Physical and Chemical Manipulation of Carbon Nanotubes
and Graphene for Nanoelectronics
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
by
Richa Sharma
B.Tech in Chemical Engineering
Indian Institute of Technology
Delhi, India, 2005
FEB 0 9 2011
LIBRARIES
ARCHIVES
Doctor of Philosophy in Chemical Engineering
Massachusetts Institute of Technology
Cambridge, MA, 2010
© 2010 Massachusetts Institute of Technology.
All rights reserved.
Lj
Signature of Author:
teparLment 01 Utiemical Engineering, September 28, 2010
i
I
Certified by:
Michael S. Strano
Professor, Department of Chemical Engineering
Thesis Supervisor, September 28, 2010
Accepted by:
William Deen
Professor, Department of Chemical Engineering
Chairman, Committee for Graduate Students, September 28, 2010
Abstract
The electron confinement in carbon nanomaterials provides them with many interesting
electronic, mechanical and optical properties, thus making them one of the best suited materials
for electronic and sensor applications. However, at present practical realization of nano-scale
electronics faces two major challenges: their assembly into functional electronic circuits, and
precise engineering of these building blocks. New methods of physical and chemical
manipulation are needed to address these challenges. The work presented in this thesis aims to
understand and design physical and chemical manipulation methods for carbon nanostructures.
More specifically, this thesis is concerned with two main topics on manipulation of carbon
nanomaterials: First, the problem of the top-down, parallel placement of anisotropic
nanoparticles and secondly, chemical manipulation via controlled chemical functionalization.
Physical manipulation of nanostructures has been achieved by designing a method for
creating high aspect ratio cylindrical droplets with nano-to-micro scale diameters on a wafer by
engineering the substrate surface chemistry, liquid surface tension and liquid film thickness. The
substrate surface is manipulated by chemisorption of monolayers of hydrophobic and hydrophilic
molecules in form of alternating rectangular strips. The cylindrical droplets selectively form on
the hydrophilic strips. The hydrodynamic flow patterns that evolve within the droplets during
evaporation are able to orient and position the entrained carbon nanotubes with parallel
alignment with nanometer precision.
With respect to chemical manipulation, this thesis work focuses on graphene and
graphene nanoribbons (GNR). In this work first detailed structure-reactivity relationships for
electron-transfer chemistries of graphene and GNR are developed. For GNR, these relationships
demonstrate the dependence of the ribbon reactivity on width and orientation of carbon atoms
along the edges. Large variations in reactivity are predicted for ribbons of different widths and
family type suggesting selective chemistries may be developed to sort or preferentially modify
the GNRs. For graphene these structure reactivity relationships include regio-selective chemistry
and reactivity dependence on the number of graphene layers on chip. This work demonstrates
high reactivity of graphene edges and reports a spectroscopic method to analyze the edge
reactivity. This study should aid studies to control the disordered edge structure of GNR by edge
selective chemical functionalization and chemically modify graphene depending on the number
of layers stacked. The electron transfer chemistries developed in this work have also been used to
understand the role of covalent defects on graphene electron conduction. This work may be used
in future to assemble graphene sheets in three dimensions to fabricate supermolecular structures
(i.e. graphene super lattices).
Thesis Supervisor: Dr. Michael S. Strano
Title: Professor of Chemical Engineering
Acknowledgement
I would like thank to my adviser Michael Strano for giving me the opportunity to work in his lab
under his guidance. I would also like to thank my committee members, Charles Cooney, Karen
Gleason, Alan Hatton and Tomas Palacios for their encouragement and insightful questions.
Thanks to the members of my research group at MIT, especially Jong Hyun Choi for his
guidance on doing research.
I am grateful to the department of Chemical engineering at MIT and UIUC, ISN (MIT), CMSE
(MIT), MTL (MIT), CNS (Harvard), MRL (UIUC) for providing necessary resources to do
research.
I thank my husband for his support and understanding. Having him on my side made my PhD
journey a possibility. I thank my parents and brother for their support and guidance in building
my academic career. My mother's unfathomable belief in God kept me grounded and strong. I
would also like to thank my uncle V.K Tripathi whose insights in science and engineering made
me interested in pursuing a career in research. Finally, I am grateful to my parents-in-law for
their support and guidance.
Dedication
For God...
...and to my parents, brother and husband for their love.
Table of Contents
ABSTRACT.........................................................................
...... 2
ACKNOWLEDGEMENT...........................................................................3
DEDICATION............................................................................4
TABLE OF CONTENTS.................................................................................5
LIST OF FIGURES............................................................................
...... 8
10
LIST OF TABLES......................................................................................
1 BACKGROUND AND RELEVANT LITERTURE............................................11
1.1 Carbon....................................................................................11
1.2 Introduction to Graphene...................................................................11
1.2.1 Electronic Propertiesof Graphene.............................................13
1.2.2 MechanicalPropertiesof Graphene...........................................15
1.3 Introductionto Single Walled Carbon Nanotubes....................................16
1.3.1 Single Walled CarbonNanotube Structure,Nomenclature and Species.....16
1.3.2 ElectronicPropertiesof Single-Walled Carbon Nanotubes.................18
1.3.3 MechanicalPropertiesof Single-Walled Carbon Nanotubes..................21
1.4 Introduction to GrapheneNanoribbons...................................................21
1.4.1 GrapheneNanoribbon Structure, Nomenclature and Species..................21
1.4.2 GrapheneNanoribbonEdges...................................................24
1.5 Thesis Motivation and Objectives............................................................25
2 SYNTHESIS AND CHARACTERIZATION OF GRAPHENE AND SWNT............28
2.1 Synthesis of Graphene......................................................................28
2.1.1 Mechanical Exfoliation method..................................................28
2.1.2 Chemical Vapor Deposition method...........................................31
2.1.3 Graphene Oxide synthesis........................................................32
2.2 Characterizationof Graphene............................................................34
39
2.3 Synthesis of IndividualCarbon Nanotubes...........................................
2.4 Characterizationof SWNT dispersion..................................................40
3 PHYSICAL MANIPULATION OF SINGLE WALLED CARBON NANOTUBES ON
CHIP WITH PINNED CONTACT EVAPORATION REGIME OF CYLINDRICAL
DROPLETS.................................................................................
..43
3.1 Motivation andApproach..................................................................43
3.2 Modes of Evaporationof Dropletson Solid Surface.....................................44
3.3 Platform to Create CylindricalDroplets on Chip......................................46
3.4 Formation and Evaporationof Micrometer DiameterCylindricalDroplets.........48
3.5 Hydrodynamics in Micron Sized CylindricalDroplet.................................52
3.6 ParallelAlignment andPlacement of SWNT..........................................55
3.7 Comparison of ExperimentalResults with the Continuum Hydrodynamic
Modeling.........................................................................................
57
3.8 Equilibriumdeposition of SWNT........................................................61
4 DE-PINNED CONTACT AND TRANSITION REGIME EVAPORATION OF
CYLINDRICAL DROPLETS............................................................................64
4.1 Formationand evaporation of nanometer diameter droplets........................64
4.2 ParallelAlignment and CenterlinePlacementof SWNT.............................65
4.3 Hydrodynamics in Nanometer Sized CylindricalDroplet...............................70
4.4 Design of Single SWNT devices..........................................................74
4.5 Conclusions......................................................................................76
5 CHEMICAL MANIPULATION OF GRAPHENE NANORIBBONS: STRUCTURE
REACTIVITY OF GRAPHENE NANORIBBONS.................................................77
5.1 Motivation and Approach..................................................................77
5.2 Electron Transfer Theories....................................................................79
5.2.1 Marcus Theory.....................................................................80
5.2.2 Gerischer-Marcustheory........................................................81
5.3 ElectronicBand Structure of GNR..........................................................83
5.4 Structure Reactivity for Armchair GNR.................................................87
5.5 Structure Reactivity for Zigzag GNR........................................................93
5.6 Summary ofArmchair and Zigzag Reactivity..........................................96
6 CHEMICAL MANIPULATION OF GRAPHENE: STRUCTURE REACTIVITY OF
GRAPHENE.............................................................................................98
6.1 Motivation andApproach...................................................................98
6.2 ExperimentalDesign.........................................................................100
6.3 Analysis of Chemical Functionalization...................................................101
6.4 Electron transferchemistryfor single and multi- layer graphene...................103
6.5 Substrate Influence on GrapheneReactivity.............................................113
6.6 Electron transferchemistryfor graphene edges and bulk..............................116
6.7 Conclusions.....................................................................................122
7 CHEMICAL FUNCTIONALIZATION OF GRAPHENE DEVICES: ROLE OF
COVALENT DEFECTS ON GRAPHENE CONDUCTIVITY..................................124
7.1 M otivation and Approach ................................................................
124
7.2 Fabricationof Graphene Devices.......................................................125
7.3 GrapheneDevice Chemistry and Electron Transport.............................129
7. 4 Conclusions..................................................................................136
8 CONCLUSIONS AND FUTURE RECOMMENDATIONS..................................137
9 BIBLIOGRAPHY.......................................................................................140
APPENDIX A: ROLE OF SURFACE TENSION IN FORMATION OF CYLINDRICAL
.... 151
DROPLETS..........................................................................
APPENDIX B: SEM AND AFM IMAGES OF SWNT DEPOSITION IN NANOMETER
SIZED CYLINDRICAL DROPLETS.................................................................153
APPENDIX C: PROFILING VARIATION OF D/G AND G PEAK PERPENDICULAR
TO GRAPHENE EDGE...................................................................................155
APPENDIX D: CHEMICAL FUNCTIONALIZATION OF GRAPHENE DEVICES.....156
List of Figures
FIGURE - 1.1 DIMENSIONALITIES OF GRAPHITIC MATERIALS
FIGURE - 1.2 ELECTRONIC BAND STRUCTURE OF GRAPHENE
FIGURE - 1.3 DIAGRAM DESIGNATING VARIOUS SPECIES OF CARBON NANOTUBES
FIGURE - 1.4 ELECTRONIC DENSITY OF STATES OF SWNT
FIGURE - 1.5 SCHEMATIC DRAWING OF GRAPHENE NANORIBBONS
FIGURE - 1.6 ELECTRONIC DENSITY OF STATES OF GNR
FIGURE -2.1 MECHANICAL EXFOLIATION OF GRAPHENE FROM GRAPHITE FLAKES
FIGURE - 2.2 FABRICATION AND TRANSFER OF CVD GRAPHENE
FIGURE -2.3 SOLUTION PHASE FABRICATION OF GRAPHENE
FIGURE - 2.4 RAMAN SPECTRA OF SINGLE AND BILAYER GRAPHENE
FIGURE -2.5 RAMAN SPECTRA OF GRAPHITE
FIGURE -2.6 ABSORPTION SPECTRA OF SWNT SUSPENSION IN DEUTERIUM OXIDE
FIGURE - 3.1 MODES OF EVAPORATION FOR DROPLETS ON SOLID SURFACE
FIGURE -3.2 PLATFORM TO CREATE CYLINDRICAL DROPLETS
FIGURE - 3.3 FORMATION AND EVAPORATION OF CYLIDRICAL DROPLETS ON CHIP
FIGURE - 3.4 INTERNAL FLOW PATTERN IN AN EVAPORATING CYLIDRICAL DROP WITH
CONSTANT AREA
FIGURE - 3.5 NANOTUBE POSITIONING IN MICROMETER DIAMETER DROPLETS
FIGURE - 3.6 HYDRODYNAMICS IN A CYLINDRICAL DROP EVAPORATING WITH PINNED CONTACT
AREA
FIGURE - 3.7 COMPARISON OF EXPERIMENTAL RESULTS WITH THE CONTINUUM HYDRODYNAMIC
MODELING
FIGURE - 3.8 AFM TOPOGRAPHY IMAGES OF EQUILIBRIUM DEPOSITION OF SWNT
FIGURE - 4.1 NANOTUBE POSITIONING IN NANOMETER DIAMTER DROPLETS
FIGURE -4.2 DIAMETER OF THE DROPLET CONTROLS POSITIONING OF THE NANOTUBE
FIGURE - 4.3 STATISTICS OF POSITIONING OF NANOTUBES
FIGURE - 4.4 DROPLET DIAMETER GOVERNS THE MECHANISM OF EVAPORATION
FIGURE - 4.5 VARIATION IN THE CONTACT ANGLE OVER TIME DUE TO EVAPORATION FOR
CYLIDRICAL DROPLETS OF DIFFERENT SIZES
FIGURE - 4.6 FABRICATION OF SINGLE NANOTUBE DEVICES
FIGURE - 5.1 SCHEMATIC OF ELECTRONIC TRANSFER CHEMISTRY OF ARMCHAIR GNR
FIGURE - 5.2 CALCULATED BAND STRCUTURE OF ARMCHAIR AND ZIGZAG GNR
FIGURE -5.3 ELECTRONIC DOS AND RELATIVE RATE CONSTANTS FOR ARMCHAIR GNR WITH TB
BAND STRUCTURE INCLUDING THIRD-NEAREST NEIGHBOR INTERACTIONS AND EDGE
DISTORTION
FIGURE - 5.4 RELATIVE RATE CONSTANTS FOR ARMCHAIR GNR WITH BAND STRCTURE FROM
NEAREST NEIGHBOR TB CALCULATION WITHIN THE HUCKEL APPROXIMATION
FIGURE - 5.5 RELATIVE RATE CONSTANTS FOR ARMCHAIR GNR OBTAINED FROM MARCUS
THEORY
FIGURE - 5.6 RELATIVE RATE CONSTANTS FOR ZIGZAG GNR
FIGURE -6.1 SCHEMATIC OF THE ELECTRON TRANSFER CHEMISTRY OF GRAPHENE
FIGURE - 6.2 ELECTRONIC DENSITY OF STATES OF SINGLE AND BILAYER GRAPHENE CLOSE TO
FERMI LEVEL
FIGURE - 6.3 AUGER ELECTRON SPECTROSCOPY ANALYSIS OF SINGLE GRAPHENE SHEET AFTER
ELECTRON TRANSFER CHEMISTRY
FIGURE -6.4 NEGATIVE ION TOF-SIMS SPECTRUM OF REACTED MULTILAYER GRAPHENE SHEET
FIGURE - 6.5 RAMAN ANALYSIS FOR GRAPHENE ON CHIP CHEMISTRY ON SILICON SUBSTRATE
FIGURE - 6.6 DEPENDENCE OF D/G PEAK RATIO ON THE NUMBER OF GRAPHENE LAYERS
FIGURE - 6.7 ENERGY OVERLAP OF THE DENSITY OF ELECTRONIC STATES OF SINGLE AND
BILAYER GRAPHENE AND VACANT OXIDATION STATES OF THE ELECTRON WITHDRAWING
SPECIES.
FIGURE - 6.8 RAMAN SPECTRA OF PRISTINE AND FUNCTIONALIZED CVD GRAPHENE SHEET ON
S102 AND SAPPHIRE WAFERS
FIGURE - 6.9 HIGHER EDGE REACTIVITY
FIGURE - 6.10 GRAPHENE EDGE VS BULK REACTIVITY
FIGURE - 6.11 POLARIZATION DEPENDENCE OF D PEAK PRE AND POST ELECTRON TRANSFER
CHEMISTRY
FIGURE -6.12 RAMAN SPECTRA OF SINGLE GRAPHENE OXIDE SHEET AT BULK AND EDGE
FIGURE - 7.1 SCHEMATIC OF DEVICE FABRICATION.
FIGURE- 7.2 DESIGN OF LITHOGRAPHY MASK USED FOR GRAPHENE DEVICE FABRICATION
FIGURE - 7.3 MICROSCOPIC IMAGES OF CVD GRAPHENE DEVICES
FIGURE -7.4 CHEMICAL STRUCTURES OF THE DIAZONIUM SPECIES REACTED WITH GRAPHENE
DEVICES
FIGURE -7.5 SCHEMATIC OF ON CHIP DEVICE CHEMISTRY
FIGURE -7.6 RAMAN SPECTRA OF GRAPHENE AT DIFFERENT LEVEL OF FUNCTIONALIZATION
FIGURE - 7.7 RESISTIVITY AND RESISTANCE VS D/G RATIO FOR PRISTINE CVD GRAPHENE FOR 4BROMOBENZENE DIAZONIUM SALT
FIGURE-7.8 RESISTIVITY AND RESISTANCE VS D/G RATIO FOR PRISTINE CVD GRAPHENE FOR 4(PROP-2-YN-1-YLOXY)BENZENE DIAZONIUM SALT
FIGURE-7.9 RESISTIVITY AND RESISTANCE VS D/G RATIO FOR PRISTINE CVD GRAPHENE FOR 4NITROBENZENE DIAZONIUM SALT
FIGURE- 7.10 RAMAN SPECTRA OF GRAPHENE OXIDE
LIST OF TABLES
TABLE 1- SUMMARY OF REACTIVITY TRENDS PREDICTED FOR VARIOUS GRAPHENE
NANORIBBON TYPES
Chapter 1 Background and Relevant Literature
1.1 Carbon
Carbon has four valence electrons, one 2s electron and three 2p electrons. These four
electrons have very similar energies, so their wave functions mix easily facilitating sp, sP2 or sp3
hybridization. In carbon, these valence electrons give rise to 2s, 2px, 2py, and 2pz orbitals while
the two inner shell electrons belong to a spherically symmetric Is orbital that is tightly bound
and has an energy far from the Fermi energy of carbon. For this reason, only the electrons in the
2s and 2p orbitals contribute to the solid-state properties of graphite. The ability to hybridize
allows carbon to form interesting OD (dimensional), 1D, 2D, and 3D structures.
1.2 Introduction to Graphene
Graphene was first discovered by Novoselov, Geim et al. in 20041. It is a flat monolayer
of carbon atoms tightly packed into a 2D honeycomb lattice, and is the basic building block for
all graphitic materials of other dimensionalities (Figure 1.1). For example, graphite is a stack of
graphene planes weakly coupled by van der Walls force; carbon nanotubes are made of rolled-up
graphene; graphene nanoribbons are rectangular strips of graphene; and fullerenes are made of
wrapped graphene. In graphene, the 2s, 2 px and 2py orbitals hybridize to form three new planar
orbitals called sP2, each containing one electron. These orbitals are directed along lines with
angles of 1200 degrees, and are responsible for the hexagonal lattice structure of graphene. The
chemical bonding (sigma bonds) of the carbon atoms in graphene is maintained by these three
orbitals, and mechanical properties of graphene are determined by the rigidity of the bond. The
non-hybridized pz orbital is perpendicular to the plane formed by the carbon atoms and these
orbitals of different atoms combine to form the 7Ebonds. It is the n orbitals that are responsible
for the unusual and outstanding electronic properties of graphene.
a)
b)
c)
d)
e)
-
Figure 1.1: Dimensionalities of graphitic materials. (a,b) Three dimensional graphite. (b)
Graphene sheets stack to form graphite. (c) Two dimensional graphene. (d) One dimensional
carbon nanotubes and (e) graphene nanoribbons.
1.2.1 Electronic Properties of Graphene
The electronic properties of graphene, graphite, carbon nanotubes and graphene
nanoribbons are determined by the bonding a and antibonding a* orbitals that form the electronic
valence and conduction bands for these carbon based nanomaterials. In graphene the 7Eand H*
bands touch at the corners of the 2D hexagonal Brillouin zone2 -3 (Figure 1.2).These corners are
labeled by their momentum vector denoted by K and K'. The Fermi surface of graphene is
reduced to these six corner points where the cones of carrier touch are referred to as the "Dirac"
points. Thus, graphene is a semimetal or zero band gap semiconductor. Close to the Fermi
energy, the E-k relation is linear. This is in contrast with the usual quadratic energy-momentum
relation obeyed by electrons at band edges in conventional semiconductors 4 . The energy
spectrum of graphene close to the Dirac point is well represented by the equation 1.1 where vF is
the Fermi velocity, p is the momentum, and E is the energy. The value of VF is c/300, where c is
the speed of light. The energy given by equation 1.1 resembles that of ultra-relativistic particles.
Consequently, graphene exhibits electronic properties for a 2D gas of charged particles described
by an equation of the form of the relativistic Dirac equation rather than the nonrelativistic
Schradinger equation with an effective mass.
I-
-.
.......
........................
..........
- ----
±
, ==:: -
-
61
4,
>
-4
-2
-7
-61
kx
Figure 1.2: Electronic band structure of graphene. E-k relation of graphene. The valence and
conduction bands touch at the corners of the hexagonal Brillouin zone.
The electronic structure of graphene can be quite accurately described by the tightbinding Hamiltonian 2-3 . The a and a* bands describe the electronic band structure of graphene.
The bonding and antibonding a bands are neglected in the tight binding calculations since (1)
they are well separated in energy and too far away from the Fermi level of graphene, (2) by
symmetry the overlap between the pz orbitals and the sp3 orbitals is zero. Equation 1.2 is the
electronic dispersion obtained from the first nearest neighbor tight binding calculations, where a
=VJac-c (ac-c =1.42A is the C-C bond length) and y is the transfer integral between first-
-
.-
-
-.
neighbors 7c orbitals with values -2.9-3.1 eV. The k=(k,ky) vectors that belong to the first
hexagonal Brillouin zone constitute the ensemble of the available electronic momenta.
