ELECTRONIC STRUCTURE OF CARBON NANOTUBE SYSTEMS MEASURED WITH SCANNING TUNNELING MICROSCOPY

BY

DANIEL JAY HORNBAKER

B.S., Michigan State University, 1996 M.S., University of Illinois at Urbana-Champaign, 2000

THESIS

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics

in the Graduate College of the University of Illinois at Urbana-Champaign, 2003

Urbana, Illinois

iii

ELECTRONIC STRUCTURE OF CARBON NANOTUBE SYSTEMS MEASURED WITH SCANNING TUNNELING MICROSCOPY

Daniel Jay Hornbaker, Ph. D. Department of Physics

University of Illinois at Urbana-Champaign, 2003 Dr. Ali Yazdani, Advisor

Carbon fullerenes are unusually structured molecules with robust mechanical and electronic

properties. Their versatility is astounding; envisioned applications range from field emission

displays to impregnated metal composites, battery storage media, and nanoelectronic devices.

The combination of simple constituency, diverse behavior, and ease of fabrication makes these

materials a cornerstone topic in current research.

This thesis details scanning tunneling microscopy (STM) experiments investigating how

carbon nanotube fullerenes interact with and couple to their local environment. Scanning

tunneling microscopy continues to be a key method for characterizing fullerenes, particularly in

regards to their electronic properties. The atomic scale nature of this technique makes it

uniquely suited for observing individual molecules and determining correlations between locally

measured electronic properties and the particular environment of the molecule.

The primary subject of this study is single-wall carbon nanotubes (SWNTs), which were

observed under various perturbative influences resulting in measurable changes in the electronic

structure. Additionally, fullerene heterostructures formed by the encapsulation of C60 molecules

within the hollow interiors of SWNTs were characterized for the first time with STM. These

novel macromolecules (dubbed “peapods”) demonstrate the potential for custom engineering the

properties of fullerene materials.

iv

Measurements indicate that the properties of individual nanotubes depend sensitively on

local interactions. In particular, pronounced changes in electronic behavior are observed in

nanotubes exhibiting mechanical distortion, interacting with extrinsic materials (including other

nanotubes), and possessing intrinsic defects in the atomic lattice. In fullerene peapods, the

presence of interior C60 has a dramatic effect on the electronic structure of the composite

molecule that manifests as a pronounced spatial modulation in electron density at energies near

1 eV. Coincident with this modulation is the appearance of characteristic features in the

electronic band structure indicative of coupling between the unoccupied electronic states of the

component fullerenes. These results illustrate the important role local environment plays in the

behavior of nanotubes, and suggest the possibility of harnessing these effects to tailor nanotube

properties for specific functionality.

v

In memoriam…

Clifford James Adrian (1974-1992) and Richard John Adrian (1975-1998).

They were brothers to me.

And George (1983-1994); he was a good, good dog.

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Acknowledgments

This research was carried out as part of the experimental scanning tunneling microscopy

group headed by Dr. Ali Yazdani. I am tremendously grateful for the unique opportunity of

having been Dr. Yazdani’s first graduate student.

Michael Vershinin assisted in the early design and construction of the laboratory’s

centerpiece instrument, a low temperature, ultra-high vacuum scanning tunneling microscope.

Shashank Misra provided crucial design and construction input, and assisted in daily microscope

operation. Group postdocs Drs. Se-Jong Kahng and Franck Rose both contributed time to these

experiments.

The component of this project involving carbon nanotube peapods was a joint

collaboration with our colleagues at the University of Pennsylvania; thanks to Drs. David Luzzi,

Brian Smith, and Charlie Johnson for fabricating and characterizing the samples we studied, and

Drs. Gene Mele and Charlie Kane for developing a theoretical framework in which to interpret

our results.

