC for the first 28 hours and suddenly changes to 25 ºC. .28[Figure courtesy of ACS Nano,Reprinted from Link: http://dx.doi.org/10.1021/nn800354m] ............................................................................ 22 Figure 3-3. The typical atomic configuration of the unit cell used in our ab-initio calculations. The left panel corresponds to the situation where the graphene sheet is at the minimum energy distance of about 3.6 Å. The right panel is the situation where the graphene layer is at a larger distance. The contours in the figure show the charge transfer and are colored to signify the magnitude of the electron excess when 28 bringing the graphene and SiO2 substrate together. [Copyright (2011) by ACS Nano, Reprinted from the Link : http://dx.doi.org/10.1021/ nn800354m ]...................... 25 Figure 3-4. (a) The distance dependence of the amount of charge transferred from the SiO2 substrate to graphene measured in number of electrons Q transferred (left-axis, -3 in unit of 10 e/carbon-atom) and net induced surface charge density n0 (right-axis, in unit of 1013e/cm2). (b) Excess charge per unit length versus distance along z- axis(perpendicular to the graphene layer). The top panel is the situation with the distance between graphene and SiO2 substrate at equilibrium. The bottom
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