(1.1)
E= vFP
E4(kx,ky)= i
1 + 4 cos
Vikxa Cos
+ 4 (cos
2
(1.2)
1.2.2 Mechanical Properties of Graphene
The strong C-C bond covalently locks carbon atoms in place giving them outstanding
mechanical properties 5-6. A suspended single layer of graphene is one of the stiffest materials
characterized by a remarkably high Young's modulus of ~1 TPa . Corrugations or ripples
further increase thickness and rigidity of graphene. Corrugations of graphene are expected to
increase its effective rigidity 7 by a factor (H/a)2 where H is the characteristic height of
corrugations and a is the effective thickness of single layer graphene. This increase due to ripples
can be dramatic in the case of large-scale corrugations. Graphene can be stretched elastically by
as much as 20% as no other crystal5 . Graphene unlike any other materials, shrinks with
8
increasing temperature at all values of temperature because membrane phonons dominate in 2D .
Also, graphene exhibits simultaneously high pliability (folds and ripples) and brittleness and it
fractures like glass at high strains9.
1.3 Introduction to Single Walled Carbon Nanotubes
1.3.1 Single Walled Carbon Nanotube Structure, Nomenclature and Species
Carbon nanotubes were discovered in 1991 by means of transmission electron
microscopy (TEM) 1" in the multi-walled form. Multi-walled carbon nanotube (MWCNT)
consists of concentric shells of cylinders of graphene. Similarly, a single walled carbon nanotube
(SWNT) can be visualized as a rolled sheet of graphene
-4.
SWNT mean diameter is 1-1.5nm
depending on the method of synthesis15 19, with lengths of several hundred nanometers to
millimeters 20 . They are quasi one-dimensional molecular wires with high aspect ratios and can be
either semiconducting or metallic14. Conceptual formation of a nanotube involves rolling up
the graphene sheet along the chiral vector, Ch : nal
+
ma2 (Figure 1.3) where a1 and
a2
are
original graphene lattice vectors14 In nanotube notation, Ch is denoted by the integers (n, m)
and is unique to each nanotube. Nanotubes denoted by (n, 0) are zigzag tubes, due to the zigzag
pattern formed by the graphene lattice and the tubes of type n = m, are armchair tubes. The
nanotube circumference is the magnitude of the chiral vector (Ch) and thus nanotube diameter is
calculated from equation 1.3, where ac-, is the length of the carbon - carbon bond in graphene
and is equal to 0.1421 nm.
d=
=Ch
-ac-.
n2 +nm + m 2
The angle between a1 and Ch is the chiral angle is given by equation 1.4.
(1.3)
cosO=
al
h
|aj -Ch|
_
n+m/2
(1.4)
n 2+nm+m2
The translational period (equation 1.6), T, of the nanotube unit cell is given by the unit lattice
vector, T, which is perpendicular to Cb equation 1.5.
C=
h
T
T
-
V 1Ch
(2m + n)a, - (2n + m)a 2
2
(1.5)
2
(1.6)
Above dR= q if n-m is not a multiple of 3 and dR = 3q if n-m is a multiple of 3, with q being the
highest common divisor of (n, m).
-- -
..........
............
................
.............
1 _
-:=
--
-- -
-
- - M:Z=-,:,=== -:__
:::::-_ ::::::::::::
Figure 1.3: Diagram designating various species of carbon nanotubes. Adapted from Bachilo
et al". A nanotube is formed by rolling a graphene sheet from the (0,0) point to the center of any
other hexagon in the lattice along the roll-up vector. The indices (n,m) are used to designate the
number of hexagons across and down, respectively. The semiconducting nanotubes are labeled in
blue, while the semiconductors are labeled in red. The unmarked lattice units represent metals
(along the armchair axis) and semimetals (all remaining unmarked lattices).
1.3.2 Electronic Properties of Single-Walled Carbon Nanotubes
The electronic behavior of SWNT show significant deviation from the behavior of
graphene. This is mostly because the finite dimension perpendicular to the tube axis introduces
quantization of the energy levels leading to subgroups of "metallic" and "semiconducting"
carbon nanotubes.
To calculate the electronic structure of SWNT from that of graphene the zone folding
approximation is used13 . For 1D carbon nanotube the wave vector perpendicular to the nanotube
axis, kl, is quantized. The reciprocal lattice vector, kz, of the nanotube is parallel to the nanotube
axis and takes continuous values. Therefore, the allowed states in the nanotube are just parallel
slices of the graphene Brillouin zone. The length and number of these lines is dependent on the
nanotube (n, m) indices. The nanotube electronic structure can then be calculated from the
graphene band structure along the parallel lines. It is important to note that zone folding neglects
any effect from the curvature of the nanotube. The valence and conduction bands of graphene
meet only at the K and K' points (Figure 1.2). Therefore, if one of the allowed nanotube states
intersects the K point the nanotube is metallic. However, if the K point is not encompassed in the
nanotube allowed states, the nanotube has a band gap and is semi-conducting. The determination
of the nanotube type (metallic or semiconducting) based on zone folding can be easily done by
the remainder of (n-m)/3 division. The remainder of (n-m)/3 is related to the mapping of the
highest occupied and lowest unoccupied levels of SWNTs to the energy levels of graphene that
are closest to the Fermi energy, and this leads to the broad categories of "metallic" (n-m=3i, i is
an integer) and "semiconducting" (n-m=3i+1 and 3i+2) SWNTs.
Electronic density of states of carbon nanotubes
The electronic density of states (DOS) per unit volume for any three dimensional
structure is given by equation 1.72. Where o is the frequency and dSo is an area element on the
surface in k-space corresponding to the selected frequency, 0o. Vk w(k) is the group velocity
evaluated from the gradient of the electron dispersion relation.
D(o) =
1f
87r3
(1.7)
-dS
Vk&)(k)
For a one-dimensional system the equation 1.7 can be simplified to equation 1.822
19
...................
......
_ - .-I......................................
1
DE=2 LdSk-i)IaeI
1
ak1
(1.8)
Where E is the energy being probed, 1 is the length of the 1D Brillouin zone, and k is root
of the equation E-E(k)=O. The DOS of a semiconducting (6,5) and a metallic nanotube (11,5) are
shown in Figure 1.4. The narrow peaks representing large electron densities are termed Van
Hove singularities and are a typical feature of one-dimensional systems. These Van Hove
singularities dominate the optical properties of nanotubes because the concentration of electrons
is so high. For semi-conducting nanotubes there exists an energy gap centered around the Fermi
level where there is no electron density. In the case of metallic nanotubes, there is no energy gap.
1.0-
1.0-
0.5L
0.5
>0.0-
0.0
W
-0.5-
, . , . . . , , , .
-1.0
0.0 0.5 1.0 1.5 2.0 2.5
Density of States (states/eV/atom)
L
-0.5-1.0
0.0 0.2 0.4 0.6 0.8 1.0
Density of States (states/eV/atom)
Figure 1.4: Electronic density of states of SWNT. (a) DOS of semiconducting (6.5) carbon
nanotube. (b)DOS of metallic (11,5) carbon nanotube.
1.3.3 Mechanical Properties of Single-Walled Carbon Nanotubes
Single-walled carbon nanotubes have exceptional mechanical properties like graphene
due to the strength of the sP2 hybridized carbon-carbon bond. For individual single-walled carbon
nanotubes, a Young's modulus as high as 1.25 TPa 23 has been measured. Such outstanding
24
mechanical properties make SWNT a promising reinforcing material in composites . The elastic
properties drop considerably for nanotube bundles due to tubes sliding past one another in the
bundles and resulting in a lack of load transfer. Shear modulus of 20 nm diameter ropes is about
1GPa and that for the 4 nm diameter ropes it is about 6 GPa25 . Therefore the nanotubes should be
incorporated as individual tubes and not bundles to get the maximum enhancement in
mechanical properties.
1.4 Introduction to Graphene Nanoribbons
1.4.1 Graphene Nanoribbon Structure, Nomenclature and Species
Graphene Nanoribbons (GNRs) are 1D planar structures in the form of thin strips of
graphene or unrolled SWNT (Figure 1.5). GNRs are good candidates for the 1D components for
electronic devices because of their planar geometry. The GNR were introduced as a theoretical
model by Mitsutaka Fujita et a12 6 to examine the edge and nanoscale size effect in graphene on
27
the electronic states. Intrinsic graphene is a semi-metal or zero-band gap semiconductor' . This
prevents its direct application as field-effect transistors (FET). However, this can be overcome
by patterning or etching graphene sheet into ribbons of nanometers width28 3 1. This confines the
32-33
electrons in the transverse dimension and creates a band gap due to the quantum constraint
Many theoretical -" and experimental28,32 results propose this induced band gap to be inversely
proportional to the ribbon width. ID graphene ribbons appear to be similar to 1D SWNTs insofar
as they can be either semiconducting or metallic and have in common an electronic density of
states that has quantized states in the form of van Hove singularities, but they differ from one
another insofar as the properties of 1D GNR are dominated by their edges. The electronic
properties of GNR are discussed in detail in chapter 5. The DOS of GNRs can also be calculated
using equation 1.7 and are presented in Figure 1.6 for most commonly studied (a) armchair and
(b) zigzag GNR.
There are various types of GNRs defined by the arrangement of the carbon atoms along
the ribbon edges. Two main classes, with the edges assumed to be terminated by hydrogen
atoms, are armchair and zigzag GNRs (Figure 1.5). There is a difference of 300 in the axial
direction between the two edge orientations. The ribbon width (w) depends on a single index N
which denotes the number of dimer lines for armchair ribbons and for zigzag ribbons it is the
number of zigzag lines parallel to the ribbon length. The electronic band structure of the GNR
including band gap and DOS depend on the width and the crystallographic orientation of the
ribbon26,38. This dependence offers opportunity to tailor the electronic properties of GNR.
However, it also imposes a requirement of nanometer precision control in fabricating the GNR to
achieve sufficient reproducibility in their performance. Current fabrication techniques have not
achieved this level of precision. Therefore, detailed research on manipulating the GNR structure
and edges is highly desired.
b)
1 2 3"4 5 6
W
Figure 1.5: Schematic drawing of Graphene Nanoribbons. (a) Armchair GNR (N=10) with
10 C-C dimer lines. (b) Zigzag GNR (N=6) with 6 zigzag chains running parallel along its
length.
.
..................
a) 10
..........
b)
10
o
o
-6
32
10
10
S1101
10
-1
-5
-0.5
6
7
0
0.5
1
-1
-0.5
E(eV)
0
0.5
1
E (eV)
Figure 1.6: Electronic density of states of GNR. (a) DOS of armchair GNR with N=5,6 and 7.
(b) DOS of zigzag GNR with N=6 and 32.
1.4.2 Graphene Nanoribbon Edges
The two main orientation of GNR edges are armchair and zigzag. The first experimental
observation of the armchair and zigzag edge orientation was made by scanning tunneling
microscopy (STM) and spectroscopy (STS) for graphite edges 39. Later, STM lithography was
used to fabricate narrow GNR down to a width of 2.5 nm, corresponding to 10 carbon ring units
along the width of ribbon. The STM measurements revealed higher oscillations in the electronic
density of states for the narrow ribbons than for the wider ribbons due to increased contribution
of irregular edges31 . Theoretically calculations have also shown that edge irregularities might
induce electronic states within the bang gap region of the GNR 40 .
For GNRs edges play a crucial role in determining their electronic and magnetic
properties. However, current fabrication (lithography) methods are unable to control the edge
structure of GNRs and the edges are'always very rough38 . Such edge disorders can significantly
43
change the electronic properties 41-42 of GNRs by effects such as Anderson localization and
Coulomb blockade 4 4 effect. Thus future work on GNR should be focused in controlling their
edge structure.
1.5 Thesis Motivation and Objectives
The electron confinement for the carbon nanomaterials provides them unusual electronic,
mechanical and optical properties making them one of the best suited materials for electronic and
4 5 46
sensor applications. However, the practical realization of nano-scale electronics - faces two
major challenges: their assembly into functional electronic circuit and the precise engineering of
these building blocks. Physical and chemical manipulation methods need to be developed to
address these issues. However, due to the extremely small size of these nanomaterials, it is very
hard to manipulate them both physically and chemically. Research work of this thesis is
motivated to understand and design physical and chemical manipulation methods for these
nanostructures. This dissertation is concerned with two main topics on manipulation of carbon
nanomaterials: First, the problem of the top-down, parallel placement of anisotropic
nanoparticles and secondly, chemical manipulation via controlled chemical functionalization.
Motivated by the first aspect of the challenge (physical manipulation), I have designed a
method for creating high aspect ratio cylindrical droplets with nano-to-micro scale diameters on
a wafer by engineering the substrate surface chemistry, liquid surface tension and liquid film
thickness. The substrate surface is manipulated by chemisorption of monolayers of hydrophobic
and hydrophilic molecules in form of alternating rectangular strips. Surface tension of the liquid
is manipulated by controlled addition of surfactant to enable rupturing of the liquid film into
cylindrical droplets on the hydrophilic patterns. This work also discusses a method to make thin
liquid films for creating high aspect ratio nanometer sized (diameter) cylindrical droplets. The
hydrodynamic flow patterns that evolve within the droplets during evaporation are able to orient
and position the entrained carbon nanotubes (anisotropic nanoparticles) with parallel alignment.
A detailed study on droplets with diameter in the range of 150nm-5.5ptm relates the size of
evaporating cylindrical droplets to their mode of evaporation, and hence their internal flow
pattern. Finally, single nanotubes devices were fabricated using this technique.
With respect to the second aspect of the challenge (chemical manipulation), I focus on
graphene and graphene nanoribbons (GNR) - an emerging class of nanomaterial. In this work
first detailed structure-reactivity relationships for electron-transfer chemistries of graphene and
GNR are developed. For GNR, these relationships demonstrate the dependence of the ribbon
reactivity on width and orientation of carbon atoms along the edges. For graphene these structure
reactivity relationships include regio-selective chemistry and reactivity dependence on the
number of graphene layers on chip. This work is the first to demonstrate high reactivity of
graphene edges and report a spectroscopic method to analyze the edge reactivity. This study
should aid future studies to (1) separate, sort and preferentially modify ribbons by electronic
structure, ribbon width and orientation of carbon atom along the edges. (2) Control the
disordered edge structure of GNR by edge selective chemical functionalization. (3) Chemically
modify graphene depending on the number of layers stacked. (4) Assemble graphene sheets in
three dimensions to fabricate supermolecular structures (i.e. graphene super lattices).
Chapter 2 Synthesis and Characterization of Graphene and SWNT
The unique electrical and chemical properties of graphene and SWNT cannot be
exhibited while they are in multi layer or aggregated form respectively. As such, the single
graphene sheet and individual nanotube synthesis is important for electronic and chemical
studies of these carbon nanomaterials. Methods utilized to fabricate and characterize single
graphene sheet and individual SWNT for this thesis work are discussed in this chapter.
2.1 Synthesis of Graphene
In this thesis work graphene has been fabricated by three different methods including (1)
mechanical exfoliation by scotch tape method (2) chemical vapor deposition (CVD) and (3)
graphene oxide synthesis from modified Hummer's method followed by reduction of the
oxidized sheets. These methods are discussed in detail in this chapter including a description of
the characterizing techniques.
2.1.1 Mechanical Exfoliation Method
Graphite is a layered material and can split into planes consisting of graphene sheets. To
fabricate graphene using this method a small piece of graphite flake is put on scotch tape and
peeled several times' (Figure 2.la,b). Each time the flake splits into thinner flakes. Peeling is
repeated until a faint, gray cloud appears on the entire tape. The tape is then put on silicon wafer
with 300nm of thermal silicon dioxide. Silicon wafer with 300nm of silicon dioxide is a
preferred substrate to get the maximum contrast and thus make the visual detection of graphene
easier. Tweezer is used to press the tape softly on the wafer for several minutes. The tape is
peeled slowly to get graphene exfoliation and deposition on the wafer (Figure 2.1c). Microscope
is used to search for graphene (Figure 2.1 c) on the substrate. Yield of graphene is generally poor
using this method and thus the technique is fit only for experimental use. However, this method
gives highly pristine graphene. The mechanical exfoliation method is extensively used in this
thesis work to fabricate graphene sheets on substrate and study the electron transfer chemistries
for pristine single, bi and multi layer graphene.
.
....
.......
.........
a)
b
C)
Figure 2.1: Mechanical exfoliation of graphene from graphite flakes. (a) Graphite flake on
scotch tape. (b) Repeated peeling of the graphite flakes on the scotch tape to thin down the flake
and cover the tape. (c) Microscopic image of graphene single and bilayer on silicon wafer with
300nm thermal silicon oxide.
2.1.2 Chemical Vapor Deposition Method
Electronic applications require large area graphene that may be manipulated to make
complex devices on a large scale. To meet these requirements chemical vapor deposition (CVD)
growth techniques have been developed for large area synthesis of high quality graphene.
47 4 8
Graphene by CVD method has been successfully grown on metal substrates including nickle -
and copperi 9 . For this thesis work CVD graphene grown on copper substrates has been used for
0
device fabrication. Graphene is first grown on copper foils at temperatures up to 1000 C by
CVD of carbon using a mixture of methane and hydrogen. This is followed by graphene transfer
process on the desired substrate. Schematic in Figure 2.2 describes in detail the graphene transfer
process. The transfer of the CVD derived graphene films to a non specific substrate is enabled by
the wet etching of the underlying copper film48 . This is carried out by treating the film first with
an aqueous copper etchant followed by 10 wt% hydrochloric acid solution treatment. Etching is
done only after PMMA as a support material is coated on the copper-graphene surface. This
results in a free-standing PMMA/graphene membrane that can be handled easily and placed on
the desired target substrate (graphene facing the substrate and PMMA film exposed to air).
Finally, PMMA is removed by annealing in hydrogen and argon gasses at 500'C to yield a
graphene film on the desired substrate. For the device work in this thesis CVD single graphene
sheet on silicon wafer with 300nm thermal oxide are mainly used.
.
.......
.............
.........
a)
b)
c)
d)
e)
f)
Figure 2.2: Fabrication and transfer of CVD graphene. (a) Copper foil. (b) CVD growth of
graphene on copper foil in carbonaceous gas environment. (c) Graphene on copper foil. (d)
Etching copper in copper etchant and then in HCl. (e) Free standing graphene on PMMA as
supporting film after all copper is etched away. (f) The free standing graphene is picked up by
the silicon wafer with 300nm thermal oxide.
2.1.3 Graphene Oxide Synthesis
Solution phase synthesis of graphene sheets is important for several applications
including solution based sensing and depositing graphene on heat sensitive materials. CVD
graphene cannot be grown on heat sensitive materials and for such materials graphene sheets can
be directly deposited for its solution. Fabrication of single graphene sheets in solution from
graphite flakes using polymers or surfactants on a large scale has not been successful as in the
case of carbon nanotubes. The size of graphene sheets are generally below 2pm for such
methods 0 52 . On the contrary, synthesis of graphene oxide synthesis by modified Hummer's
method gives a high concentration of large single graphene sheets in solution. For this thesis
32
work modified Hummer's method
3
developed by Eda et al was used to fabricate single graphene
sheets in solution. Method is briefly discussed in Figure 2.3. Graphite is first pre-oxidized by
treatment with strong oxidizing agents including H2SO4 , K2 S2 0 8 and P20 5. This is followed by a
strong oxidation step involving concentrated H2 SO4 and KMnO 4. The two oxidation steps
introduce carboxylic acid and phenolic hydroxyl group on the graphene sheets in graphite and
thus increases the inter layer distance. The increase in interlayer distance reduces the Van der
Waals force between the stacked graphene sheets. This modified form of graphite is termed as
graphite oxide. Mild sonication of graphite oxide leads to exfoliation of single graphene oxide
sheets in water. Graphene oxide sheets can be reduced to graphene in solution by hydrazine
treatment or by annealing the sheets deposited on substrate in an inert atmosphere of argon or
nitrogen. The AFM topographic images of the large single graphene sheets obtained by this
method are presented in the Figure 2.3b.
;..:
..........
....
...
I --. .
.....................................
....
. ..
.....
..........
......
Oxidation
Graphite
............
Exfoliation in
water
Graphite oxide
0
Graphene
oxide colloids
Figure 2.3: Solution phase fabrication of graphene. (a) Graphite flakes or powder is oxidized
by Hummers method to increase their interlayer distance by introducing carboxylic acid and
phenolic hydroxyl groups. This oxidized form of graphite is called graphite oxide. To separate
the individual graphene sheets graphite oxide is sonicated in water to obtain graphene oxide
colloids. (b) AFM topographic images of the single graphene oxide sheets deposited on silicon
wafer with 300nm of thermal oxide.
2.2 Characterization of Graphene
Raman Analysis
The unique Raman scattering spectra of graphene for single layers, bilayers, and few
layers reflect changes in the electron bands structure and thus allow identification of number of
graphene layers, which is critical for graphene based research. Most importantly, Raman is a non
destructive and high throughput analysis technique. The two most intense features of a graphene
Raman spectra are the G peak at ~ 580 cm' and 2D peak at -2700 cm 1 (Figure 2.4,5). G peak is
due to the tangential stretching vibration between two carbon atoms in the unit cell. The 2D peak
is the primary peak used to identify the number of graphene layers. Peak at ~1350 cm' referred
as D peak corresponds to presence of defects. D peak is due to a second order process and is
actually symmetry disallowed in a pristine graphene sheet. In a first order process, an electronhole pair is created and the electron (or hole) is then scattered off of a phonon before electronhole recombination and emitting a scattered photon. In the case of a second order process a
second scattering event takes place where the electron (or hole) is scattered off of a defect or
another phonon with opposite wavevector, in order to keep the momentum conservation. Then
the electron-hole pair recombines emitting a scattered photon. In the case of the D band the
second scattering event is due to defects in the graphene lattice, which can be either missing
atoms, substitutions or presence of functional groups on carbon atoms in the lattice.