Support for this research was provided by the U. S. Department of Energy through the

Frederick Seitz Materials Research Laboratory under contract DEFG-02-96ER4539, the National

Science Foundation through CAREER award NSF-DMR-98-75565, and the American Chemical

Society through the Petroleum Research Fund. All research in this thesis was conducted at the

Frederick Seitz Materials Research Laboratory at the University of Illinois in Urbana.

vii

Contents

Preface.................................................................................................................................x Chapter 1 Introduction........................................................................................................1

1.1 Reference...............................................................................................................1 Chapter 2 Background........................................................................................................2

2.1 Carbon Fullerenes..................................................................................................2

2.1.1 Buckyballs .................................................................................................3 2.1.2 Nanotubes..................................................................................................6

2.2 Scanning Tunneling Microscopy.........................................................................11

2.2.1 Principle of Operation..............................................................................12 2.2.2 Surface Topography.................................................................................15 2.2.3 Tunneling Spectroscopy ..........................................................................16 2.2.4 Atomic Manipulation...............................................................................19

2.3 Previous STM Measurements of Fullerenes........................................................19

2.3.1 STM of Buckyballs..................................................................................20 2.3.2 STM of Nanotubes...................................................................................21

2.4 References............................................................................................................24

Chapter 3 Experimental ....................................................................................................27

3.1 Instrumentation....................................................................................................27 3.2 Samples................................................................................................................33

3.2.1 Fabrication of Carbon Peapods................................................................34 3.2.2 Preparation for Measurement ..................................................................35

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3.3 STM Characterization of Samples.......................................................................40

3.3.1 Substrate Characterization.......................................................................42 3.3.2 Imaging and Spectroscopy of Nanotubes................................................43

3.4 References............................................................................................................47

Chapter 4 Unfilled Single-Wall Nanotubes......................................................................49

4.1 General Properties of SWNTs.............................................................................49 4.1.1 Bias Dependent Imaging..........................................................................49 4.1.2 End Caps..................................................................................................52 4.1.3 Strained Nanotubes..................................................................................52 4.1.4 STM-Induced Cutting..............................................................................55 4.1.5 Discussion................................................................................................56

4.2 Tube-Tube Interactions and Pseudogaps in Metallic Nanotubes........................57

4.2.1 Spectral Characterization of Pseudogaps ................................................58 4.2.2 Discussion................................................................................................61

4.3 Interactions with Adsorbates...............................................................................62

4.3.1 Common Adsorbates ...............................................................................62 4.3.2 Cobalt Dosing of Nanotubes....................................................................64 4.3.3 Discussion................................................................................................69

4.4 Stone-Wales Defects............................................................................................71

4.4.1 Theory......................................................................................................71 4.4.2 STM Characterization of a Stone-Wales Defect .....................................72 4.4.3 Discussion................................................................................................75

4.5 References............................................................................................................76

ix

Chapter 5 Nanotube Peapods............................................................................................79 5.1 STM Imaging of Peapods....................................................................................79 5.2 Tunneling Spectroscopy of Peapods....................................................................82 5.3 STM-Induced Motion of Encapsulated C60 .........................................................84 5.4 Theory..................................................................................................................88 5.5 Discussion............................................................................................................90 5.6 References............................................................................................................91

Chapter 6 Summary ..........................................................................................................92 Appendix A Derivation of the (n-m) = 0(mod 3) Condition ............................................93 Appendix B Notes on Data Acquisition and Processing..................................................97 Vita...................................................................................................................................103

x

Preface

Throughout the past decade a vast amount of literature has accrued on the subject of

carbon fullerenes. In writing a thesis in which fullerenes are a central topic, one must take care

to avoid getting caught up in details not germane to the work at hand. Consequently, I have

avoided foraying into areas of fullerene research that are only marginally related to the

experiments described here. Nanotube research is currently advancing at a rapid pace; I have

included as much up-to-date information as possible.