For this thesis work graphene has been extensively analyzed by confocal Raman
spectroscopy to (1) estimate the number of graphene layers stacked (2) determine degree of
covalent functionalization by electron transfer chemistries and (3) analyze edge Vs bulk
reactivity. Figure 2.4-5 shows a significant change in shape and intensity of the 2D peak of
graphene (single and bilayer) compared to bulk graphite. The 2D peak in bulk graphite consists
of two components 2D 1 and 2D254, roughly 1/4 and 1/2 the height of the G peak, respectively.
For a graphene sheet a single and sharp 2D peak with ~4 times more intensity than the G peak is
observed. FWHM of the 2D peak of single graphene sheet is ~30cm' and is the feature most
commonly used to confirm presence of n=1 graphene sheet in this thesis (Figure 2.4b). The 2D
peak also upshifts with increase in the number of graphene layers from single (Figure 2.4b) to
bilayer (Figure 2.4c) and to graphite (Figure 2.5b). Figure 2.4 shows microscopic images and
Raman spectra of single and bilayer graphene. The graphene sheet is deposited on a silicon wafer
with 300nm thermal silicon dioxide and the sheet is fabricated with the mechanical exfoliation
method using scotch tape.
..
............
......
...............................
b)
30000.
30000-
i 20000-
20000.
D
10000-
100000
1100
c)
1700
2300
Raman shift
2900
(cm-1)
2600
2700
2800
2600
2700
2 OO
Raman shift (cm-1)
10000
10000-
C0
Co
(D5000-
.~5000
1700
2300
Raman shift
2900
(cm-1)
Raman shift (cm- )
Figure 2.4: Raman spectra of single and bilayer graphene. (a) Microscopic images of single
(L 1) and bilayer (L2) graphene. The light blue color corresponds to the single graphene sheet and
the dark blue color is for bilayer graphene. The sheets are deposited on silicon wafer with 300nm
of thermal silicon dioxide. (b) Raman spectra of single layer graphene. The 2D peak is a single
.......
. ......
. . . ..
sharp peak with FWHM ~ 30cm- 1. (c) Raman spectra for bilayer graphene. FWHM of the 2D
peak is ~54cm-1. The Raman analysis is for pristine graphene made by scotch tape mechanical
exfoliation technique. Absence of D peak indicates graphene is defect free.
a00
'Juq
C,)
C: 3000
Cn
(D
)
1700
Raman
2300
2
shift (cm- 1)
30
0
2500
2600
2700
2800
Raman shift (cm- 1)
Figure 2.5: Raman spectra of graphite. (a) Microscopic images of graphite. The white color
sheet is graphite on silicon wafer with 300nm of thermal silicon dioxide. (b) Raman spectra of
graphite.
2.3 Synthesis of Individual Carbon Nanotubes
The unique and outstanding electrical and optical properties of SWNT cannot be fully
exhibited while the SWNT are in aggregate form. Researchers over the past several years have
developed several techniques to get individual nanotubes with no aggregation in solution and on
chip/substrate. CVD growth method is commonly used to get an array of individual SWNT on
various substrates55-56. Synthesis of nanotubes in solution is also of critical importance since it
enables use of the nanotube separation techniques 57, deposit nanotubes on heat sensitive
substrates 58 that otherwise cannot withstand high temperature of CVD growth conditions and
make nanotube hybrid structures 59. The individual dispersion of SWNT is also of prime
important for device fabrication from nanotube suspended in solution. The preparation of SWNT
samples in this thesis work is mainly based on their solution phase dispersion. The dispersion of
raw and aggregated nanotubes into solution starts with mixing raw SWNT in water with
dissolved surfactant. Sonication is then used to break the nanotube bundles held strongly by the
Van der Waals force 60 . Cuphorn or probe-tip or bath ultrasonicator can be used depending on the
desired intensity of sonication and the volume of solution to be processed. Intensity is highest for
cup horn ultrasonicator (180 watts) and smallest for bath ultrasonicator. The commonly used
power
for probe-tip ultrasonicator is 3-10 watts. For this thesis work mostly cuphorn
ultrasonicator is used to prepare aqueous SWNT suspensions and bath ultrasonicator for organic
solvent based suspensions.
To make the SWNT aqueous solution 40 mg of High Pressure Carbon Monoxide (HiPco)
nanotubes from Rice Research Reactor (run 107) were dispersed in 200mL of water with 2
weight percent sodium dodecyl sulfate. When added to water, the aggregated raw nanotubes
appear as a distinctly solid black separate phase. The solution is homogenized for one hour at a
frequency of 6.5 min-' to mix the two distinct phases. In order to break the SWNT bundles, the
solution is ultrasonicated using a cuphom ultrasonicator operating at 90% amplitude for 10
minutes (180 watts). At this point the solution is a mixture of individual SWNT, small bundles,
large bundles, and other impurities including amorphous carbon and iron nanoparticle catalysts
from the HiPco process. In order to separate out the individual SWNT and small bundles, the
solution is ultracentrifuged at 30000 rpm for 1-4 hours. A solid pellet at the bottom contained the
large bundles and impurities. The clear, gray supernatant containing the individual SWNT and
small bundles is decanted into a separate container for characterization and subsequent
experimentation.
2.4 Characterization of SWNT Dispersion
Absorption Spectra
SWNT suspension with individual nanotubes absorb strongly from the UV to the near
60
infrared regions with distinct peaks arising from different species (n,m) of nanotubes' ' (Figure
2.6). This includes features for Ell and E22 transitions for semi-conductors and the El transition
for metals. For higher energy transition there is a large degree of overlap between nanotube
species, due to the heterogeneous nature of SWNT samples. Bundling of nanotubes broadens and
down shifts the absorption transitions and disappearance of absorption bands will occur when
SWNT have undergone a covalent chemical reaction, as electrons from the conduction band are
no longer available for photoexcitation. The absorbance is directly related to the amount of
nanotubes that are dispersed in solution. The wavelength chosen for estimating the SWNT
concentration is 632 nm, which corresponds to a valley in the spectrum. To determine the SWNT
concentration a valley is specifically chosen because it is representative of the overlap of
multiple nanotube peaks, as opposed to a peak, which is weighted toward one specific nanotube.
This metric gives a more general measure of nanotube concentration. The extinction coefficient
of SWNT is approximately 0.036 mg' L cm-1 at 632 nm.
1.61.2Cn
C:
0.80.4-
300 600 900 120015001800
Wavelength (nm)
Figure 2.6: Absorption spectrum of SWNT suspension in deuterium oxide. Distinct peaks
arise from different species of nanotubes.
Raman Analysis
Carbon nanotubes exhibit strong resonance Raman scattering, where the intensity of the
Raman peaks is enhanced when the nanotubes are excited near an allowed optical transition
61
energy- Eii. Resonance enhancement allows collection of a spectrum from a single nanotube
and nanotubes dispersed in solution. Raman spectra of SWNTs have four primary peaks
including radial breathing mode (RBM), D, G and G' peaks. The D and G' peaks of SWNT are
similar to the D and 2D peaks of graphene respectively.
RBMs are observed from ~ 100 to 400 cm-1 and are nanotube specific 6 2, absent in other
graphitic materials including graphene. These peaks arise from the symmetric radial vibrations
of carbon atoms and their frequency is inversely proportional to the nanotube diameter. The G
band of nanotubes is directly related to the graphite and graphene G band. The curvature and ID
confinement of SWNT causes the two degenerate modes of G peak to split resulting in G- and G*
peaks 63. The observed frequencies for these bands are ~1570 and ~1590cm-1 for the G- and G+
bands, respectively. The RBM and splitting of G peak are the two main features present in
SWNT but absent in graphene and thus are important as they allow to rapidly distinguish
between the two families.
Chapter 3 Physical Manipulation of Single Walled Carbon Nanotubes on
Chip with Pinned Contact Evaporation Regime of Cylindrical Droplets
3.1 Motivation and Approach
An important problem in nanotechnology is the large-scale, top-down placement of
nanostructures from solution with controlled orientation and position on a substrate surface. Such
control is essential for advances in nanoelectronics
64-65
sensor development
669
6-69
and synthesis of
photonic arrays7 . Researchers have developed several techniques to physically manipulate
nanostructures on chip. These include dielectrophoresis 7 1-72, gas flow 7 3, magnetic alignment74,
electrospray,
and self-assembled monolayers (SAMs) with high affinity for nanoparticles
76 78
assembled via microcontact printing or dip-pen nanolithography (DPN) - . Only DPN
technique gives individual nanotube alignment with high precision. Other techniques have
mainly demonstrated alignment of networks rather than individual nanotubes or nanorods.
However, DPN is too slow to practically apply in a nanomanufacturing context for a large scale
assembly.
Several researchers have utilized evaporating droplets79 to assemble nanoparticles such as
SWNT, but it is not obvious that such approaches can yield precision of single-particle
deposition. Additionally, the spherical geometries of the droplets utilized are less advantageous,
confining materials to circular or ring-shaped patterns 8 0 that are not easily incorporated into
complex electrical devices, such as field effect transistors and metallic interconnect applications,
for which parallel alignment of single nanotubes and bundles of nanotubes is respectively
desired.
Motivated by the challenge to solve the problem of physical manipulation of
nanoparticles on chip, a new method has been designed in this thesis work for creating high
aspect ratio cylindrical droplets with nanometer to micrometer scale diameters at precise
locations on a patterned wafer. The method is developed by engineering the (1) substrate surface
chemistries, (2) nanotube surface chemistries, (3) liquid surface tension, and (4) film thickness of
the liquid forming cylindrical droplets. In this method, the distinctive hydrodynamic flow
patterns that evolve within the droplets during evaporation are able to orient and position the
entrained SWNTs. Cylindrical droplets with diameter 3-5.5plm position nanotubes along the
edges and droplets with diameter 150nm- 1pjm position nanotubes along the centerline. This work
shows how different evaporation regimes can control the orientation and placement of nanotubes
on the substrate surface and findings are validated with a model of evaporative mode switching.
3.2 Modes of Evaporation of Droplets on Solid Surface
There are three modes of evaporation by which a sessile droplet may evaporate on solid
surface. In one mode, the contact angle remains constant and the contact area decreases, which is
also called depinned contact or shrinking8 1 . In the second mode the contact area is constant with
decreasing contact angle, known as pinned contact 1 . The nature of the
contact lines during
evaporation is a function of several factors, including the rheological properties of the
- ::..:..z :vvl
...........
..............
- -....
.....
.........
............
- .-.....
evaporating liquid, surface roughness and heterogeneity, the rate of the evaporation, and the
evaporation mechanism. As observed by several researchers, evaporation may be by only one of
the above modes8 2-8 3 or by a third mode that is a combination of the first two modes, particularly
pinned contact drying followed by shrinkage drying8 4~85. Many believe that the origin of the third
mode (evaporation mode switching) is the existence of contact angle hysteresis on a surface84.
Accordingly, the hysteresis leads to an evaporation mode initially with an unchanged contact
area and a diminishing contact angle until the receding contact angle is attained. After this, the
constant contact angle (depinned contact) mode supersedes.
Depinned Contact
Pinned Contact
Constant Contact Area
Decreasing Contact Angle
/
Constant Contact Angle
Decreasing Contact Area
Mixed mode
Pinned Contact
6=9 R_,
Depinned Contact
Figure 3.1: Modes of evaporation for droplet on solid surface
3.3 Platform to Create Cylindrical Droplets on Chip
In this new method a platform is developed to create micrometer to nanometer diameter
cylindrical droplets on chip. This is achieved by patterning the substrate surface with alternating
rectangular strips of a polar (cystamine) and nonpolar (octadecanethiol, ODT) self assembled
monolayer using micro-contact printing
86
as represented in Figure 3.2. The width of the
patterned strips are in the range of 150nm-5.5pm (polar SAM) and 1.5~3pm (non polar SAM)
respectively. Figure 3.2 shows AFM topography image of such a patterned surface with the
width of polar and non polar stripes ~ 3.5gm and -2.5pm respectively.
For micro-contact printing a PDMS stamp with lines and spaces is used (Figure 3.2a).
The stamp is made from photoresist/PMMA master fabricated with photo/electron-beam
lithography technique depending on the desired feature size. The PDMS stamp is coated with
solution of octadecanethiol (ODT) in ethanol. This is followed by drying of the stamp to allow
all the ethanol to evaporate. The stamp is then lightly pressed with no shaking on gold coated
silicon substrate, followed by rinsing the substrate with excessive ethanol to ensure ODT
monolayer formation on gold. The light pressing ensures that ODT molecules only on the lines
are contacted to the substrate but not the ones that are in the spaces. The regions which are
contacted by the lines of the stamp finally have non-polar (ODT) SAM (Figure 3.2b). After
drying, this substrate it is dipped in a solution of cystamine in ethanol (Figure 3.2c), followed by
rinsing in ethanol to ensure monolayer of cystamine (polar) in regions not covered with ODT
molecules (Figure 3.2d,e). The cylindrical droplets are then created by putting a thin film of
nanotube solution on the patterned substrate. No SWNT deposit when the patterned substrate is
immersed into SWNT solution for 30 minutes with no subsequent drying (i.e. no droplet
formation). This confirms that the nanotube deposition is solely caused by the formation and
evaporation of the cylindrical droplets and not due to interaction between polar SAM molecules
and SWNT. SWNT suspended in water with 1 wt % sodium dodecyl sulfate (SDS) surfactant is
used as the nanotube solution. Surfactant aids in lowering the surface tension of water. Pure
water does not form cylindrical droplets due to its high surface tension (y=72dyn/cm) (Appendix
A shows a picture of pure DI water completely leaving (dewetting) the patterned substrate
without forming any droplets). Liquids of very small surface tension i.e. ortho-dichlorobenzene
also do not form the cylindrical droplets. This suggests that intermediate surface tension is
required to create the nano-micrometer diameter cylindrical droplets. This chapter discusses (1)
formation, evaporation and microflow pattern for the droplets with diameter 3-5.5pm also
referred as micron sized cylindrical droplets in this thesis. Similar discussion for the nanometer
sized cylindrical droplets with diameter 15Onm-1 Im is done in chapter 4.
-
a) Spaces
b)
.........
..
..
.
.....
c)
ss SS SS
Lines
with ODT PDMS
Stamp
Gold coated
SiO2 wafer
d)
amine terminated
SAM (polar)
methyl terminated
SAM (non polar)
Cystamine
in ethanol
Substrate
e)
polar (cystamine) non polar (ODT)
Figure 3.2: Platform to create cylindrical droplets. Micro-contact printing of alternating polar
and non-polar SAMs on gold coated silicon wafer. (a) PDMS stamp with alternating lines and
spaces. Lines of width 2.5ptm have ODT molecules. This is pressed on the gold surface to get (b)
alternating ODT monolayer on the gold surface. (c) The substrate with alternating lines of ODT
SAM is dipped in a 2mM solution of cystamine in ethanol forming (d) polar SAM in the regions
uncovered by the ODT SAM. (e) AFM topography image of the substrate in d.
3.4 Formation and Evaporation of Micrometer Diameter Cylindrical Droplets
This section involves a detailed description of formation and evaporation of cylindrical
droplets with diameter in the range of 3-5.5pm. First, the substrate is patterned (Figure 3.3a) with
alternating hydrophobic and hydrophilic SAMs as described in Figure 3.2. The solution of
nanotubes in water with 1 wt% SDS is deposited by either immersion of the patterned substrate
into it or by application of few of its drops to cover the substrate surface forming a thin,
homogeneous film (microscopic image in Figure. 3.3b). As the film dries and spreads, its height
decreases and reaches a critical value where the surface free energy is minimized by segregating
into the desired cylindrical droplets on the polar SAM region with aspect ratio exceeding 1000
(Figure 3.3c). The width of the polar and non-polar SAMs ultimately becomes the diameter and
regular pitch respectively of a parallel array of cylindrical droplets of aspect ratio exceeding
1000. Figure 3.3 shows both the microscopic images and schematics of the process over time and
all the microscopic images are 223X magnified. This process of transition from continuous
surface of liquid film to cylindrical droplets begins from several points within the film and they
propagate along the length rapidly. The contact area of the droplets remains constant (pinned) to
the polar SAM as they dry with edges pinned to the edges of the polar SAM (Figure 3.3c-d), (the
real time video is included in
http://web.mit.edu/stranogroup/Public/paper2.wmv).
The
evaporative process terminates due to the fast contraction along the length of cylindrical drop,
leaving a solvent-free surface (Figure 3.3e-f). Cylindrical droplets after formation remain for an
average time of 1.5 second before complete evaporation due to the rapid length contraction
(evaporation at free ends). The hydrodynamics in the interior of these micrometer sized
(diameter) evaporating cylindrical droplet is determined by their pinned mode of evaporation and
the resulting internal flow is then used to control the nanotube positioning on the substrate.
A1lill
thi fil of
namthab. ggiii
- ..
......
....
:.::......
...
..
I-- I .,- v:-
_
:'--_---:I__
:.....
......
..........
.
14.6 9se
Figure 3.3: Formation and evaporation of cylindrical droplets on chip. (a) Micro-contact
printing on gold is used to create rectangular polar stripes flanked by rectangular nonpolar
domains (AFM topography image). Widths of the stripes are -3.5 gm and -2.5gm respectively
over a length of 10mm. (b) Thin nanotube solution layer on the patterned substrate. (c) At critical
height the liquid film (t=0) segregates into cylindrical droplets of -3.5pm diameter. These
cylinders are formed only on the polar SAM region. (d) As the cylindrical droplets dry, the
contact area of these cylinders remains pinned to the width of polar pattern, with decreasing
contact angle. This drying process establishes a radial flow field within the drop pushing the
entrained SWNT to the outermost edge of the polar SAM and aligning them before deposition.
(e) The process terminates as the ends of the cylindrical droplets contract rapidly (cylindrical
section of -3.5 diameter remain for ~ 1.5 s) leaving a solution free surface with deposited SWNT
on the edges of the polar SAM. (f) Drops that have a larger diameter (more than three times) than
the droplets with average diameter of~3.5 gm take a longer time to evaporate. Hence they can be
seen on the surface even after most of the droplets have dried.
3.5 Hydrodynamics in Micron Sized Cylindrical Droplet
Solvent evaporates at a constant, pinned contact area for micron sized cylindrical droplets
created on chip (Figure 3.3) therefore an internal flow should exist (Figure 3.4) similar to the
case of spherical droplets80'87. Petsi and Burganos 88 derived an analytical solution for the
potential flow inside evaporating cylindrical droplet evaporating with pinned contact. The
potential flow in the droplet follows V2qp = 0 (irrotational and incompressible flow), where the
velocity potential is described by v = V p where q and v are velocity potential and velocity
respectively. Using a bipolar coordinate system, they showed that the resulting velocity
components in Cartesian coordinates are:
coshacosp+1
cosha+cos#8
va,)=v,
sinhasinp
V-v
cosha+cos/p
va,)
+
sinhasinp3 v,
cosha+cos#
3.1.a
+ coshacosp+1
v,3.1.b
+
cosha+cos#8
Where the velocity components in a bipolar coordinate system (a,
V, (a
)
=
- 2 (sh
c
v (a,/6) = 2-(cosh a +
c
+
cos /)J cosh A,/ sin hax
0sinh
(u, + J / p)cos
AO(t)
iohsfsacos
0 sinh AOt)
x
,z )88are:
d
3.2.a
da']A
da'
3.2.b
0 cosha'+cosO (t)
[j
L0 cosha'+cos9,(t)
52
Here, J is the local evaporation flux, O (t) is the contact angle at time t, p is the liquid density,
and un,(t) is the normal component of the surface velocity at time t given by:
Um(t) =
p sin 0,(t)
(t)
-
0,(t)cos0,(t)
(cos
(t)-
1-
sin 2
))
3.3
J is assumed to be constant over the surface of the drop and equal to Jo. Both uns(t) and 0, (t) are
functions of time, and for a constant contact area evaporation the contact angle decreases with
time as:
dO,(t)
dt
JTOT
sin 3 0,(t)
()
2pR 2
34
sin 0,(t) - 0, t) cos 0, t)3.
Where R is the radius of the droplet and JTOT is the total evaporation rate per unit length of the
droplet given by:
2RJO c(t)
sin 0,(t)
3.5
...
...........
;; ;;; .. - , . ,
.......
.....
. .............
..........
a)
,.:
:-= =: :,::
:::: - -
..
b)
0.6
0.5
:::-:
: ::::::::::::::::::::::::::
...................
.....
Contact angle =60*
0.4'
0.24
0.1
2R
0
0.2 0.4 0.6 0.8 1
r/R
Figure 3.4: Internal flow pattern in an evaporating cylindrical drop with constant contact
area. (a) Cylindrical droplet. (b) Velocity vector field in the droplet.
In this thesis analytical solution for the potential flow inside the micron sized cylindrical
droplets (equation 3.1-3.5) is solved to obtain the local flow field in terms of velocity vectors as
presented in Figure 3.4b. The length of arrows is directly proportional to the magnitude of the
velocity at that location. As indicated by Figure 3.4b the magnitude of the velocity increases as
r-> R (close to the edge) and velocity vectors throughout the droplet are directed towards the
edges. This edge directed internal flow is responsible for placement and alignment of SWNT
along the droplet edges of micron sized cylindrical droplets as discussed in the next section.
3.6 Parallel Alignment and Placement of SWNT
When cylindrical drops as described in Figure 3.3 are created with SWNT solutions,
subsequent AFM topographic images taken after solvent evaporation reveal individual nanotubes
are highly aligned and positioned in very close proximity to the polar/nonpolar SAM interface
(Figure 3.5). The parallel placement of individual (unbundled) nanotubes at pre-defined locations
has not been achieved before using different techniques 7 1 ,73-74,76,89. For this work section analysis
on a statistically significant population of deposited SWNT confirmed that they remain
unbundled when deposited using this process. The number density of SWNTs at the interface
increases with solution concentration (from Figure 3.5a-c) as expected and continuous "wires" of
nanotubes are created using a concentration of 9.7 mg/L (Figure 3.5c). The inset to Figure 3.5b
shows a nanotube height near 1nm, corresponding to the diameter of a single SWNT. This
hydrodynamic deposition is observed not only for long SWNT (electric arc, average
length-2.5[im) (Figure 3.5a-c), but also for shorter SWNT (HiPco, average length-0.8pm)
(Figure 3.5d) suggesting this method is independent of the nanotube length. In compiling several
AFM topographic images, some placement errors (Figure 3.5b) was observed, where positioning
or alignment deviated from the typical observations (Figure 3.5a,d), although these were rare
(statistics appear below). These errors generally include SWNT lying along the center of polar
SAM or an offset (Ax/R ~ 0.1-0.2) from its edge. This technique is fairly reliable in reproducing
several desired features such as: edge deposition, excellent parallel alignment to the long axis of
the cylindrical droplet, and preservation of individual SWNT for both long and short SWNT.
......
....
........
. ......
...........................................
4ftmi
2.0 section analysis
0
4pmn
D ob I, _
1
2
...........
Figure 3.5: Nanotube positioning in micrometer diameter droplets. AFM topographic images
of individual nanotubes aligned and placed along the edges of the polar SAM (white ovals
highlight SWNT). (a) Highly aligned and positioned SWNT with low coverage for 4.6 mg/L
concentration SWNT solution with the inset showing the section analysis of the area in the
dotted region demonstrating deposition of individual SWNT (height ~1nm). (b) Moderate
coverage for 6.2 mg/L SWNT solution. (c) High coverage of SWNT resembling continuous
wires of nanotubes for 9.73 mg/L SWNT solution. (d) Aligned short individual SWNT (HiPco,
average length ~ 0.8ptm). SWNT in a-c are electric arc synthesized (average length~ 2.5[tm).
3.7 Comparison of Experimental Results with the Continuum Hydrodynamic Modeling
evaporation from the
curvilinear surface
e= 150
Oc =300
Pinned contact
area evaporation
2R
2R
0e
0 C =300
0
150
onntact
area evaporation
04 .2
0.1
Pinned
C 01
-
0.2
0.
r/R
0.6
0.8
1
0
0.2
0.4
0.6
0.8 1
r/R
Figure 3.6: Hydrodynamics in a cylindrical drop evaporating with pinned contact area. (a)
Solvent evaporating from the curvilinear surface of a cylindrical droplet with constant, pinned
contact area and decreasing contact angle from 300 to 15'. White arrows represent the internal
flow field in the droplet that carry entrained nanotubes to the outer edges of the droplet. (b)
Velocity vector field in the cylindrical droplet drying with pinned contact area and decreasing
contact angle from 30' to 15*. (Note: y axis is not in scale with the x axis)
A simple model based on the analytical solution (equation 3.1-3.5) is developed to
explain the observations of nanotube placement in the evaporating cylindrical droplets. A
cylindrical droplet evaporating with pinned contact area of diameter 2R~3.5iim is considered
with entrained SWNTs (Figure 3.6a). Using the velocity field in the evaporating cylindrical
droplet obtained by solving equation 3.1-3.5, the trajectory of a massless body was traced by
integrating the transient field that evolves as the free surface of the drop moves downwards with
pinned contact drying. The resulting placement was found to be dependent both on the initial
position of the massless probe in this field and on the final contact angle. The final contact angle
is defined as the angle when the drop vanishes due to contraction along its length. Figure 3.6b is
the scaled velocity distribution predicted for an evaporating droplet with starting and final
contact angle of 300 and 150 respectively. The experimental results of nanotube positioning were
directly compared with results obtained by solving the trajectories from flow field simulations. A
histogram of the position of the deposited SWNT from the interface of the polar/non polar SAM
(Figure 3.7b) was produced by compiling the exact position and orientation of over 372 SWNT
from 20 AFM images. The majority of deposited SWNT reside near 0.8-1 times the cylinder
radius (R) from the centerline (defined as r = 0, Figure 3.7a), with some deposition errors near
the centerline of the polar SAM. The error in alignment angle was compiled by defining 0 = 0
as a perfectly orientated SWNT lying parallel to the interface (Figure 3.7a). The experimental
data set shows nearly a negligible error in alignment at 00, and it was therefore deemed
unnecessary to simulate this variable (Figure 3.7c).
b)
120
c) 400
100
300
cn
80
200
100
u
0.2
0.4
0.6
0.8
0
-100*
1
r/R
-50*
0*
50*
Angle of alignment (0)
d) 300
0
200
c initial =30
0
c fina =
25
100
0
0
0.2
0.4
0.6
0.8
r/R
r/R
400
0.2
Oc iniia =30'
300
200
100
Sfinal =20*
0.1
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
r/R
r/R
c niial =
200
0.2
100
0.1
30
Oca =15*
*
00
0.2
0.4
r/R
0.6
0.8
1
0
0.2
0.4
r/R
0.6
0.8
Figure 3.7: Comparison of experimental results with the continuum hydrodynamic
modeling. (a) Width of the polar SAM becomes the diameter of the cylindrical droplets (2R) that
have their center along the centerline (r=0) of the polar SAM, 0 is the angle of alignment.
Experimental data compiled for 372 SWNT from 20 AFM images, with (b) the resulting
placement with reference to the center line as r/R = 0 and (c) parallel alignment with reference 0
(angle of alignment) as zero for SWNT parallel to the SAM edges. (d) Simulated statistical
deviations in placement obtained by calculating the trajectories of massless probes in flow field
of drying cylindrical droplet. Accuracy of deposition depends on the total deposition time (or
final contact angle). If an initial contact angle of 30' decreases to 25' or 200, the resulting
histogram show some placement errors with similarities to experimental data in b. Note the small
population near the center line is due to very low velocities in the region close to the axis
(droplet center, r=0). (e) If the droplet survives for longer times (final contact angle below 150)
then placement is perfect with all probe particles reaching the polar SAM edges with no error in
placement.
To simulate the statistical deviations in placement, the transient, quasi-static flow field
was simulated as described in Figure 3.6. At constant evaporation flux, the height of the free
surface and contact angle decrease according to equation 3.3 & 3.4 respectively, and the
resulting trajectories of massless probes were found by integration of this transient field. The
probes were equally distributed in the droplet cross-section to do this simulation. For massless
probe particles with varying initial position, the final placement was recorded as that point where
the trajectory ended when the final contact angle was reached (i.e. angle when the drop vanishes
due to shrinkage along the length). Most of the particles reach the droplet edge much faster than
those starting near the center (r/R<0.1). It was assumed that particles that do not reach the
substrate (y=0) before droplet evaporation end up at a point vertically translated downwards
when the final contact angle was reached. It is found that the variation in the placement is a
function of the starting contact angle and the total deposition time (or the final contact angle).
For a rapid time to complete evaporation, or small change in contact angle, the droplet collapses
(due to contraction along the length) before particles located near the centerline can translate to
the edge. Figure 3.7d,e plots trajectories of several massless probe particles starting at different
locations within a cylindrical drop of initial contact angle 300. If the process terminates at 25' or
20' (Figure 3.7d), the simulated histogram shows some placement errors at small r (close to the
droplet center). If the process terminates at longer time (Figure 3.7e), with 150 as final contact
angle, the placement is perfect with all the particles reaching the droplet edge (r/R=1) as inferred
from the simulated histogram. The center of the droplet has a stagnation point at r/R = 0, region
of low velocity for r/R < 0.1, and placement errors normally result from particles initially placed
here.
3.8 Equilibrium Deposition of SWNT
Equilibrium deposition is guided by the interaction between the nanotube and the SAM
molecules, unlike the cylindrical droplet alignment method developed in this thesis. This section
does a comparison study of the equilibrium deposition of SWNT with placement by micro flow
in cylindrical droplets. To achieve this gold coated silicon substrate surface was patterned with
SAM (alternating nonpolar (ODT) and polar (2 methylamine)) as discussed in Figure 3.2.
Equilibrium deposition was done by immersion of the patterned wafer in ortho dichloro benzene
(ODCB) based SWNT solution for 12 seconds. Immersion was followed by instantaneous
rinsing of substrate in ODCB (solvent) with no drying of SWNT solution on the substrate. The
AFM topography image of the substrate shows a network of SWNT bundles deposited in the
polar region (Figure 3.8).
There are few important distinctions between the hydrodynamic method of alignment and
placement and the equilibrium deposition method. Firstly, SWNT wrapped with anionic
surfactant have no chemical affinity for the patterned surface and will not deposit on a polar
SAM under equilibrium conditions (Immersing the substrate in SWNT solution followed by
rinsing in the solvent). Several recent studies have explored the equilibrium deposition of SWNT
for pattered substrate76 78 . In these systems, the particle interacts directly with chemical moieties
on the surface resulting in adhesion 90 . This restricts these methods to organic solvents in
practicality since water dispersion of nanotubes generally needs a surfactant. In contrast, the
micro-hydrodynamic method of alignment and placement should be operative for particles
independent of their surface chemistry.
Secondly due the restriction of the equilibrium deposition to organic solvents the
deposited SWNT would be mainly less useful bundles rather than single SWNT (Figure 3.8).
However, using the micro-hydrodynamic method of alignment and placement deposition of
individual SWNT has been demonstrated (Figure 3.5).
Thirdly, equilibrium deposition gives SWNT deposition as a networks/mesh (Figure 3.8)
with many nanotubes-nanotube junctions. These crossings/junctions offer resistance to the
flowing charges, which are expected to reduce the device current and hence performance.
However, the parallel alignment of unbundled nanotubes from micro-hydrodynamic method is
free from such barriers. Hence, this process of alignment seems to be a promising platform to
develop more efficient SWNT devices (FETs, interconnects).
I...........
...
..........
...........
Nonpolar SN
V
(01D1)
Figure 3.8: AFM topography images of equilibrium deposition of SWNT. AFM images
show aligned SWNT network (mesh) in the polar SAM region. They lack individual SWNT and
parallel alignment.
Chapter 4 De-Pinned Contact and Transition Regime Evaporation of
Cylindrical Droplets
4.1 Formation and Evaporation of Nanometer Diameter Droplets
Cylindrical droplets with diameter in the range 175 to 950nm are referred as nanometer
sized droplets in this thesis. The platform to create the nanometer diameter cylindrical droplets is
a patterned gold surface with alternating rectangular stripes of polar and non polar SAMs as
reported for micrometer diameter cylindrical droplets in chapter 3. However, the master to make
the PDMS stamp is made from PMMA and fabricated with electron-beam lithography due to
their sub micron feature sizes. The formation of droplets occurs when a thin homogenous film of
1% wt SDS-SWNT solution deposited on the patterned area segregates into the desired
cylindrical droplets on the polar SAM region. For creation of micron sized (2R > 3 Im) droplets
the solution can be deposited by either immersion of the substrate into it or by application of a
few drops to cover the surface forming a homogenous film. However, to successfully create
nanometer sized cylindrical droplets (175 to 950nm) a thin film of nanotube solution was
required on the patterned area to ensure its facile rupturing into nanometer sized droplets. For
this purpose, the foam from SDS-SWNT solution was used to create the desired thin film of few
micrometers in thickness. The evaporation of the nanometer sized droplets was over in less than
one second.
4.2 Parallel Alignment and Centerline Placement of SWNT
Cylindrical Droplets with diameter below I pm show centerline placement and alignment
of the nanotubes as presented in AFM images of Figure 4.1 (SEM images are included in
Appendix B). This includes cylindrical droplets with 2R (diameter) ~ 175, 425 and 950nm
(Figure 4.la, b and c respectively). Figure 4.1d & e are high magnification images and show
perfect parallel alignment and centerline positioning of nanotubes with moderate and high
coverage respectively for 350nm wide polar SAM. SWNT coverage depends on their
concentration in the solution and the number of times the deposition is done. Inset in Figure 4.1d
is the section analysis of area in the dotted region demonstrating deposition of individual SWNT
(height -1.3 nm). The accuracy of this centerline deposition is more than 95% (95% of the
nanotubes deposit within ±5% of r/R=0). Short nanotubes in Figure 4.1 f (length
-
200-600 nm)
also show similar results. This proves that centerline positioning like the edge positioning is also
independent of nanotube length.
.......................
..............................
. ..........................
...........
c)
)l
0. 5pa i
1
m
_2p1
Figure 4.1: Nanotube positioning in nanometer diameter droplets. AFM topographic images
showing parallel alignment and placement of individual nanotubes along the centerline of what
were nanometer and sub micron sized cylindrical droplets before evaporation (2R ~ 175-950
nm). (a) 175nm, (b) 425nm, and (c) 950nm width polar SAM (2R). (d-e) High magnification
images showing a high degree of parallel alignment and positioning of the nanotubes with
moderate and high coverage respectively for 350nm wide polar SAM. (d) Section analysis shows
the height of a single nanotube (1.3 nm). (f) Short nanotubes (length ~ 200-600nm) aligned on
450 nm wide polar SAM.
A clear transition in nanotube position is observed with the change in the diameter of the
cylindrical droplet. The results are mapped in Figure 4.2. It is centerline deposition, r/R=0 for
nanometer and submicron sized droplets (2R- 175-950 nm) as represented in Figure 4.2a, b (2R
~ 300nm, ~ 950 nm respectively). Edge deposition, r/R=1 for micron sized droplets (2R > 3 pim)
as represented in Figure 4.2e, f (2R ~ 3.1pjm, 5.5 jim respectively). Both these regimes have
almost perfect parallel alignment of nanotubes with negligible error. A transition/disordered
regime (Fig. 4.2c,d, 2R ~ 2pm) exists between the two regimes of perfect alignment and
positioning. In this transitional regime, SWNT deposit at some intermediate r/R (0 <r/R<1) that
is not fixed. Additionally, they lack perfect parallel alignment and deposit with notable bends
along their length. The statistics of nanotube positioning is presented in Figure 4.3 in form of a
bubble chart and histograms. The bubble chart clearly shows the three regimes of SWNT
positioning (centerline, edge and intermediate). The bubble chart is compiled for the positions of
1160 nanotubes from 70 AFM images where the size of each bubble is proportional to the
number of overlapping data points. (Note that the large bubble area does not imply variation of
placement location - it is proportional to the number of overlapping counts observed at precisely
the center of the bubble at the specified r/R.) Figure 4.3b, c are histograms for the centerline and
edge deposition respectively showing the accuracy of positioning in these regimes.
r al r------------------------------------- D)
I
r-----------------------------
C)
2tm
e)
- -- - - -- -- --
3pm
I
d)
2pmr
- - - f)
- - - -
- - -
- -I4
I
3ptm
PolaSAMNon Polar
SAM
Figure 4.2: Diameter of the droplet controls positioning of the nanotubes. (a-b) Centerline
deposition: For nanometer and sub micron width (2R) all nanotubes deposit at the center of the
polar SAM (r/R=0) with parallel alignment to the edges. (a) 2R ~ 300nm, (b) ~ 950 jim, (c-d)
..................
Transition region: For width - 2 pm, the nanotubes position at some intermediate r/R (O<r/R<1)
and lack consistent parallel alignment (2R ~2 pm). (e-f) Edge deposition: For width > 3 pm all
nanotubes deposit at the edges of the polar SAM (r/R=1) with a high degree of alignment parallel
to the SAM edges (e) 2R- 3.1 pm (f)5.5 ptm.
1.2
I
1
0.8
Centerline
deposition
|
e~
0.6
Edge
depo sition
I
I
Transitionni
I..
region
I
*: I
Ig
:*-~
eIe3
OA -
" 3500
i
Aek
0
0
1000
.
0
..-
0.2 -
I.
1500
2000
2500
3000
3500
Diameter (2R) (pm)
/
600
:400
CO
200
0
c)
I
i-100
Z 80
60
40
0
4t 20
0
0N
,
o 01
O/R
Qo
r/ 0*
r/R
Figure 4.3: Statistics of positioning of nanotubes as a function of diameter of droplet for
1160 nanotubes from 70 AFM images. (a) Bubble chart where the size of each bubble is
proportional to the number of overlapping data points. For width less than 1pm 95% of the
nanotubes deposit within ±5% of r/R=O (centerline of the polar SAM) as represented in the
histogram in (b). For a polar SAM width ;> 3pm most of the nanotubes deposit at the edges of the
polar SAM as represented in the histogram (c).
4.3 Hydrodynamics in Nanometer Sized Cylindrical Droplet
A switching in nanotube positioning from edge to centerline is observed with change in
cylindrical droplet diameter form micrometer to nanometer regime. An approximate model for
the mechanism of cylindrical droplet evaporation is developed in this thesis to better understand
the role of droplet diameter in positioning of the trapped nanotubes. For this analysis of the realtime video microscopy of the formation and evaporation of micron sized cylindrical droplets (2R
~ 3.5 pim) was done. For micron sized droplets it was noted that (1) their evaporative mode is
pinned contact area (i.e. 2R remains constant), (2) evaporation terminates as the ends along the
length of the cylindrical droplet contract rapidly and (3) the final contact angle does not decrease
to zero (or even to the receding contact angle (,)
as the contact along the width remains pinned
throughout). A schematic of the mechanism under these conditions is presented in Figure 4.4.
The fast contraction along the length is attributed to the high evaporative flux at these ends. This
evaporative flux is equated to the rate at which the contraction occurs (or the velocity of the
moving ends) and was found to be approximately 1000 times higher than the normal evaporative
flux.
- .. -
.....
...
...
...
a)
R=R 0 _
R
R
R=Ro
R=R0
0 >=R
>0 R
Pinned contat
mnnea contact
b)
R=R 0
Of >O R
0 > 0R
R=R 0
Pinned contact
=OR
R< Ro
0
=0 R
Mode switching to depinned contact
C)
6C =2W
0.2.
0.2
-30?1
0
0.2
0.4
0.10
A.6
0.8
1
Mode
0
0.2
OA
r/R
0.6
0.8
switching
1
10.05
0
0.2
0.4
r/R
0.6
08
1
Figure 4.4: Cylindrical droplet diameter governs the mechanism of evaporation. (a) Micron
sized droplets (2R > 3 pm) start evaporating with pinned contact area and decreasing contact
angle (0, -+ Of). This drying process establishes an outward radial flow field within the droplet.
The evaporation process terminates as the ends along the length of the cylindrical droplets
contracts rapidly due to rapid drying at free ends. Termination takes place before the contact
angle drops below the receding contact angle (OR ,Of >OR). This maintains pinned contact along
the width (2R = constant) throughout the evaporation. (b) Nanometer and sub micron sized
(narrow) droplets (2R < 1p[m) start evaporating like large droplets with pinned contact along the
dO
1
width. The contact angle rapidly falls down ( d" oc -)
to receding contact angle 0 Rand is
dt
R
maintained constant thereafter. At this point the evaporation mode switches to depinned contact
(shrinking) resulting in a radially inward flow field. (c) Velocity vector field representation in the
nanometer or sub micron sized droplets: initially evaporating with mode 1 which switches to
mode 2 after contact angle reaches 0R .
Degan et al. 80 solved for evaporative flux J(r) of an evaporating spherical droplet at r distance
from the center and showed
3.6
J(r)oc (R-r)- where A= (r-20)/(2; -20,)
Here R is the radius and OC the contact angle of the spherical droplet.
For hydrophilic substrates (0 < 0, < / 2) we expect A to be non-negative and J(r) very large
near the contact line (r->R). The ends along the length of a cylindrical droplet can be
approximated by edge of hemi-spherical droplet and hence, here a comparatively high value of
evaporative flux is expected according to equation 3.6. This is also supported by our calculations
of J(r) from video microscopy of droplet evaporation that yield a value Js (flux from the open
ends along the length) 1000 times more than normal evaporative flux JO (the flux from the
droplet curvilinear surface).
Petsi and Burganos88 '9' derived the rate of decrease of the contact angle for cylindrical
droplets evaporating with pinned contact in equation 3.4. This proposes that the rate of decrease
in contact angle is inversely proportional to the radius of the droplet (
dt
-). Hence, a
R
cc
faster decrease in contact angle of nanometer and submicron sized droplets is expected compared
to micron sized droplets (Figure 4.5). This mechanism gives a better understanding of the
centerline and edge deposition. It appears that the nanometer and sub micron sized droplets start
their evaporation with pinned contact (decreasing contact angle) like micron sized droplets
(Figure 4.4b). A rapid fall in the contact angle causes it to quickly attain the receding contact
....
......
1.11
1- ....
....................
................
......
.
..................................
......
..
. . ........
...
...
....
........
....
..
..
....
- -
angle value (0,) and thereafter the evaporation mode switches to a depinned contact (Fig. 4.5b).
This mode switching consequently reverses the flow inside the droplet from edge-directed to
centerline-directed where it carries and positions the SWNT. This mode switching is not seen for
the micron sized droplets because of a comparatively slower decrease in the contact angle. And
before the contact angle can reduce to the value of 6 , the evaporation along the length causes
the droplet to evaporate completely. To explain the transition region, it follows that the contact
angle is able to drop down to the receding contact angle value resulting in evaporation mode
switching and flow reversal. However, the second mode (depinned contact) does not survive for
sufficient time as contraction along the length causes termination of the drying process. During
this short time for survival of the second mode of evaporation the SWNT is unable to reach the
centerline resulting in their deposition at an intermediate position.