For readers seeking a general overview of the subject, I recommend Science of Fullerenes

and Carbon Nanotubes (Dresselhaus, Dresselhaus and Eklund, Academic Press, 1996) and

Carbon Nanotubes: Synthesis, Structure, Properties, and Applications (Dresselhaus, Dresselhaus

and Avouris, Springer-Verlag, 2001). These books reflect the breadth of the subject and are

must-have references for the serious fullerene enthusiast. A good starting point for learning

more about the technique of scanning tunneling microscopy is Introduction to Scanning

Tunneling Microscopy (Chen, Oxford University Press, 1993).

1

Chapter 1 Introduction

Since their discovery by Iijima in 1991 [1], carbon nanotubes have tantalized researchers with

their possibilities. Despite having a simple chemical makeup, nanotubes exhibit a remarkably

complex mix of physical properties, including extreme mechanical resilience, exceedingly large

aspect ratios, and superior field emission properties. Of particular technological importance is

that nanotubes come in both semiconducting and metallic varieties, making them a natural basis

for developing nanoelectronic applications.

This thesis details experiments performed on nanotube systems using scanning tunneling

microscopy (STM). The aim is to examine the interactions of nanotubes with local environments

on an atomic scale and determine how these interactions affect nanotube properties. These

experiments culminate in the investigation of nanotube “peapods,” a novel fullerene system that

demonstrates the importance and potential of inter-fullerene interactions.

The text is organized in a straightforward manner. Chapter 2 introduces the background

material required for the subsequent chapters. Chapter 3 details the instrumentation, materials

and procedures. Chapter 4 presents results and analysis of experimental measurements of single-

wall nanotubes. Chapter 5 focuses on investigations of peapod heterostructures, with an

emphasis on how electronic coupling between constituent fullerenes results in observation of

new phenomena. Finally, Chapter 6 provides a brief summary of the findings and a prospectus

for future work.

This thesis is written to be reasonably self-contained. Several basic physical concepts are

reviewed for the reader, and illustrations are abundant. A significant fraction of STM data

comes in the form of images, and this is reflected in the numerous figures appearing in the

document. References are cited at the end of each chapter, and are cited anew in each chapter

they appear for simplicity.

1.1 Reference [1] S. Iijima, Nature 354, 56 (1991).

2

Chapter 2 Background This chapter introduces background material necessary for interpreting the results presented in

subsequent chapters. A brief history and characterization of carbon fullerenes is presented,

followed by an introduction to the technique of STM. The chapter concludes with a survey of

previous STM measurements of fullerenes.

2.1 Carbon Fullerenes

Carbon is the sixth element in the periodic table, with a ground-state electronic configuration

1s22s22p2. Because the second-level valence states are half-filled, bonding between carbon

atoms can occur in multiple ways. Of the various forms of solid carbon, the two most abundant

allotropes are diamond and graphite (Fig. 2.1).

Diamond is composed of carbon organized into a 3-dimensional tetrahedral array

dominated by sp3 orbital hybridization (Fig. 2.2). It is renowned for its extraordinary hardness,

and is an electrical insulator with a band gap ∼5.5 eV in width. Under ambient conditions its

lattice structure is only metastable, but a large activation energy barrier slows the decay rate into

the lower-energy graphite state to geologic time scales.

Figure 2.1: Allotropes of carbon. Some are more popular than others.

3

Graphite consists of a stacked array of 2-dimensional carbon sheets with a hexagonal

lattice structure. The relatively weak inter-planar bonding allows the sheets to glide easily across

one another, making graphite a good lubricant. The in-plane atomic bonding is sp2 in character,

while the out-of-plane pz orbitals form a band structure that lends graphite its semimetallic

conduction properties. The electronic structure of graphite has important consequences for the

conduction properties of carbon nanotubes.

2.1.1 Buckyballs

While the possibility of a stable closed-cage molecular structure for carbon was first suggested in

1970 [1], the existence of fullerenes was not verified experimentally until 15 years later [2].