O030
0030
25
mode 1
D= 4pm
D= 0.8pm
25
mode 1
20
W20
15
00 > OR
10
2
15mode
5-
00>
0 100
Of > O
5
0
0.2
0.4 0.6 0.8
time (sec)
1
1.2 1.4
0
R
mode switchi
0.2 0.4 0.6 0.8
R
1
1.2 1.4
time (sec)
Figure 4.5: Variation in the contact angle over time due to evaporation for cylindrical
droplets of different sizes. Blue shows the simulated and red shows the expected behavior. (a)
4 [tm diameter droplet: The change in contact angle for micron sized (wide) droplets is small and
final contact angle does not reach6R . The only mode of evaporation is pinned contact and
contraction along the length leads to termination of evaporation. (as seen in the movie). (b) 0.8
ptm diameter droplet: The contact angle decreases rapidly for nanometer and submicron sized
(narrow) droplets. Blue line represents the change in contact angle if the mode of evaporation
was pinned contact throughout (The final contact angle would go to zero unlike for the wider
droplets in (a)). However,OR is always greater than zero and hence mode switching takes place
at a non-zero contact angle.
4.4 Design of Single SWNT Devices
This thesis shows that the evaporating cylindrical droplets can be used to position, align,
deposit and electrically connect individual (unbundled) SWNT over pre-patterned Au electrodes.
Cylindrical droplets were created and evaporated over 600 nm channel electrodes resulting in
individual nanotubes spanning the gap. Electrode pairs 20 ptm wide with SAM pattern (as
discussed above) resulting in -3.5 ptm diameter patterned cylindrical droplets (-2.5 ptm pitch)
typically show two or more individual SWNT spanning the electrode gaps (Figure 4.6a) at 6
mg/L SWNT solution concentration. AFM section analysis confirms that the connected SWNT
are indeed individual and isolated. Remarkably, with no additional processing (i.e. annealing,
subsequent lithography, metal sputtering, selective etching or breakdown of metallic nanotubes)
SWNT were electrically characterized and readily identified as having either metallic or semiconducting behavior. While contact resistance remains large due to the SAM interface between
the SWNT and gold, three types of electrical responses from current (Id) versus gate voltage (Vg)
characteristics are observed: one with significant Vg-Id modulation and high on-off ratio (-100)
(Figure 4.6b) indicating only semiconducting (SC) nanotubes, second type with negligible or no
Vg-I modulation (Figure 4.6c) indicating only metallic nanotubes, and a third with much lower
on-off ratio (-2-10) indicative of both SC and metallic (Figure 4.6d). The trapping of single
SWNT across the gap significantly reduced the number of the third type. It can be anticipate that
similar methods will lead to rapid and high throughput electrical screening of a given SWNT
74
....
.......
.
.......
.....
.
. .. .............
:::::
....
------
ensemble, enabling a clear determination of the number of semi-conductors and metals in a given
formulation. The high accuracy in parallel alignment and placement of this technique looks
promising for production of devices such as field effect transistors (FETs) and interconnects on a
large scale from solution-based SWNT.
(a)
(b)
() 2
r.
o~se
Ak24-
-O0AS
10
V.
-
20
Iv
j
.x
-30
-10
19
VP(VOts)
30
-30
-10
10
.I.-3-.
0.25
X1vpolts)
Figure 4.6: Fabrication of single nanotube devices. Demonstration that the technique can
align, place and electrically contact SWNT over pre-patterned Au electrodes forming SWNT
devices with individual and parallel SWNT bridging electrode gaps. Microhydrodynamic forces
in a micron sized cylindrical droplet have been utilized to align and place individual SWNT over
patterned electrodes from solution, forming electrically connected nanotubes without subsequent
processing. Au electrodes are 20 pm in width with 600 nm channel length. (a) AFM image
(amplitude) showing parallel SWNT bridging the electrode gap on almost all polar SAM edges.
AFM section analysis in the inset demonstrates height of a single SWNT (- nm). (b) The
contacted SWNT on such devices show electrical conductance, with measurable Id-Vd-Vg
characteristics without any additional processing such as annealing or selective breakdown of
metallic. Contacted SC (on/off ratio >100) (c) metallic SWNT (no variation in Id with Vg) and
(d) both SC and metallic (on/off ratio ~2) are observed from the electrical testing.
4.5 Conclusions
In summary, the size of evaporating cylindrical droplets controls their mode of
evaporation, and hence their internal flow pattern can be directly utilized to align and position
nanoparticles with nanometer precision. Placement is along the centerline for narrow
(nanometer- and submicrometer-sized) droplet and along the edges for wider (micrometer-sized)
droplets, due to the internal flow patterns directed inward and outward, respectively. The
proposed model for the evaporation-mode switching successfully explains the transition of
placement of SWNTs with changing droplet size. As an application, the process was used for the
top-down parallel alignment and placement of individual SWNT from solution on electrodes.
SWNT bridging up the electrode gap are free from nanotube-nanotube junction/crossing and
bundles. Hence, such a parallel and accurate self-assembling system may present a promising
alternative to conventional manufacturing of devices nanoscale components.
Chapter 5 Structure-Reactivity Relationships for Graphene Nanoribbons
5.1 Motivation and Approach
There
are various
(GNRs)
types of Graphene Nanoribbons
defined by
the
crystallographic arrangement of the carbon atoms along the ribbon edges 26 as discussed in
chapter 1. Depending on the type of ribbon they are either metallic or semiconducting with band
gap inversely proportional to the ribbon width 2 1,3 2. The semiconducting and metallic ribbons are
potential candidate materials for transistor92 and interconnect
93
applications, respectively.
However, the diverse electronic properties of GNRs impose a requirement to achieve nanometer
precision control in their on-chip fabrication or separation of ribbons in the solution phase
32
synthesis. Current fabrication techniques have not achieved this level of precision yet .
Therefore, to achieve these goals detailed research on manipulating the GNR structure and edges
is highly desired.
The motivation for constructing structure-reactivity relationships for GNR in this thesis
comes from the desire to selectively modify just one type in a mixture or to separate and sort the
various classes for specific electronic applications. E-beam lithography of the graphene sheet has
been successfully used to fabricate GNRs of widths ~10-100nm but it is a low throughput
technique and has difficulties in reaching widths of a few nanometers, and smooth edges.
Thus
arises the need for solution processed GNRs. Xiaolin Li, et al. recently produced solution phase
GNRs made by exfoliation of expandable-graphite. 2 8 Yet, pristine GNRs in solution, like SWNT,
have not been fabricated and there is currently an intense ongoing effort in this direction. Once a
vial containing millions of individually dispersed GNRs is produced, there will be an immediate
need to separate the GNRs according to their widths and crystallographic orientations. This is
due to the substantial variation in electronic properties of different GNRs. The GNR structure
reactivity results should provide an aid to developing selective electron transfer chemistries for
GNR, methods to separate and sort ribbons by electronic structure or methods to preferentially
modify GNR of different ribbon widths and orientations of carbon atoms.
Each carbon in GNR lattice is sP2 hybridized and the forth valence electron of carbon is
present as a n (delocalized) electron that can be transferred to an electron withdrawing group.
The electron transfer will be followed formation of covalent bond and transitioning the sP2
carbon into sp3. The rate of electron transfer from the GNR to the electron withdrawing group
should directly depend on the electronic band structure of the GNR. In this chapter the structurereactivity relationships for electron-transfer chemistries of graphene nanoribbons with diazonium
salt have been derived. These relationships are represented as relative reaction rate constants
calculated by considering different electronic structure approximations of GNRs and the
Gerischer-Marcus (GM) and Marcus theories of electron transfer. To do these calculations first
the electronic density of states (DOS) are calculated for the one dimensional GNR from their
electronic band structure. The rate constants are then determined by the energy overlap of the
DOS of GNR and vacant oxidation states of the electron withdrawing species. This thesis
explicitly considers most of the available band structure models for GNRs to understand how
they cause perturbations in their structure influence reactivity. Ab initio calculations provide the
highest accuracy but are not scalable to a complete family of ribbons to predict trends. The tight
..11
- .,....I..- - I.......
------------...- '-........
-;, 1-1-- I -
- .: 1- -
..- -
-
....-
' ---- -
::::::
;::::::::::
::::::
:::::::::::::::::::::::
-::: : :=::::::::
:::::::
:::zz;
.;wz..z:::::
: ::
binding approximation is known to give an accurate description of the low energy properties of
graphene.
Accuracy has been observed to improve by considering long range interactions, i.e.,
stepping beyond nearest neighbor interactions. By considering third-nearest neighbor interactions
for graphene, the accuracy of the band structure competes with first principles calculations, as
has been shown by Reich et al. recently 2 3 . For these reasons, explicitly several different
approaches to represent the electronic structure of GNR are considered in this thesis.
F4 B~
N-
X
electron transfer
Figure 5.1: Schematic of electronic transfer chemistry of armchair GNR.
5.2 Electron Transfer Theories
The two electron transfer theories used in this thesis work are Marcus and GerischerMarcus. Marcus theory yields rate constants for electron transfer between donor and acceptor
molecules as a function of (a) free energy of the electron-transfer step (AGO)
and (b) the
reorganization energy (A) required to alter the atomic configurations of the reacting species so
that isoenergetic electron transfer can take place in accordance with the Franck-Condon
79
principle. Gerischer-Marcus theory provides rate constants based on the convolution of the
densities of states (DOS) of the acceptor and donor species.
5.2.1 Marcus Theory
Marcus theory94-9s estimates the rate constant for an outer-sphere electron-transfer
reaction (kET
va reirK) by equation 5.1, where v, is the attempt frequency, reI is the tunneling
factor, and rn the nuclear factor. Tunneling can be neglected (re, ~1) if the electronwithdrawing molecule is physically close to the GNR during electron transfer, i.e., the reaction is
assumed to be adiabatic. The nuclear factor is expressed in terms of the reorganization energy
(A) and the free energy94 of the electron-transfer reaction AG'NR
.
These assumptions simplify
kET to equation 5.2.
kET
k ET
5.1
Vn Kel Kn
±(A
+
AGGNR
,n eXp - (4kT5.2
4 AkT
52
AGONR is also the electrochemical driving force and is determined by the Fermi level
(E GNR) and the band gap (EGNR) of the GNR (equation 5.3). The Fermi level (EF) is given by
equation 5.4, where WF is the work function.
EGNR
EAGGNR)
EF
=
E
NR -2
5.3
-RED)
=-WF
5.4
Equation 5.4 assumes vacuum to be at zero energy level. Yan et al. reported that all
zigzag and armchair GNRs (semiconducting or metallic) are found to have almost the same work
function (WF) of 4.58 eV, which is slightly lower than the WF of graphene (4.66 eV)9 6 . On the
other hand, in the case of SWNT, the WF varies with diameter. 97 This has been attributed to the
curvature effect that induces surface dipoles and makes their work functions diameter-dependent.
With these assumptions, EFNR=-4 .58 eV is obtained. In this work p-nitrobenzene diazonium salt
is used as a model electron acceptor. It has a half-wave potential of 0.45 eV98 corresponding to a
value of -5.15 eV for E'?. If E'NR is fixed at the zero energy level of GNR, then the redox level
of the acceptor relative to it is -0.57 eV. For these calculations an approximate value of -0.6 eV
is used for the redox level.
5.2.2 Gerischer-Marcus Theory
According to the more detailed Gerischer-Marcus theory 9 , charge transfer depends on
the electronic density of states (DOS) of the reacting species and is not restricted to their Fermi
81
levels only. This is very important for one dimensional structures like nanotubes and GNRs that
posses van Hove singularities as a typical feature of their DOS. GM theory was previously used
by Heller et al. for graphene, metallic SWNTs and semiconducting (SC) SWNTs to describe the
kinetics of electrochemical charge transfer to SWNT electrodes. 00-'ui Recently, this model was
used to estimate the reaction rates for electron acceptor reagents and SWNTs. 102 The model is
summarized in equation 5.5-5.6. The electron-transfer reaction rate
(kET)
is given by equation
5.5. W,(A, E) is the distribution of the unoccupied redox states of the electron acceptor in
solution given by equation 5.6,
DOSGNR
is the electronic density of states of GNR 99 andso, is
the proportionality function.
GNR
EF
kNR _
n
W,,(2, E) =
ox ((E)DOSGNR
1
-4rAkT
(
exp -
(E)Wox (A,E) dE
(E
- E
x
''j")
5.5
)) 2
5.6
4 AkT,
The DOS for GNRs are calculated by the general expression provided by White and
Mintmire22 for a one dimensional system as discussed in chapter 1. Figure 5.3b shows the energy
overlap of the electronic states of GNR (DOS) (Figure 5.3a) and vacant oxidation states of the
electron withdrawing species (Wox) for the armchair GNR. This overlap directly determines the
electron transfer rate from GNR to the electron-withdrawing group. Assuming sox is independent
of energy and Eo, and v, are same for all GNRs, they cancel out in calculations for the relative
rate constants. The reorganization energy A lies in between1 0 3 0.5 and 1 eV. For SWNT selective
chemistry A was obtained by fitting the model to experimental data. A value of 0.54 eV for
Marcus theory and 0.71 eV for GM theory was obtained. 10 2 Similar fitting cannot be done yet for
GNRs due to the lack of equivalent experimental data. Hence, the values of A are approximated
with those estimated previously for SWNT.io2
5.3 Electronic Band Structure of GNR
Electronic band structure of GNR family has been obtained from tight binding and first
principle calculations. A nearest neighbor tight-binding electronic dispersion band calculation
within the HUckel approximation has been used by Nakada and co-workers 26 to predict zigzag
and armchair GNR electronic band structure. These calculations predicted three different
armchair families, N=3p, 3p+1 and 3p+2, where p is an integer. Family 3p+2 is predicted to be
all-metallic and the rest all semiconducting with a band gap decreasing with ribbon width (Figure
5.2a, b). These calculations also predict a special center band for zigzag GNR consisting of the
highest valence and lowest conduction bands. This band is almost flat within the region
2ff/3
k
,
Z, where the bands sit in the very vicinity of the Fermi level (Figure 5.2c). The y
component of the wave vector (ky) is the component along the length of ribbons. This special
band is directly attributed to the charge density distribution at the ribbon edges where they are
localized on the zigzag edge sites. The flatness of the center band increases with ribbon width
(Figure 5.2d). The dispersion relation close to the ky=n (flat band) can be approximated by
equation 5.7 where Dk is given by equation 5.8 and t is the hopping matrix element.10 4
83
E(k)= 2tNDN-'(1 -
Dk
2
Dk =
2 cos(ky / 2)
Interestingly, there is no such charge density localization along the armchair edges.
a) 2
3p+2
=3p
0.6
4
5
-6
--- 7
A
3p+1
4~~~mi
0.3
-1
n
-2
0 10 20 30 40 50
c) 3
2
N=6
0.5
0
-0.5
0.2
0.4
0.6
First
band
0.5
0.8
e)
3p+2
m 3p
*
A
-- 5
U/
--
6
--
c3
7
"
-o
A
A
O.5
-1C
A 3p+1
A
1
M
-
AA
A
A
0
-201
02
Q3
04
05
0
10
20
30
40
50
N
Figure 5.2: Calculated band structure (E(ky)) of armchair and zigzag GNRs. (a-d) Nearestneighbor TB band calculation within the Hickel approximation for (a) armchair having (b) band
gap (c) zigzag ribbons (d) First band of zigzag showing the increase in its flatness with increase
in width. (e-f) TB band structure and band gap including up to third-nearest neighbor interactions
and edge distortion for armchair.
First principle GNR band structure calculations have also seen a refinement over the past
few years. These calculations have been done by (1) a first principles many-electron Green's
function approach within the GW approximation35 (2) using local (spin) density approximation
[L(S)DA]. 34 They describe all GNRs as semiconductors with a direct band gap. According to
these calculations the band gaps of armchair GNR originate from quantum confinement and edge
effects. In the case of zigzag GNRs, the band gap arises from a staggered sublattice potential due
to spin-ordered states at the edges. Both predict size-dependent band gaps for armchair and
zigzag ribbons but the gaps are significantly higher according to the GW calculations.3 s
On the inclusion of third-nearest neighbors, the tight binding (TB) model quite accurately
23
describes the first principles band structure for graphene over the entire Brillouin zone. On
similar lines, Gunlycke and White36 recently proposed a tight binding model for armchair GNRs
(Figure 5.2e) that includes up to third-nearest neighbor carbon-carbon interactions and edge
distortion. The third-nearest neighbor TB band structures of armchair ribbons are in good
agreement with the first principle L(S)DA results. This model, like others divides armchair
ribbons
into
three
families
(N=3p+l,
3p,
3p+2
where
p
is
0 <E 3p2 <E 3p <E 3p1 (Figure 5.2f), where Eg is the band gap of GNR.
an
integer)
with
5.4 Structure Reactivity for Armchair GNR
In general, an increase in the armchair GNR reactivity is observed with increase in N for
all three families (N=3p+l, 3p, 3p+2) by various calculations using different electron transfer
theories and ribbon band structure models as summarized in Table TI and Figure 5.3, 5.4 and
5.5. However, this increase in reactivity slows down for higher N or remains almost unchanged
for N > 30 (or 40, value of N depends on the band structure models involved in calculations).
Most of the electronic structure approximations including third-nearest neighbor TB,
first-nearest neighbor TB within Huckel approximation, first principles using L(S)DA, and first
principle Green's function within the GW approximation (GF-GW) are used in conjunction with
either electron transfer theory (Marcus or GM theory). These models predict that the 3p+2 family
has the highest reactivity, and the ordering of overall reactivity is 3p+2>3p>3p+l. However, the
magnitude of the reactivity difference in armchair families depends on the band structure and
electron transfer models involved in the calculations. It should be noted that the difference in
electron transfer rate constants predicted from first-neighbor TB Huckel model predicts little
difference between the 3p and 3p+1 families. However, the difference in rate constants predicted
by first principles (L(S)DA and GF-GW) and third-neighbor TB between all three families
appears sufficiently great that a dispersion containing limited ribbon width should be easily
separated by selective reaction into three different families. All the electron transfer rate
constants for GNRs are normalized to an infinite width ribbon. The N=83 armchair GNR is
selected as the infinite ribbon for our calculations of relative electron transfer rate for both
armchair and zigzag ribbons. In the case of GM and Marcus theory predictions all the electron
transfer rates are normalized w.r.t to the rate of N=83 armchair ribbon (TB with first-nearest
87
neighbor interaction) obtained from the GM and Marcus theory respectively. Interestingly, the
electron transfer rates for wide armchair and zigzag ribbons approach a common value when
estimated using the TB calculations, and the narrow zigzag ribbons are the most reactive.
I0
'10
1
-6
-24
0.6
Oxidation
-
states
10
20.2
D5
0
-0.2
110
10
-
5
-- 7
-0.6
5
-1
-0.5
0. 5
0
E(eV)
1
2
1
0
Diaz W0 (A, E)
1010
GNR DOS
c)
1.5
*,
1
+
+,n
0.5
E.
0
:0.75
z 0.5
0.25
0
A
AA
ALA
i~A
0
,
-
25
50
N
75
100
+
3p+2
A 3p+1
A
+E -
0
25
50
N
75 100
Figure 5.3: Electronic DOS and relative rate constants for armchair GNR with TB band
structure including third-nearest neighbor interactions and edge distortion. (a) Density of
states (DOS). (b) Energy overlap of vacant oxidation states of electron withdrawing group (pnitrobenzene diazonium) and DOS of GNR (N=6,24). (c) Gerischer-Marcus relative rate
constant. (d) Marcus relative rate constant.
In the case where armchair GNR band structure is calculated by TB with third-nearest
neighbor interactions and edge distortion, GM theory (Figure 5.3c) predicts reactivity ratios as
high as 3000 between wide and some narrow ribbons (~ k4 6/kio).
Moreover, when N is
decreased further, N=7 ribbon of the (3p+l) family is found to have zero reactivity. From these
calculations it is concluded that the small width ribbons, which are the most interesting from the
electronic and electro-optical perspective, can be most easily sorted for armchair families.
According to this band structure and GM electron transfer model, the reactivity difference
between the three armchair GNR families for all N is significantly great as to enable sorting. It is
observed from this set of calculations, for example, that the N=1 1 (3p+2 family) is almost 100
times more reactive than N=13 (3p+l), and 5 times more that N=12 (3p). Applying the less
detailed Marcus theory to the 3 rd NN TB representation (Figure 5.3d) yields similar results, with
reactivity trends across N and across the three families preserved. One notable exception is the
loss of the maximum in reactivity for the 3p+2 family. This phenomena arises from the higher
DOS in the tail of the van Hove singularities in small N, a feature not captured in the simpler
Marcus theory. This maximum is not observed for 3p and 3p+l families due to steep fall of band
gap for small N values within these families. A decrease in band gap increases the overlap of the
DOS of GNR and W of the electron-withdrawing species. Hence, the electron transfer rates for
3p and 3p+l increase monotonically by overcoming the opposite tail effect of the van Hove
singularities for small N.
An important exception is the case of TB band structure including first-nearest neighbor
interactions within Htckel approximation for armchair GNR. The reactivity trend of armchair
GNRs calculated in this manner is found to be quite different from other band structure models.
According to the GM theory, the reactivity of 3p+2 family decreases with an increase in N
(Figure 5.4a). For the 3p+2 family, N=8 is ~ 2 times more reactive than N=83 (wide ribbon).
This decrease can be attributed to the zero band gap (Figure 5.2b) of these ribbons and the higher
DOS in the tail of van Hove singularities of small N. For the 3p and 3p+1 semiconducting ribbon
families, reactivity increases with an increase in N but the variation in reactivity is very small,
especially for N>12. Marcus theory also predicts similar results for the 3p and 3p+l families
with slightly greater differences in reactivity among narrow and wider ribbons (Figure 5.4b). For
3p+2, the reactivity trend predicted by the simpler Marcus is very different to that predicted by
GM, illustrating the importance of integrating over all of the electron density when data is
available. The reactivity is same for all members of this family due to their zero band gaps. Both
GM and Marcus theories predict that the electron transfer chemistry is less selective for graphene
ribbons described by nearest neighbor TB band structure than in the case when the band structure
is calculated by TB with third-nearest neighbor interactions and edge distortion underscoring that
these factors play a critical role in GNR chemistry. The primary reason for the loss of selectivity
in this case is the diminished band gap variation for TB nearest neighbor band structures over
third-nearest neighbor TB band structures.
In the case of first principles representations of the electronic structure, only Marcus
theory can be applied because of the computational cost of producing the electronic band
structure of an entire family of ribbons. Where information on how the electronic band gap
scales with ribbon width is available in the literature, electron transfer rate constants can be
calculated if one assumes that transfer occurs primarily at the band edge or at a DOS singularity,
which is approximately true for GNR 105 . For first principle [L(S)DA] calculations using Marcus
......
.....
(Fig. 5a), the reactivity trend is qualitatively similar to that of GM for 3 rd NN TB with increasing
reactivity with increasing N. Interestingly, narrow ribbons in this depiction including specifically
N=3,4 and 7 have almost zero relative reactivity.
3
.
1 .. """**
0.75
2-
z
0.5
1-
,.
+3p+2
S3p
3p+1
0.25
0
0
0
25
50
75
100
0
25
50 75 100
Figure 5.4: Relative rate constants for armchair GNR with band structure from nearest
neighbor TB calculation within the Huckel approximation. (a) Gerischer-Marcus relative rate
constant. (b) Marcus relative rate constant.
...........
............................................
b)
1.00
0.75
1.004
0.50 -
+
0.25 -
0.6
3pb
30.4
+
=
so=
A
*
A
A
~~
3p+ 1
0.2-
* ,EAA
0.00 -_M1AA
rA I
0
. . ......
....
. .....
10
20
A_-0
--
30 40
0
15
30
45
N
Figure 5.5: Relative rate constants for armchair GNR obtained from Marcus theory. GNR
band gap is obtained from: (a) First principles using [L(S)DA]. (b) First principles Green's
function approach within the GW approximation.
Marcus electron transfer rates for the first principle GF-GW (Figure 5.5b), if accurate,
appear to be most promising for a selective chemistry based on N. Ribbons with N=4,7, 10 and
13 (3p+1), N=6,9 and 12 (3p) and N=5 (3p+2) are predicted to have almost zero relative
reactivity. The large band gap of these narrow ribbons makes the electrochemical driving force
for the electron transfer almost negligible. This huge variation of band gap for GNR of different
widths creates a significantly large variation in their reactivities also. In general, for armchair
GNR it is noted that the third-nearest neighbor tight binding approximation and both first
principles have similar overall trends of structure reactivity, with reactivity increasing with N
with few exceptions. The activity between armchair families is also consistent across all three
theories with 3p+2 > 3p > 3p+l. From the perspective of selective chemistry and separation,
these results are promising.
5.5 Structure Reactivity for Zigzag GNR
The reactivity trend is opposite for zigzag ribbons as compared to armchair ribbons for
the most detailed GM theory applied to first-nearest neighbor TB calculation within the Htickel
approximation. A decrease in reactivity with an increase in width is predicted by these models.
Additionally these models estimate that narrow zigzag ribbons are more reactive than armchair
ribbons of similar width or more. However, both first principles calculations using L(S)DA and
GF-GW approximations predict increasing reactivity with N, but for these, only Marcus theory
based calculations were possible. The edges of zigzag GNR determine the special center band.
However, due to the complicated shape of this center band, Marcus theory is unable to accurately
account for it and hence the contribution of edges to reactivity is not taken fully into account.
Table Ti gives a summary of the reactivity trend of GNRs estimated by various electron transfer
and band structure models.
The full band structure for a given zigzag GNR is available from a nearest neighbor tightbinding band calculation within the Hickel approximation, so we apply this structure to both
GM and Marcus electron transfer theories. This model predicts all zigzag GNRs to be metallic.
However, these results are contradicted by the recent results from first principle calculations that
propose all the zigzag ribbons as SC. GM theory based on the GNR electronic DOS that are
directly related to the band structure calculate a decrease in the ribbons reactivity with increase
in their width (Figure 5.6b). The energy overlap of the electronic states of GNR (DOS) and
vacant oxidation states of the electron withdrawing species (W0,) directly determines these
electron transfer rates (Figure 5.6a). From these calculations, N=5 is approximately 3 times more
:: 86_ :::::_:::-.
.......
-::,
.............
_ __ - _ :...................
..
.........................................
-
reactive than N=20. A major contribution to the reactivity of the zigzag GNR is made by the
center band that arises due to the localization of charge density at the zigzag edge sites. It is this
enhanced role of edges that makes the narrow ribbons more reactive than the wider ones. This
structure-reactivity relationship for zigzag ribbons appears promising for applying a reactive
handle selectively to separate them or selectively modify their electronic structure.
-
6
- 32
-- Oxidation
states
).6
A
A
A A
0
2
1
0
Diaz W (2,E)
101
5
10
N
15 20
GNR DOS
x 10
4
c~0.4
A
A
A
0.8
9
-o1
0.3
0.2
0.10
0.6
42
0.4
A A
0.
20
10
30
6
8
10
0
12
N
Figure 5.6: Relative rate constants for zigzag GNR. (a) Energy overlap of vacant oxidation
states of electron withdrawing group and DOS of zigzag GNR (N=6). (b) Relative rate constant
obtained from Gerischer-Marcus thoery for first-nearest neighbor TB within the Hfickel
approximation band structure of GNR. (c-d) Marcus relative rate constant for GNR band gap
obtained from (c) First principles using [L(S)DA]. (d) First principles Green's function approach
within the GW approximation.
The structure of zigzag GNRs are too complex for Marcus theory to be applicable. The
edge state along the zigzag edge creates reactive electrons of the highest chemical potential for
all of the GNR species. It is not clear how to account for this complex center band by Marcus
theory. GM theory, which can only be applied to the nearest neighbor tight-binding band
calculation within the Hickel approximation for the systems considered in this work, is more
accurate for the calculation of electron transfer rates in this case. However, recent first principle
calculations contradict the metallic behavior predicted from TB formalisms and instead assert
that all members of the zigzag GNR class are semi-conducting with a band gap that decreases
with increasing N. To assess how this impacts the predicted reactivity, we applied Marcus theory
to band gaps correlated from the first principle calculations. The band gap decreases with
increase in N. According to Marcus theory the reactivity increases with an increase in N. As per
[L(S)DA] calculated band gaps there is a small difference in the reactivity (Figure 5.6c). For
example N=4 is only 2 times more reactive than N=32. For the GF-GW approximation (Figure
5.6d) the reactivity of narrow ribbons is significantly smaller than others due to the large band
gaps that result (N=6, Eg - 1.36). For example N=6 is 100 times less reactive than N=12. These
calculations predict a very high selectivity for narrow zigzag ribbons.
Electron transfer rate calculations generally support the hypothesis of chemical reactivity
variation with ribbon width. The complex shape of the center band makes GM theory more
reliable over Marcus for estimating the electron transfer rates for the zigzag ribbons. If the TB
band calculations are assumed to be more accurate then ribbon reactivity is predicted to decrease
with increasing ribbon width potentially providing a chemical handle to separate them.
5.6 Summary ofArmchair and Zigzag Reactivity
Electron
transfer theory
GM
Armchair
Electronic
structure basis
third-nearest
neighbor TB
Armchair
third-nearest
Marcus
GNR Type
Electron transfer
reactivity trend
Increase with increase in N
except for 3p+2 family for
N> 14.
Armchair
first-nearest
neighbor TB
(Hickel)
GM
Armchair
first-nearest
neighbor TB
(Hiekel)
first principle
L(S)DA
Marcus
first principle
GF-GW
Marcus
Armchair
.
Armchair
Increase with N for all
families.
neighbor TB
Marcus
Increase with N except for
3p+2 family for which rate
decreases for small N. For
N>23 rates are almost
same for all ribbons.
Increase with N except for
3p+2 family for which
rates remain unchanged
due to zero band gap.
Increase with N for all
families.
Increase with N for all
families. Significantly
large variation in reactivity
due to large band gap SC.
Zigzag
Zigzag
nearest neighbor
TB (HGckel)
first principle
GM
Decrease with N.
Marcus
Increase with N.
Marcus
Increase with N.
L(S)DA
Zigzag
first principle
GF-GW
Table 1: Summary of Reactivity Trends Predicted for Various Graphene Nanoribbon
Types, Electronic Structure Approximations and Electron Transfer Theories.
Reactivity of GNR directly depends on the ribbon width and the orientation of carbon
atoms at their edges. Relative rate constants for the more accurate GM electron transfer theory
and tight binding approximations predict that armchair and zigzag GNR have opposite trends in
reactivity with the former increasing with width and the latter decreasing. In Zigzag ribbons the
major reactivity contribution comes from edge states. Zigzag ribbons of small width are then
predicted to be the most reactive among all GNR. This reactivity trend for zigzag GNR is
reversed, however when recent first principles calculations are utilized with Marcus theory that
predicts the presence of large semiconducting gaps for narrow ribbons with correspondingly low
reactivity. These results should provide an aid to developing selective electron transfer
chemistries for GNR, methods to separate and sort ribbons by electronic structure or methods to
preferentially modify GNR of different ribbon widths and orientation of carbon atoms.
Chapter 6 Chemical Manipulation of Graphene: Structure Reactivity of
Graphene
6.1 Motivation and Approach
Theoretically, graphene has been studied for over sixty years 106-107 and widely used to
describe the electronic and mechanical properties of other carbon nanomaterials including
SWNT 2- . Recently, significant progress has been made to fabricate graphene devices i.e. fieldeffect transistors7' , and to understand their electronic properties''' 10. However, many important
issues yet need to be addressed to fully understand and utilize the outstanding properties of this
material. The edges of graphene ribbons are thought to significantly influence their electronic
and chemical properties, as discussed theoretically 15 in the previous chapter. The non-uniformity
of graphene edges and potential for dangling bonds are also issues requiring special attention16- 1.
Moreover, techniques to engineer graphene need to be developed to integrate these building
blocks into more complicated structures. In this thesis, chemical manipulation is explored as a
way to address some of the above issues. The chemical manipulation study of graphene in this
thesis includes a detailed structure-reactivity study of graphene. Another important application of
chemical manipulation of graphene may be for designing graphene based three dimensional
structures i.e graphene super lattices. The attached chemical moieties can enable linking multilayers of single graphene sheets in direction perpendicular to the sheet plane to make graphene
super lattices. However, there remains a dearth of experimental data on the chemical reactivity of
graphene and its multi-layers. Structure reactivity of graphene in this thesis is a detailed study of
the on-chip reactivity of pristine single, bi- and multi- layer graphene and also edges of single
... ............................
graphene sheets towards electron transfer chemistries with 4-nitrobenzene diazonium
tetrafluoroborate.
Pristine single and multi- layer graphene sheets are deposited by mechanical exfoliation
using scotch tape method on silicon wafers with 300nm thermal silicon dioxide. On chip
chemistry is performed in aqueous solution containing aryl diazonium reactants over the
substrate, allowing only the exposed top surface and the edges of the graphene sheet to react and
undergo electron transfer chemistry, forming a covalently bonded phenyl substituent. The salt is
water soluble nitrobenzene diazonium salt (4-nitrobenzene diazonium tetrafluoroborate). Figure
6.1 shows the schematics of the electron transfer chemistry. The chemical functionalization of
graphene in this work is probed by Raman, Auger and Time-of-flight secondary ion mass
spectrometry, after reaction on-chip to analyze the degree of functionalization and determine the
groups attached during electron transfer chemistries.
F4B
X
X
H20 (1wt% SDS)
35-40"C, 7 hours
X=N0 2, CI, OH, Br, COOH
Figure 6.1: Schematic of the electron transfer chemistry of graphene. The electron rich
graphene sheet transfers electrons to the electron withdrawing diazonium molecule.
The electronic density of states (DOS) of graphene calculated from its energy spectrum
.......
....
.......
- :z :
.-
m;z: :
I -- ::- ::::
discussed in chapter 1 is linear near the Fermi level (Figure 6.2). Figure 6.2 also includes the
DOS of a bilayer graphene. Graphene reactivity for the electron transfer chemistry is governed
by the DOS close to Fermi level. During the electron transfer chemistry an electron withdrawing
group when introduced in the vicinity of a graphene sheet withdraws an electron from the a
electron cloud and localizes it in a sigma bond that forms between the graphene carbon atom and
diazonium molecule (Figure 6.1).
Graphene
Bilayer
graphene
0.5
>M...
,
Ui
0
0.02
0.06
0.04
DOS
Figure 6.2: Electronic density of states (DOS) of single and bilayer graphene close to Fermi
level. E=0 is the Fermi level of graphene.
6.2 Experimental Design
Each silicon wafer with the single and multi- layer graphene samples is submerged in the
reactant solution for 7 hrs at 35-45*C under ample stirring to perform the chemistry. To prepare
100
the reactant solution, an aqueous solution of 1% wt SDS is added to bring the water soluble,
cationic diazonium reagents in close proximity of the highly hydrophobic graphene sheets. This
surfactant is known to form hemi-cylindrical structures on HOPG 9 . The hydrophobic tail of the
surfactant sits in the vicinity of graphene and the polar head is expected to interact with the
diazonium reagent, increasing its concentration near the surface of the graphene. After 7 hours in
the reactant, each wafer is rinsed copiously with reagent free deionized (DI) water and immersed
for 5 additional hours in DI water to ensure removal of unreacted diazonium reagent on the
graphene surface.
6.3 Analysis of Chemical Functionalization
Auger electron spectroscopy and Time of Flight Secondary-Ion Mass Spectroscopy
(TOF-SIMS) are preformed on the functionalized graphene sheet for elemental analysis and to
collect evidence of functionalization. Auger analysis is done on a single graphene sheet (N=1)
after electron transfer chemistry. Figure 6.3a, b shows the microscopic and SEM image
respectively of the graphene sheet. In Figure 6.3a the lower portion of the graphene sheet is
single while the entire sheet in Figure 6.3b is single. The Auger electron spectroscopy analysis of
the boxed region in Figure 6.3a, b with 5ptmx5ptrm analysis area is presented in Figure 6.3c.
Analysis shows the presence of nitrogen and oxygen on the single sheet. This indicates
successful attachment of the C6H4-NO 2 groups to the single graphene sheet'08. TOF-SIMS also
indicates similar results and are presented in Figure 6.4. This analysis is only restricted to the
outermost (1-2) atomic layers of the sample. TOF-SIMS is performed on multi- layer graphene
101
...
.........
. .......
.. .......
.. .......
sheets after their functionalization. The scan sizes are either 100 or 200pm. The negative ion
spectrum show presence of ions CN~ (m/z=26), NO2 (m/z=42) and CNO~ (m/z=46) clearly
indicating attachment of C6H4-NO2 groups on the graphene sheet.
b)
X10 3
U 10
0
-o
w
z -10
-20
100
C
300
o
N
500
kinetic energy (eV)
Figure 6.3: Auger Electron Spectroscopy analysis of single graphene sheet after electron
transfer chemistry. (a) Microscopic image of graphene sheet. Bottom part is a single sheet and
upper portion has 2-3 layers of graphene sheets. The dashed box marks the area for AUGER
analysis. (b) SEM analysis done during AUGER analysis on the single graphene layer portion in
(a). Dashed box highlights the area (5 gm X 5 pm) of AUGER analysis. (c) Nitrogen (N)
102
... I. ........................................--
:.-.-
_
U:z
MU:
- : :;. : :::::: :::-- __:::-::::_
_11:
....
...
:::-,
....
indicates successful attachment of C H -NO2 to the single sheets. 0 has contributions from both
SiO 2 and NO 2 groups.
x 105
100
50
150
m/z
Figure 6.4: Negative ion TOF-SIMS spectrum of reacted multilayer graphene sheet. TOFSIMS analysis is only restricted to the outermost (1-2) atomic layers of the sample. In the on chip
electron transfer chemistry only the topmost graphene sheet is functionalized with the nitro
diazonium salt. Presence of signal corresponding to CN (m/z=26), CNO~ (m/z=42), and NO~2
(m/z=46), confirms successful attachment of C6H4-NO2 group to the topmost graphene layer.
6.4 Electron Transfer Chemistry for Single and Multi- layer Graphene
Reactivity of pristine single and multi- layer graphene is probed by graphene on-chip
electron transfer chemistry. A substantial difference between the reaction conversion of a single
sheet and its multilayer including bilayer graphene is observed. These observations are made for
the species on the same substrate/chip and thus undergoing the same reaction conditions. Single
103
graphene sheet is found to be far more reactive than the bi- or multi- layer. This conclusion is
primarily based on the disorder to tangential (D/G) Raman peak intensities of the graphene preand post-functionalization. The Raman G mode in the absence of resonance enhancement or
formal charging, it is expected to be largely unaffected by chemical reaction as observed for
carbon nanotubes10 9. Graphene can be identified in terms of its number and orientation of layers
by means of inelastic and elastic light scatterings, such as Raman and Rayleigh spectroscopies"" as discussed in chapter 1. Raman spectroscopy also has been successfully used as a highly
sensitive gauge to monitor of doping, defects, strain and chemical functionalization for carbon
1012-114
nanotubesio9,
115-120
. Moreover, in case of the Raman spectroscopy of
and graphene
graphene there is no resonant enhancement unlike carbon nanotubes. The absence of this
resonance effect for graphene greatly simplifies the interpretation of relative disorder to
tangential (D/G) peak intensities in the Raman spectrum. Previously, it has asserted that the D/G
peak ratio should be uniformly related to the number of defects per area for single walled carbon
nanotubes10 9,12 1 and therefore, in this work the D/G ratio is used as a measure of the extent of
chemical functionalization.
104
n=1
600001
pristine
functionalized
15000-
D/G=O. 185
10000i
5000-
1100
n
2000
2000
2900
Raman shift (cm-1)
2900
Raman shift (cm-I)
105
.............................
.....
............
...
..
......
...
...........................
.............
functionalized
n=2
pristine
40000
D/G=0.012
- 20000 -
25000
0
1100
.0-d
2000
2900
1100
Raman shift (cm-')
2000
2900
Raman shift (cm)
e)
60000
pristine
n- oc 50000
functionalized
D/G-O
30 25000
30000-
0
1100
2000
0
1100
2900
Raman shift (cm)
2000
2900
Raman shift (cm)
Figure 6.5: Raman analysis for graphene on chip chemistry on silicon substrate. (a)
Microscopic images of a single layer (right), bilayer (left) and (b) multilayer (n-oo) of graphene.
(c-e) Raman spectra of pristine (left) and functionalized (right) sheets: (c) spot L1 on single sheet
with inset showing expanded 1300-1700 cm- 1 region, (d) spot L2 on bilayer and (e) spot L3 on
multilayer (n-oo, graphite). There is no D peak for the pristine samples (left spectra). The D/G
ratio after reaction of single layer (0.185) is about 15 times higher than for a bilayer (0.0 12) and
greater for other multilayers (-0). The Raman spectra are at 532 nm excitation.
106
According to the Raman analysis before and after functionalization a high density of defects are
introduced for single graphene sheets than for multilayers by covalent functionalization. The
D/G peak ratio after reaction is almost an order of magnitude higher for a single graphene sheet
than for bi- and multi- layers, even on the same reacted wafer. Figure6.3a, b show the
microscopic images of the single, bi- and multi- layer of graphene sheets with labels Li, L2 and
L3 spots on these sheets respectively. The Raman spectra are at 532 nm excitation. The left
spectrum in Figure 6.5(c-e) is that of pristine graphene sheet and the spectrum in the right are
after on-chip functionalization. For these measurements the laser spot is focused on the central
region of the sheet at least 5 ptm away from the edge to ensure that the signal had no edge
component. The spectra labeled functionalized are collected after the electron transfer chemistry
at the identical spots as the pristine sheet controls. These locations are identified after chemistry
by using the features of the graphene as distinctive microscopic markers. The D/G peak increase
for single sheet (Figure 6.5c) is almost an order of magnitude higher than for bi- (Figure 6.5d)
and multi- layer (Figure 6.5e) graphene.
Reactivity data for several single and multi- layer graphene specimens on different silicon
substrates is summarized in Figure 6.6 in form of normalized D/G ratios Vs the number of layers.
Slight variations in total conversion exist between graphene species on different substrates,
presumably due to variations in the experimental conditions. To account for these variations for
each silicon chip housing the graphene samples, the D/G ratio is normalized by its largest value
D/Go found for a graphene sheet on the substrate. This is invariably a single layer (N = 1). This
allows to eliminate the differences in the extent of reaction for different substrates arising from
apparently minor variations in reaction conditions and sample preparation. The conclusions
107
.........
..
.....
.
remain unchanged if this normalization is ignored. The relative reactivity is expressed as a ratio
as (D/G)/(D/G)o. A sharp decrease is clearly observed in the D/G ratio with an increase in the
number of sheets from one (N=l) to infinite (graphite). All the reactivity analysis is done for
defect free graphene due to absence of D peak for pristine graphene. Therefore, the D peak after
the electron transfer chemistry can be entirely attributed to the attachment of functional groups
(C6H5-NO 2 ) to the graphene carbon atoms. Attachment of these functional groups changes the
hybridization of some graphene carbon atoms from sP2 to sp3 and therefore disrupts the
symmetry resulting in the disorder (D) peak.