Laser ablation of a graphite target was used to create carbon clusters. Mass spectra of the

resultant vapor revealed the synthesis of molecules in two main groups – rings consisting of 10-

30 atoms, and larger molecules with predominantly 60 and 70 member atoms [3]. Researchers

soon theorized that these high-mass molecules possessed a closed-cage configuration. The name

“ fullerene” was coined after R. Buckminster Fuller, an architect renowned for his construction of

geodesic domes resembling the structure of these molecules (Fig. 2.3).

1.40 Å

1.46 Å

Figure 2.3: Patent drawing for a geodesic dome (left) and a ball-and-stick model of a C60 molecule with nonequivalent C-C bonds highlighted (right). Note the similarity in structure.

Figure 2.2: Illustration depicting types of valence orbital hybridization in carbon (from ref. 1). Unshaded lobes denote primary bond directions.

4

The fullerene lattice is similar to the hexagonal graphite lattice in that it consists of a

2-dimensional surface. To create large curvature in a graphene sheet, the substitution of

pentagons for hexagons is required. Geometrically, there are multiple arrangements that form a

closed structure, but Euler’s theory for polyhedra dictates that exactly 12 faces of the cage must

be pentagonal, with any additional number of hexagonal faces. Thus, the smallest possible

fullerene (C20) is composed solely of 12 pentagons. But the curvature induced by the pentagons

comes with a price in the form of strain energy (the sp2 bonds are bent out-of-plane, resulting in

significant sp3 character). This penalty is minimized by separating the pentagons in the lattice as

much as possible. The smallest fullerene in which no two pentagons are adjacent is C60. The

structural stability of C60 makes it the most abundant product of any fullerene growth process,

typically 3-6 times more likely than the next most abundant product, C70.

The C60 molecules (often referred to as “buckyballs” ) are composed of 12 pentagonal and

20 hexagonal faces in a soccer-ball arrangement. The carbon bonds come in two varieties:

single bonds along the 60 pentagonal edges, which measure 1.46 Å in length, and 30 electron

rich double bonds between adjacent hexagons, which are 1.40 Å in length [4]. The mean

molecular diameter as measured with NMR is 7.10 Å [5], consistent with the expected

geometrical diameter of 7.09 Å when considering the atoms as points.

The electronic structure of C60 can be accurately approximated by considering its

icosahedral symmetry. Each carbon atom contributes four valence electrons to the molecular

structure. The σ-bonded sp2 electrons can be safely neglected as core-level molecular states,

leaving 60 radially-oriented pz orbital electrons to form the valence states. The irreducible

representations of the icosahedral point group are used to determine the appropriate molecular

orbital eigenfunctions. The spherical shape of C60 suggests an approximation of these molecular

orbitals based on spherical harmonics Y,m. Since each angular momentum state can

accommodate 2(2 +1) electrons, the first 50 electrons completely fill all states up to = 4,

leaving 10 electrons for the 22 = 5 states.

Relative energy splittings within each level can be determined using a variety of

computational methods. The lowest energy = 5 states belong to the 5-fold degenerate hu

representation. These states account for the remaining 10 electrons, and are the highest occupied

molecular orbitals (HOMOs) in the ground state. The lowest unoccupied molecular orbitals

5

(LUMOs) are t1u states (Fig. 2.4), which are experimentally observed to reside ∼1.9 eV above the

hu levels in energy [8]. The t1u molecular orbitals have the character of atomic p orbitals in that

they are 3-fold degenerate and transform into one another under rotations about the [111] axis.

In contrast, the hu orbitals have transformation properties resembling atomic d orbitals.

In bulk, C60 forms a molecular solid with a face-centered cubic crystal structure at room

temperature held together by van der Waals attraction. The nearest-neighbor distance is 10.02 Å,

with an intermolecular separation (2.92 Å) similar to the spacing between layers in graphite

(3.35 Å). Due to the relatively weak nature of van der Waals interactions, the constituent

molecules rotate freely at room temperature. As the temperature is lowered below 260 K,

rotations begin to freeze out and the buckyballs orient themselves relative to one another, leading

to a lowering of the crystal symmetry to that of a simple cubic structure.