1.0
D/G)/(D/G)o
0.8*
k/kgraphite (GM)
/N
0.6
I
0.4-
0.2
0.0A
0 1 2 3 4 5
00
N
Figure 6.6: Dependence of D/G peak ratio on the number of graphene layers (N). The ratio
is normalized to the maximum value encountered on the substrate. The data set combines results
from graphene sheets from multiple silicon substrates. (N=oo corresponds to graphite). 1/N (red)
represents the expected D/G scaling with N if the topmost graphene sheets of multi layers have
the same reactivity as that of single sheet. Calculations based on the Gerischer Marcus theory of
the reactivity normalized to graphite k/kgraphite for the case of no electronic puddles (green).
108
The simplest explanation for this trend of increasing reactivity with decreasing layer
number in Figure 6.6 is that the Raman process, which also samples interior carbon atoms
shielded from the chemical treatment but not the scattering process, is contributing to an
increasing G peak intensity for a given D band caused by functionalization of presumably only
the outer layer. In the absence of resonance, the trend would then scale as
1
N
where N is the
layer thickness. This trend is plotted in Figure 6.6 to clearly rule out this interpretation, as the
1
experimental diminution is obviously greater than N. Therefore, it is concluded that single layer
graphene sheets have higher reactivity than bi- and other multi- layers of graphene.
Another explanation for observations in Figure 6.6 is that the electron transfer reactivity
differences between single, bi- and multi- layer graphene sheets is due to differences in their
DOS. The DOS close to the Fermi level (Figure 6.2) for these structures is related to their
electron transfer rates by estimated by Gerischer Marcus theory, as discussed in chapter
599,102,122. According to the Gerischer-Marcus theory the electron-transfer reaction rate
(kET)
for
graphene is given by equation 6.1. As discussed in chapter 5, W, (2, E) is the distribution of the
unoccupied redox states of the electron acceptor in solution. DOSGraphe2(N=1/N=2) is the electronic
density of states of graphene for N=1, and of bilayer graphene for N=2 and e,
is the
proportionality function.
EGraphene
EF
kE7aphene =n
fox (E) DOSGraphene(N=1/ N=2) (E)W,, (A, E) dE
E,,dox
109
6.1
Graphene
Bilayer
0.5
-
graphene
-0.5
1
Diaz W(E)
0.04
0.02
DOS
0
0.5
-0
-0.5
Dirac point down shift,
500 meV
Energy overlap
Diaz WIx(AE)
0
0.02
0.04
0.06
DOS
Figure 6.7: Energy overlap of the density of electronic states of single and bilayer graphene
and vacant oxidation states of the electron withdrawing species (W., ). (a) No shift in Dirac
point of pristine graphene (b) 500meV down shift of the Dirac point of pristine graphene.
(Energy overlap is calculated in between the dotted lines)
Figure 6.7 shows the energy overlap of the DOS of single and bilayer graphene DOS and
vacant oxidation states of the electron withdrawing species (W,, ). This overlap directly
110
determines the electron transfer rate from graphene and bilayer graphene to the electronwithdrawing group. Assuming e,
is independent of energy and e.
and u,, are same for
graphene and bilayer graphene, they cancel out in calculations for the relative rate constants. The
reorganization energy A lies in between 0.5 and 1 eV and a value of 0.9 for A is used. These
calculations suggest bilayer graphene to be almost 1.6 times more reactive than a single layer
graphene, opposite the trend of what is observed experimentally in this work. Therefore, these
electron transfer rate calculations based on DOS of pristine single layer, bilayer of graphene 12 3
and graphite12 4 do not support the higher reactivity of single graphene sheet .
A more likely explanation for the shift in the graphene Dirac point and thus also the
justification for the enhanced electron transfer is the ionized impurities on SiO 2 substrate that can
lead to local puddles of electrons and holes with finite densities 1m-17. The potential of charged
impurities in the substrate moves the Dirac point up and down in different points of space
creating alternating in space electron and hole puddles. The electron puddles increase the
available electron density for electron transfer by increasing the number that overlap with vacant
oxidation states of the reactant. Thus presence of the electron puddles should increases the
reaction rate of chemistry discussed in Figure 1. The effects of substrate surface charged ionized
impurities should be more enhanced in a single layer than over bi- or multi- layer graphene
because the screening length of graphite 128 is only 5 A in the c-axis and is comparable to the
interlayer distance ~ 3.4 A. We expect similar short screening length for bi- and multi- layer
graphene 129and therefore ionized impurities in the underlying substrate should have a stronger
correlative effect on single layer than in top layers of bi- and multi- layer graphene. Generally,
the layer in direct contact with the SiO 2 substrate should be most affected by the ionized
impurities. However, in the case of bi- or multi- layer graphene, it is presumably only the top
layer that undergoes electron transfer chemical functionalization and this layer should be least
affected by charged impurities in the substrate.
The role of shifting in Dirac point of single graphene sheet due to electron puddles on
reactivity is analyzed by the Gerischer Marcus theory. This shifting is neglected for the bi- and
multi- layer graphene due to the screening of substrate charge effect for the topmost graphene
sheet. The Gerischer Marcus theory based calculations suggest that reactivity of the single
graphene sheet significantly increases by a downshift of the Dirac point. Reactivity of single
graphene sheet is almost three times that of a bilayer if the Dirac point downshifts by 500meV.
This is due to increase in the overlap of electronic DOS of graphene and vacant oxidation states
of the 4-nitrobenzene diazonium tetrafluoroborate. Therefore, contribution of the ionized
impurities on SiO 2 substrate seems to be likely the plausible explanation for substantially
increasing the on chip reactivity of single graphene sheet towards electron transfer chemistries.
Another possible explanation is the existence of mechanical ripples in the graphene sheet.
Simulation of chemical activity of corrugated graphene within density functional theory predicts
an enhancement of its chemical activity if the ratio of height of the corrugation (ripple) to its
radius is larger130 than 0.07. According to these simulations growth of the curvature of the
ripples results in appearance of midgap states which leads to increase of chemisorption energy.
For suspended graphene layers a single layer has been found to be more microscopically
corrugated than a bi or multi- layer 13r1-132
112
6.5 Substrate Influence on Graphene Reactivity
Graphene is necessarily supported on a substrate of some kind. Electronic properties of
graphene are found to be strongly coupled to the characteristics of the underlying substrate (i.e
substrate flatness and charge impurities). Many researchers are interested in using covalent
chemistry to modify the surface of pristine graphene, but all of these efforts have considered the
reaction on SiO 2 substrate exclusively. An important goal for the chemists is to understand the
role of the underlying substrate on the chemical properties of graphene. In this thesis work it is
shown that the reactivity of graphene is dominated by its underlying substrate.
The method employed to do this study is to prepare single graphene sheet on the
substrates including silicon wafers with 300nm thermal silicon dioxide and sapphire by transfer
of CVD graphene grown on copper foil. The detailed method of CVD graphene transfer is
discussed in chapter 2. The chemistry is done by placing an aqueous solution containing aryl
diazonium reactants over the substrate with graphene, allowing only the exposed top surface to
undergo electron transfer chemistry, forming a covalently bonded phenyl substituent. The
electron transfer chemistry is conducted on the entire wafer in water with 2 mM water soluble
nitrobenzene diazonium salt (4-nitrobenzene diazonium tetrafluoroborate) obtained from Sigma
Aldrich. The silicon and sapphire wafers are covered with CVD graphene from the same copper
foil with identical transfer process. Silicon and sapphire wafers are submerged in the reaction
solution for 1.5 hrs at 30'C under ample stirring. The reactant solution is aqueous with 0.5 wt %
anionic surfactant sodium dodecyl sulfate (SDS). After reaction, each wafer is rinsed copiously
with reagent free deionized (DI) water and immersed for 2 additional hours in DI water to ensure
removal of unreacted diazonium reagent on the graphene surface.
113
Interestingly for identical reaction conditions substantial different covalent reaction conversions
of graphene on silicon and sapphire wafers is observed. Graphene on silicon wafer is found to be
substantially more reactive than graphene on sapphire wafer for the same reaction conditions. In
this work relative disorder to tangential (D/G) peak intensities in the Raman spectrum are used as
a measure of the extent of chemical functionalization. For graphene on SiO 2 wafer, chemical
functionalization introduces a strong rise in D peak intensity (or D/G ratio) (Figure 6.8b).
However, for reaction under identical conditions this rise of D peak is absent for graphene on
sapphire (Figure 6.8d). These results are interesting since they suggest a correlation between
graphene reactivity and supporting substrate. The Raman spectra are at 633 nm excitation.
The most plausible explanation for the reactivity difference of graphene on silicon and
sapphire wafer is a combined effect of (1) substrate surface charge impurities and (2) ripples in
graphene. Both these effects are expected to modify the electronic band structure of graphene.
Takahiro et al investigated graphene on a single-crystalline sapphire surface by measuring
topographical and frictional force AFM images1 33 . The measured height of graphene on sapphire
was found to be approximately 0.36 nm. This value is almost equal to the intrinsic graphene
thickness. Although Si0 2 layers on Si substrates are useful from the point of view of visibility of
graphene, their interface with graphene is not atomically flat. Heights of graphene on SiO 2
surfaces have been estimated to be 0.9 nm in air and 0.42 nm in ultra-high vacuum1 34 . Thus,
these observations of researchers indicate that graphene is closely attached on the sapphire
surface without floating areas in air. Thus graphene on sapphire has a highly flat topology with
weaker and smaller ripples than in SiO 2. Some previous studies including spatially resolved
spectroscopy
35
and theoretical calculations136 have suggested graphene ripples and charge
114
...........
..
......
...
...
....
impurities on substrate as a major cause for electron-hole puddles and mid gap states in
graphene. Both these effects are expected to be significantly reduced for the graphene on
sapphire. The higher substrate charge impurities and ripples for graphene on SiO 2 substrate
modify the band structure of graphene by (1) moving the Dirac point locally (2) introducing mid
gap states and thus increasing the electronic density of state near the Fermi level. This increase
of DOS near Fermi level of graphene leads to higher reactivity for the former. The role of
supporting substrate is thus important in chemically manipulating the graphene on chip.
a) 10000-
b) 12000
8000-
*9000
6000.
G
D
66000-
4000
3000
2000
0
1200
0
1200
1400
1600
1800
Raman shift (cm1)
c)
1400
1600
1800
Raman shift (cm-I)
d)
20000
2400
15000
.)1000C
1 1200
5000
600
1470
1290
1310
1330
1350
Raman shift (cm-')
0
1270
1300
1330
1360
Raman shift (cm')
Figure: 6.8: Raman spectra of (a,c) pristine and (b,d) functionalized CVD graphene sheet
on (a-b) SiO 2 and (c-d) sapphire wafers. D peak presence on functionalization for SiO
indicates successful attachment of C6H4-NO 2 to the graphene sheets. Negligible D peak height on2
functionalization for graphene on sapphire wafer indicates small reactivity of graphene on
sapphire. The Raman spectra are at 633 nm excitation.
115
11.....
....
....
........
...
6.6 Electron Transfer Chemistry for Graphene Edges and Bulk
F4B~
N
O2
N02
NO
N
2
N2
2
Higher reactivity
of edges
Figure 6.9: Higher edge reactivity. The number density of functional groups C6H4-NO 2 is
higher at the edges of graphene.
The dependence of graphene nanoribbons electronic properties on the edges has been
discussed in detail in chapter 5. Thus precise control of the chemistry at graphene edges is highly
desired. Higher reaction rate at edges than at bulk will enable to design edge selective
chemistries. Cangado et al' 3 7 have suggested that a perfect zigzag edge cannot activate the D
peak due to momentum conservation. Later, Casiraghi et al138 performed a detailed Raman
spectroscopy analysis of graphene edges and according to them this dependence of D peak on the
edge orientation has not been observed for real graphene samples with macroscopically smooth
edges. This is attributed to the lack of high order of carbon atom orientation along the edges.
Various Raman studies'
on pristine graphene have reported zero D peak intensity for the
bulk pristine graphene (graphene with no edge component) due to high crystallinity and absence
of defects. However, the edges exhibit finite D peak intensity since they act as defects due to
symmetry breaking and allow elastic backscattering of electrons. As expected, the D peak
intensity of graphene and graphite edges show a strong dependence on the polarization of
116
incident light 137 138. It is strongest for polarization parallel to the edge and minimum for
perpendicular.
Higher reactivity of graphene edges than the bulk interior of a single graphene sheet is
observed in this work as presented in the schematic cartoon of Figure 6.9. A new spectroscopic
test to examine the relative reactivity of graphene edges versus the interior sheet has been
developed in this work. This technique uses the polarization of various contributions to the
symmetry disallowed two phonon mode (D peak) observable in the Raman spectrum of graphene
edges. This polarization dependence of the intensity of this mode (D peak) for graphene and
graphite edges is well documented 137-138. In this technique the spatial contributions of the D peak
are deconvolved and related to reactive state. By comparing D peak intensity on the polarization
of incident light before and after chemical functionalization at edges, the contribution due to the
symmetry breaking is subtracted. Unfunctionalized or pristine graphene samples edges show
strong dependence of D peak on the direction of polarization of incident laser light. However,
this dependence is invariably lost after functionalization (Figure 6.11) indicating that the main
contribution to the larger peak D peak is from the newly introduced defects introduced by
covalent defects. Intensity increase of 2-3 times is observed for D peak at the edges than over the
bulk due to on chip functionalization. This is thus interpreted as higher reactivity of the former
over the latter (Figure 6.10). The Raman spectra are at 532 nm excitation
117
...........................
................................................................................
10pm
300 00-
pristine
bu
1k 7000-
D/G=0.417
D/G=0
3500-
150 00-
04
1100
of
2000
2900
pristine
1100
2000
Raman shift
Raman shift (cn-1)
8000.
functionalized
2900
(cm- 1 )
edge
D/G=O.I
4000
1100
2000
2900
Raman shift (cm-')
Raman shift (cm-1)
Figure 6.10: Graphene edge Vs bulk reactivity. (a) Microscopic image of a graphene sheet
with lower portion as single and upper (darker) is 2-3 layers. (b) Raman spectra of point on bulk
single graphene (spot A) and (c) point on the edge of single graphene (spot B) pre- and postelectron transfer chemistry (functionalized). Note that D/G ratio is 0 for bulk (A) and 0.1 for
edge (B) before chemistry but rises to 0.417 and 0.764 after reaction for the bulk and edge
contribution respectively for a single sheet, absent polarized filtering. The Raman spectra are at
532 nm excitation
118
..
.....................
......
0000
12000
0
D/G=0. 12
$ 6000-
5000
C
00
90
D/G=0.02
;
0
11400
1700
1400
1700
Raman shift (cm-1)
Raman shift (cm-1)
c)
1400
3200
3000
90
D/G=0.34
1600
1500
0
11 00
2000
2900
2000
00
Raman shift (cm-1)
2900
Raman shift (cm-1)
d) 50000
D/G=0.18
25000
0
110 0
2000
2900
Raman shift (cm-1)
Figure 6.11: Polarization dependence of D peak pre- and post- electron transfer chemistry.
(a) Microscopic image of graphene sheet. (b) Raman of pristine graphene sheet edge (spot E): D
119
peak depends on the angle of polarization of the incident laser light. Light parallel to the edge is
0' and perpendicular is 90'. The D/G=0.12 for 0' but 0.02 for 90' for edge of pristine sheet. (c)
Edge point E after reaction shows weak or no dependence of D peak on the angle of polarization.
(d) Point on the bulk of single graphene sheet has a lower D/G than edge and no polarization
dependence. The Raman spectra are at 532 nm excitation.
To achieve edge selective functionalization it is possible that reaction conditions may be
found where the difference in reaction rates between bulk and edge leads to exclusive reaction of
the latter, an important goal in graphene processing. This may provide a direct handle to control
the non-uniformity of edges for graphene and its nano ribbons. Figure 6.10a is the microscopic
image of a graphene sheet that is single at the bottom portion. The Raman spectra of bulk (spot
A) and edges (spot B) of single graphene sheet before and after the electron transfer chemistry
are presented in Figure 6.10b and c, respectively. D peak is absent for the pristine bulk single
graphene (spot A) and the edge (spot B) has a D/G ratio of 0.1. After attachment of the chemical
moieties higher D/G peak ratios for the edges than for the bulk of single sheets are observed. For
the edge (A) D/G ratio is 0.764 and for bulk (A) it is 0.417. This higher ratio suggests a higher
reactivity of carbon atoms along and close to the edges than in the bulk. Similar results on higher
139
reactivity of graphene edges than bulk have been later reported by Lim et a1 . Further the
investigation of the dependence of the D peak on incident light polarization in Figure 6.11
reveals the dependence of D peak on covalent defects. The D peak for pristine graphene edge is
highly anisotropic since it (spot E in Figure 6.11 a) shows a strong dependence on the incident
light polarization. The angle between the incident polarization and the edge orientation is defined
as 0. The D-band is strongest for polarization parallel to the edge (0=0') and minimum for
perpendicular (0=90') as shown in Figure 6.11 b. The D/G ratio is 0.12 for 0=00 and is almost 0
120
for 0=90'. This dependence has been previously well studied by other researchers and is
attributed to the broken symmetry of the graphene structure at edges. However, post chemical
functionalization this dependence of D peak on the incident light polarization is lost for the
edges. Figure 6.11 c shows a clear indication of the isotropic D peak that is independent of the
incident angle of polarization at edge E. The bulk of graphene sheets show no D peak
dependence on the angle of polarization of the incident light. To rule out the interpretation that
edges might simply have higher D peaks than in the bulk for the same level of functionalization
obtained the Raman spectra of the edge and bulk of graphene oxide. Graphene oxide is
synthesized from graphite by modified Hummers method 1 40 discussed in chapter 2. The intensive
oxidation involved in this method to is expected to fully functionalize graphene edges and bulk.
The Raman spectra of these graphene oxide sheets show insignificant variation in D/G ratio of
edges and bulk (Figure 6.12) indicating no enhanced D peak for edges than bulk at same level of
functionalization.
.:.......................
.................
a)
b)
900.
bulk
edge
6000
4-4I
30004
1200
0
1600
2000
Raman shift (cm-1)
0
1200 1600 2000
Raman shift (cm-')
Figure 6.12: Raman spectra of single graphene oxide sheet at (a) bulk and (b) edge. The
D/G ratio of bulk and edge is similar.
Many effects can be seen to contribute to the enhanced reactivity of the edges as
compared to the bulk (central) graphene. An altered electronic structure is expected at the edges
than at the bulk region due to symmetry breaking of the honeycomb lattice at the edges. For
edges higher electronic DOS near Fermi level than bulk graphene is suggested by previous STM
analysis 14 1. The dangling bonds at the edges can also be a major contribution to the enhanced
edge reactivity.
6.7 Conclusions
In conclusion, the on chip reactivity of mechanically exfoliated graphene (bulk and
edges) and its various multi- layers for electron transfer chemistry has been explored by Raman
122
spectroscopy, TOF-SIMS and Auger Electron Spectroscopy. Single graphene sheets are found to
be almost ten times more reactive than bi- or multi- layers of graphene. A new spectroscopic test
to examine the relative reactivity of graphene edges versus the bulk has also been developed in
this work. It is shown that reactivity of edges is at least two times higher than reactivity of the
bulk single graphene sheet, as supported by theory. This study of structure reactivity of graphene
may be important for engineering graphene on chip.
123
Chapter 7 Chemical Functionalization of Graphene Devices: Role of Covalent
Defects on Graphene Conductivity
7.1 Motivation and Approach
Structure reactivity relationships of graphene and graphene nanoribbons for electron
transfer chemistries have been discussed in great detail in chapter 5,6. The particular class of
electron transfer chemistry, as investigated and presented in this work, changes some of the
graphene sP2 carbon atoms into sp3 atoms. This change occurs by formation of a covalent
chemical bond (i.e., a covalent defect) with the n electron of the carbon atom. However, it is
primarily the a orbitals that are responsible for electron conduction and thus the unusual
electronic properties of 2D graphene. The covalent defects in the graphene lattice are a potential
source intervalley scattering. Thus a high density of these covalent defects on graphene oxide
sheets makes them close to insulating 14 2-143 . This suggests that the insulating graphene oxide
144
sheets cannot be directly used for electronic applications and further processing is required .
This makes it important to measure the effect of the electron transfer chemistry on graphene
electron conduction. To achieve this goal, chemistry was done on graphene devices in several
successive steps and the corresponding conductivity and Raman spectrum measurements were
made. This work gives an understanding of relation between covalent defects or D/G peak to
peak ratio in graphene and their conductivity. Interestingly, the graphene sheets remain highly
conducting even after heavy functionalization with D/G~1.5. Thus chemical manipulation of
graphene and graphene nanoribbons discussed in this thesis can be successfully used for building
hybrid or superlattice structures.
124
7.2 Fabrication of Graphene Devices
4 7 48
Chemical vapor deposition (CVD) process was used to grow graphene - on copper foil
and thereafter transferred on silicon wafer with 300nm of thermal oxide (Figure 7.1 a). This was
achieved by transfer method discussed in chapter 2 involving etching of copper foil and using
PMMA as a supporting film. To fabricate the devices photoresist was coated (Figure 7.1b) and
patterned using photo lithography. The chrome mask design is presented in Figure 7.2. Metal
(120nm gold with 7nm titanium as sticking layer) was evaporated into the open window by an
electron beam evaporator under good vacuum conditions (Figure 7.1c). The remaining resist is
removed and a fresh layer of resist is coated and patterned in form of rectangular stripes
protecting only the active area of the device (Figure 7.1 d). All the exposed graphene is etched by
using oxygen plasma in a reactive ion etcher (Figure le). The active area of the device is
presented in Figure If and Figure 7.3. Figure 7.3a,b are the microscopic images of CVD
graphene devices and the light blue sheet is the single graphene sheet.
125
:::::::::
;=:::: ..:
:-
,,- - -- - - -
'-
I:: -
a)
b)
c)
d)
e)
f)
=-- ,-- w:::
::::::::::
....
......
-- ..-- I.- -:............
Figure 7.1: Schematic of device fabrication. (a) Graphene on silicon wafer with 300nm
thermal oxide fabricate by transfer of CVD graphene from copper foil to silicon wafer. (b) Coat
the substrate with photoresist. (c) Lithography is used to open the windows in the resist for
putting the metal (gold with titanium as sticking layer). (d) Lithography is used to pattern resist
stripes as etching mask for graphene (e). (f) The active area of device.
126
+
f*M4fWHOlW4
W
U-W. U--.
EW-++
+8Bum
gap
14 um gap
+
+
14 um gap
+
b)
8 um gap
Figure 7.2: Design of lithography mask used for graphene device fabrication. (a) Image
reversal mask design used to open the contact windows to deposit contact metal. The two designs
used are 8ptm and 14 pm channel lengths as show above. The cross bar structures are used to
pattern the alignment marks for the next step of lithography. (b) Image reversal mask design for
etching graphene. Rectangular stripes are 40ptm wide. The cross bar structures are used to align
the etching mask with the alignment marks patterned using (a).
127
Source
Drain
4pm
Figure 7.3: Microscopic images of CVD graphene devices. Single graphene sheet is trapped
by lithography techniques between source and drain electrodes. Electrodes are gold on titanium
deposited using an electron beam evaporator.
a)
Br
/
B9
NB
N2BF
4
O
0
-<D
@ F
N2 BF4
NO2
BF4
Figure 7.4: Chemical structures of the diazonium species reacted with graphene devices. (a)
4-bromobenzene diazonium tetrafluoroborate, (b) 4-(prop-2-yn-1-yloxy)benzene diazonium
tetrafluoroborate and (c) 4-nitrobenzene diazonium tetrafluoroborate
128
....
....
.....
.
7.3 Graphene Device Chemistry and Electron Transport
a)b)
jANF4B~
Br
N=N
Figure 7.5: Schematic of on chip device chemistry. (a) Pristine graphene device. Graphene on
silicon wafer with 300nm thermal oxide. Source and drain electrodes are of gold and are
represented as Au. (b) Functionalized graphene device. The chemical reaction is electron transfer
chemistry.
CVD graphene devices are fabricated as described in Figure 7.1 schematics. Raman
spectra with confocal JY (Jobin Yvon) instrument and electrical measurements with Agilent
E5270B are performed on pristine graphene devices. Seven rounds consecutive of chemistries 145
are performed on the devices with reaction conditions similar to those discussed in chapter 6.
Details of reaction are included below. After reaction, the chip is submerged in DI water for one
hour to remove any residual diazonium salt and SDS surfactant. To remove the moisture the chip
is kept in a vacuum chamber for one hour. This is followed by repeating the Raman and
electrical measurements as done for pristine graphene. Seven rounds of chemistries are
performed on the devices. For each successive round of chemistry some or all parameters
including concentration, temperature, and time are changed to increase the density of functional
groups on graphene. A general trend of increase in disordered (D) peak and electrical resistance
is observed for the devices with each round of chemistry.
129
The details of seven rounds of chemistries and a SDS pretreatment step are as discussed
here. SDS pretreatment: graphene devices are exposed to 0.5 wt% SDS aqueous solution for two
hours at room temperature (22'C) with constant stirring at 200 RPM. Chemistry 1: Devices
exposed to 35mM diazonium salt solution in water for 22 minutes at 22'C. Chemistry 2: 35mM
diazonium salt solution in water for 15 minutes at 22'C. Chemistry 3: 35mM diazonium salt
solution in water for 45 minutes at 22'C. Chemistry 4: 70mM diazonium salt solution in water
for 60 minutes at 30'C. Chemistry 5: 70mM diazonium salt solution in water for 60 minutes at
32'C. Chemistry 6: 125.9mM diazonium salt solution in water for 90 minutes at 35'C.
Chemistry 7: 179.8mM diazonium salt solution in water for 90 minutes at 35'C. After each
round of chemistry or SDS pretreatment the chip is submerged in water at room temperature for
one hour. The stirring for all the above treatment steps is kept constant at 200 RPM. Finally the
chip is kept in a vaccum chamber to remove the residue moisture.
The graphene device chemistry is performed in an aqueous solution containing
diazonium reactants over the substrate, while allowing only the exposed top surface of the
graphene sheet to react. The diazonium salts used in this study are: (1) 4-bromobenzene
diazonium tetrafluoroborate, (2) 4-(prop-2-yn- 1-yloxy) benzene diazonium tetrafluoroborate, and
(3) 4-nitrobenzene diazonium tetrafluoroborate. The chemical structure of the diazonium species
is presented in Figure 7.4. Figure 7.5 shows the schematics of the electron transfer chemistry on
graphene device for 4-bromobenzene diazonium salt. Figure 7.5a represents a pristine graphene
device that undergoes electron transfer chemistry. Figure 7.5b shows the functionalized graphene
device. As evident from Figure 7.6, the D/G peak-to-peak height ratio of graphene increases for
each round of chemistry for 4-bromobenzene diazonium. (For comparison Raman spectra of
130
graphene oxide sheets is presented in Figure 7.10). The upward arrow in Figure 7.6 indicates the
rise in D peak or the covalent defect density with each successive round of chemistry. Note that
the G peak of graphene Raman spectra in Figure 7.6 are normalized to enable an easy
comparison for growing D peak representing the level of functionalization. These results indicate
that the covalent defect density increases for each successive round of chemistry. This is due to
the additional attachment of functional groups on graphene lattice, as presented in the schematic
of Figure 7.6. Data for additional devices is included in Appendix D. A linear relation is
observed between graphene resistivity and D/G peak to peak ratio with slope in range of 400 to
1300 for graphene devices on different chips (Figure 7.7-9). The coefficient of determination
(R2 ) for the linear data fit of each device is observed to be greater than 0.9 for most devices. The
histogram plots of the slopes and R2 are included in Figure D5 and D6 of Appendix D. Based on
these experimental observations the R vs D/G slope magnitude does not depend on the type of
benzene diazonium species which are covalently bonded to graphene. This suggests
independence (or insignificant dependence) of graphene resistivity on the type of benzene
diazonium molecule attached to graphene. Furthermore, the R vs D/G slope is found to vary
from chip to chip for same chemical. This suggests an influence of the processing conditions
involved in graphene transfer and device fabrication, besides the effect of annealing. Moreover,
the impurities in the used diazonium chemicals and decomposed diazonium chemical may have
adsorbed on the graphene sheet. This may have resulted in a perturbed the device resistance, and
consequently, the R vs D/G slope magnitude. The laboratory synthesized chemical used in this
study may have high content of insoluble impurities, and seems to have imparted in a distinct
brown color to the solution. The decrease in the resistance of some devices for some consecutive
chemistries may be explained as an effect of adsorption of aforementioned chemicals. Thus,
...........
.....
slight deviations observed in the linear relationship between R vs D/G curve could be explained
by these uncontrolled variables. However, it is noteworthy that, linearity remains the consistent
trend for most of the devices.
A linear relation of R vs D/G, as evident from the experiments presented in this thesis,
suggests that graphene resistivity is directly controlled by the defect density, which is increasing
with every chemistry step. If the chemical species were covalently bonding as clusters, the
resulting increase in the diameter of the cluster with each successive functionalization step would
have also affected the resistivity (besides the defect density). However, this would have violated
the observed linear relation of R vs D/G, as observed in the experiments. Thus, the observed
trend indicates a random (and not clustered) attachment of covalent moieties.
16000
12000
Functionalization
of graphene
08000
4000
......--
1400
1600
Raman shift (cin-1)
132
1800
_
...............
Figure 7.6: Raman spectra of graphene at different level of functionalization. The D and G
peak of graphene device for seven rounds of chemistry. With each round of electron transfer
chemistry the D peak increases as the covalent defects density increases. The Raman spectra are
at 633 nm excitation
E1200
X Device 1
X Device 2
* Device 3
-'900
600
Io
300
0
-
Device 4
Device 5
Device 6
*Device 7
0
'1200
900
-
0.25 0.5 0.75
* Device 9
A Device 10
0
1
0
0.25 0.5 0.75
D/G
c)
D/G
,-1500
300
'
-
X Device 1
X Device 2
200
* Device 3
100
Device 4
Device 5
0
Device 6
*Device 7
0
0.25 0.5 0.75
* Device 8
; 600
- 300
r
0
,5
I
N
250
0
1
-
OR t
i
0
D/G
I
I
f
0.25 0.5 0.75
D/G
*
Device 8
M
Device 9
A
Device 10
-I
1
Figure 7.7: Resistivity and resistance Vs D/G ratio for pristine CVD graphene for 4bromobenzene diazonium salt. (ab) Resistivity and (c,d) resistance change of graphene device
with increase in density of covalent defects. The covalent defects are introduced by chemical
functionalization of graphene. (a,c) devices have channel length 8jtm and (b,d) have channel
length 14[tm.
133
- NNMNNIIK
- - -
. -:-
-
-
-40-
. .. .. .
a)
b)
-E4000
~
4000
Device 1
Device2
o
4000
-~
+
A Device 3
.?2000
X Device 4
>2000
-
-
8
0 Device 6
Device 8
Device 9
Device 11
0
0 0.6 1.2 1.8 2.4
D/G
0.6 1.2 1.8 2.4
D/G
0
Device7
Device 10
X Device 5
0
Device 7
c)
d)
-/11
o 600 '-"800
E0
*
*0
1200
Device 1
X Devi
200 g
+
Device 7
800 -
A Device 3
04+.
~
Device 2
-
C
4
X Device 5
Device 8
Device 9
Device10
Device10
-
l4QQ
Di
*Device6
0
0
0
0.6 1.2 1.8 2.4
0
0.6
1.2 1.8 2.4
D/G
D/G
Figure 7.8: Resistivity and resistance Vs D/G ratio for pristine CVD graphene for 4-(prop2-yn-1-yloxy)benzene diazonium salt. (a,b) Resistivity and (c,d) resistance change of graphene
device with increase in density of covalent defects. The covalent defects are introduced by
chemical functionalization of graphene. (a,c) devices have channel length 8gm and (b,d) have
channel length 14jim.
134
-- . ..............-:::- . -
----
-, -,
-
-
-
-
a)
-1500
-
0
MMMM
.......II.IItl%It= =
-- -
-
:-
..- -
.- ..-.- :.-
b)
Device 1
E 1500
Device 2
Device 3
'1000
Device 5
I
I
I
0.25 0.5 0.75
D/G
Device 8
Device 10
A Device 11
500
Device 6
Device 7
0 0
-
Device 9
1000
Device 4
500
'X
0
X Device
12
,Device 13
-I
1
0
0.25 0.5 0.75
D/G
800
400
300
200
Device I
Device 8
Device 2
Device 3
Device 9
100
0
0.25 0.5 0.75
Device 11
200 -
Device 6
Device 7
0
Device 10
400
Device 4
Device 5
il
Device 12
Device 13
0
1
0
D/G
0.25 0.5 0.75
D/G
1
Figure 7.9: Resistivity and resistance Vs D/G ratio for pristine CVD graphene for 4nitrobenzene diazonium salt. (ab) Resistivity and (c,d) resistance change of graphene device
with increase in density of covalent defects. The covalent defects are introduced by chemical
functionalization of graphene. (ac) devices have channel length 8ptm and (b,d) have channel
length 14tm.
6000-
Figure: 7.10 Raman spectra of
graphene oxide. The peak to peak D/G
ratio ~ 1. The D and G peaks are broader
than
observed
for
covalent
functionalization studies in this thesis.
A-
3000I
1200
1600
2000
Raman shift (cm-1)
135
::M
::::::
........
-:::-..,
7. 4 Conclusions
In summary, the electron transfer on-chip covalent chemistry of CVD graphene devices
indicates that for D/G as large as 1.3, graphene sheets remain highly conductive with only 3-5
times decrease in conductance. This is in- contrast to the graphene oxide sheets which are
electrically insulating due to the high density of similar sp3 covalent defects. This indicates that
the electron transfer chemistries may be successfully used for building three dimensional or
super molecular structures from two dimensional graphene sheets for electronic applications (i.e.
interconnects). The linear relation of resistivity and D/G ratio observed in this work may be used
as a guideline to chemically engineer graphene surface with electron transfer covalent
chemistries.
136
Chapter 8 Conclusions and Future Recommendations
8.1 Conclusions
1. Cylindrical droplets of micro to nano diameter can be created on chip by surface
patterning techniques and controlling the surface tension of the liquid.
2. The microflow inside evaporating cylindrical droplets can be used to manipulate the
position and alignment of carbon nanotubes with nanometer precision. For pinned contact
evaporation of cylindrical droplets the internal flow is edge directed and this flow carries
the entrained nanotubes to the air-liquid-substrate interface. For de-pinned contact
evaporation of cylindrical droplets the internal flow is centerline directed and thus
entrained nanotubes deposit along the centerline.
3. Carbon nanotube devices with no nanotube-nanotube contact/junction/bundles can be
made by using the microflow inside evaporating cylindrical droplets.
4. Reactivity of GNR directly depends on the ribbon width and the orientation of carbon
atoms at their edges. Relative rate constants for the more accurate GM electron transfer
theory and tight binding approximations predict that armchair and zigzag GNR have
opposite trends in reactivity with the former increasing with width and the latter
decreasing.
137
5. Mechanically exfoliated single graphene sheets are found to be almost ten times more
reactive than bi- or multi- layers of graphene for electron transfer chemistries.
6. Edges of graphene are 2-3 times more reactive than the bulk. The symmetry breaking at
graphene edges changes form anisotropic to isotropic on chemical functionalization as
indicated by the D peak intensity dependence on the polarization of the incident laser
light.
7. Graphene sheets remain highly conductive with only 3-5 times decrease in conductance
for D/G (covalent defect density) as large as 1.3. This is in contrast to the graphene oxide
sheets which are electrically insulating due to the high density of similar sp3 covalent
defects.
8.2 Future Recommendations
1. The hydrodynamic flow in the interior of cylindrical droplets may be used to align and
position other carbon nanostructures including GNR and graphene.
2. Electron transfer chemistries developed in this work may be applied on GNR solution to
sort the ribbons based on their different reactivity, once a method for high production of
GNR is discovered.
138
3. Edge selective chemistry may be used on wide GNR (~100nm width) to react the edges
and carbon atoms close to the edges and thus induce a band gap by reducing the active
width of the ribbon.
4. Three dimensional carbon nanostructures may be fabricated using the electron transfer
chemistries developed in this thesis for interconnect applications.
139
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.................
....................
:..........
..........
.
..........
.
......
.
Appendix A: Role of Surface Tension in Formation of Cylindrical Droplets
Pure DI water does not form cylindrical droplets on the pattered area discussed in chapter
3 & 4. In fact, water selectively leaves the patterned area within few second after a water film is
deposited on the substrate. This may be directly attributed to the high surface tension of pure
water (y=72dyn/cm). However, when the surface tension of water is lowered by addition of
surfactant the film successfully ruptures on the pattered area into cylindrical droplets dewetting
the non polar stripes as discussed in chapter 3 & 4.
DI water everywhere
SAM pattern with no water
d)
No water
151
.
.........
-
Figure Al: Pure water on patterned surface. a) Water dropped on the gold substrate with the
SAM pattern with alternating polar (3.5 rn) and nonpolar (2.5 rn) rectangular stripes. b) Water
selectively leaves the patterned surface 2-3 s after it is dropped. c-d) are at later times 6 and 10
s).
152
1...., :::
:-W
j:- :::- -- ::
............
Appendix B: SEM and AFM Images of SWNT Deposition in Nanometer Sized
Cylindrical Droplets
b)
a)
Non Polar SAM
Non Polar SAM
Polar SAM
Polai r SAM
Figure B: SEM images showing perfect alignment and positioning of the SWNT at center
of the polar SAM. (a) Low magnification showing alternating polar (~1pm) and non-polar SAM
(2.5 im) on a large scale. (b) High magnification image of nanotubes at the center of the polar
SAM.
153
a)
b)
Figure B2: Comparison of the SWNT deposition guided by direct interaction between the
nanotubes and the SAM and that internal fluid flow. (a) Nanotubes suspended in organic
solvent (ODBC) deposited on SAM. Deposition occurs as networks only in polar SAM region.
(b) Nanotubes suspended lwt % in water with SDS deposited on the patterned area. Parallel
alignment and centerline positioning of individual SWNT.
154
Appendix C: Profiling variation of D/G and G peak perpendicular to
graphene edge
1950 1450 --- G
~~-
D/G X 2000
450
-2
0
2
4
6
8
10
Distance (pm)
Figure Cl: Profiling variation of D/G and G peak from graphene edge to bulk for
functionalized graphene (perpendicular to edge). Graphene edge is present in 0-0.5 [tm zone.
As the laser spot scans from -2 [tm to 1 ptm it crosses the edge as also suggested by the rising G
peak intensity. In the bulk region that (laser spot has no edge component) G peak intensity
stabilizes. D/G ratio reaches a maximum in the 0-0.5 ptm zone due to the higher reactivity of the
edges. In bulk graphene D/G stabilizes suggesting no role of edges in the bulk reactivity of
graphene.
155
..................
Appendix D: Chemical Functionalization of Graphene Devices
b)
2500
2000
2000
1%0/1500
1500
1000
1000
500
-g
500 -1
0
0
0.4
0.8
1.2
0
500
0.4
0.8
0.4
0.8
1.2
800
400
600
300
400
200
200
100
-
0
0
0
0.4
0.8
o
1.2
1.2
Figure D1: Resistivity and resistance Vs D/G ratio for pristine CVD graphene for 4bromobenzene diazonium salt. (a,b) Resistivity and (c,d) resistance change of graphene device
with increase in density of covalent defects. The covalent defects are introduced by chemical
functionalization of graphene. (a,c) devices have channel length 8pm and (b,d) have channel
length 14Rm. Each data series, as presented by distinct symbol, corresponds to a different
graphene device.
156
a)
b)
S1500 -
o
1500
x
1000 -
+
x
~500
*."
1
x
U 500
0
0
P4
0
0
0.25 0.5
0
-
0 0.25 0.5 0.75
1
0.75
T
c)
1
d
d) 600 *
A
+
300 x
200 -
U
A
xx
300il
-
-100
0
0
0
0.25
0.5
0.75
0
1
0.25
0.5
0.75
1
Figure D2: Resistivity and resistance Vs D/G ratio for pristine CVD graphene for 4bromobenzene diazonium salt. (a,b) Resistivity and (c,d) resistance change of graphene device
with increase in density of covalent defects. The covalent defects are introduced by chemical
functionalization of graphene. (a,c) devices have channel length 8[tm and (b,d) have channel
length 14 im. Each data series, as presented by distinct symbol, corresponds to a different
graphene device.
157
.......
.....
3000
3000 -
-
XM
2000
$0
1000
2000
-
Is
0.5
0
1
1.5
2
9)
200
0
0.5
1
I
I
1.5
2
' 1200
600
C.
I
d)
800
400
-t
D/G
D/G
c)
AA
1000 -
0
0
-
9A A
-
A A
A
o
-
A
-
.
S-4
0
P4
0
800
0.5
1
1.5
2
AA
400
0
0
0.5
D/G
D/G
Figure D3: Resistivity and resistance Vs D/G ratio for pristine CVD graphene for 4-(prop2-yn-1-yloxy)benzene diazonium salt. (a,b) Resistivity and (c,d) resistance change of graphene
device with increase in density of covalent defects. The covalent defects are introduced by
chemical functionalization of graphene. (ac) devices have channel length 8gm and (b,d) have
channel length 14tm. Each data series, as presented by distinct symbol, corresponds to a
different graphene device.
158
1500 -
*il
,.1000 .
1500 -
**
>1
1000
If
-
500 -
500
0)
I
i
0 0.25 0.5 0.75
I
I
D/G
400 -
600
: 300 200 X
100 -
S
0-
I
0 0.25 0.5 0.75
1
D/G
.
."
X
400
-
200
-
0
0 0.25 0.5 0.75
a
i
0
1
0a
i t
I
I
0.25 0.5 0.75
I
1
D/G
D/G
Figure D4: Resistivity and resistance Vs D/G ratio for pristine CVD graphene for 4nitrobenzene diazonium salt. (ab) Resistivity and (c,d) resistance change of graphene device
with increase in density of covalent defects. The covalent defects are introduced by chemical
functionalization of graphene. (ac) devices have channel length 8ptm and (b,d) have channel
length 14pm. Each data series, as presented by distinct symbol, corresponds to a different
graphene device.
159
.
.:.......................
-, -, - - - J. :- :UU:M::Mz
:::;- :: Z:;:::-:
a)
10
8
-o
S6
4
O"
2
0
600
400
800
1000
400
1200
600
800
1000
1200
Slope of Resistivity Vs D/G
Slope of Resistivity Vs D/G
Figure D5: Histogram of slope of Resistivity Vs D/G. (a) 4-bromobenzene diazonium salt.
(b) 4-(prop-2-yn-1-yloxy)benzene diazonium salt. The wide spread in slope magnitude for
different devices indicates Resistivity Vs D/G slope of graphene devices is independent of the
benzene diazonium species being covalently attached.
10
0.8
0.85
0.9
0.95
coefficient of determination (R2)
Figure D6: Histogram of coefficient of determination (R2) for linear fit of Resistivity Vs
D/G data.
160