The electronic structure of the solid is composed of bands derived from the molecular

orbitals of the individual buckyballs. The undoped solid is a semiconductor with a 1.5 eV band

gap between the hu-derived valence band and the t1u-derived conduction band, which possess

fairly narrow bandwidths of only ∼0.4 V [9]. Doping of C60 solids with alkali metal, alkali earth,

or other elements can significantly change the conduction properties, and in some cases even

result in the onset of superconductivity [10].

Exposure to ultraviolet light or hydrostatic compression of solid C60 can lead to

molecular polymerization. The bonding mechanism is the combination of parallel double bonds

on adjacent molecules into a four-member ring (Fig. 2.5) [11]. One effect of this reaction is the

reduction of the intermolecular spacing from 10 to 9 Å.

Figure 2.4: Diagram of the wavefunction for the t1u ( = 5) molecular orbital calculated using First-Principles Molecule Dynamics method (from ref. 7). Colors denote different signs of the wavefunction. This is the lowest unoccupied molecular orbital in C60. Its odd parity and 3-fold degeneracy make it very similar in character to atomic p orbitals.

6

2.1.2 Nanotubes

While C60 is the smallest fullerene possessing robust structural stability, larger fullerenes can be

formed by adding rings of hexagons around the diameter to form capsule-shaped molecules

(Fig. 2.6). As more rings are added, the capsule becomes increasingly longer while maintaining

a fixed diameter. Once the limit of exceedingly large length-to-width ratios is reached, the realm

of the carbon nanotube is entered.

Ideally, nanotubes are seamless cylinders composed of hexagons and terminated at either

end by hemispherical half-fullerenes. One can envision them as being formed from a graphene

sheet rolled onto itself (Fig. 2.7). The vector Ch = na1 + ma2 that connects equivalent atomic

positions in the unrolled sheet is called the chiral (or wrapping) vector, often denoted as an

integer pair (n, m). Not all the ways of rolling a graphene sheet produce a unique tube structure;

a naming convention is adopted in which n

m

0. This convention uniquely identifies every

possible nanotube, including its diameter D = 3 ac-c (n2 + nm + n2)1/2 / as measured from the

atomic centers (ac-c being the nearest-neighbor atomic distance, 1.421 Å for graphite).

(5, 5) Nanotube

C60 C70 C80

Figure 2.6: A progression of fullerenes culminating in carbon nanotubes (adapted from ref. 12).

Figure 2.5: Diagram of a C60 dimer. Polymerization is an activated process, induced by exposure to such things as pressure or light.

7

The chiral angle is defined as = tan-1[ 3 m / (2n + m)], and is the screw angle formed

by the hexagonal chains in the a1 direction relative to the wrapping vector. Tubes with indices

(n, 0) are traditionally called “zigzag” tubes and have = 0º, meaning the hexagonal chains form

closed loops around the circumference (see Fig. 2.8). In the other extreme, (n, n) “armchair”

tubes have a 30º chiral pitch, resulting in the rows of hexagons oriented in the a2-a1 direction

being parallel to the tube axis. Tubes not falling into either of those two classes are simply

called “chiral” tubes, and have 30º > > 0º.

Tubes can be grown singly or nested inside one another in a multi-wall arrangement, but

the basic unit is the single-wall tube. As with fullerenes in general, there are several methods for

fabricating nanotubes. The most common methods for producing appreciable quantities of high-

purity nanotube material have been electric arc-discharge between catalyst-impregnated carbon

rods [13] and pulsed laser vaporization of a graphite target [14]. More recent work using

chemical vapor deposition [15] of carbon vapor over a substrate with catalyst particles on its

surface has shown great promise for controlled growth of nanotube networks, and may be a

technique useful for device fabrication. While nanotubes come in a wide range of diameters,

typical size distributions are peaked around 14 Å regardless of the method of fabrication [13-15].

(5, 5)

a1

a2

(7, 3)

(9, 0)

Ch

θθθθ

Figure 2.7: Structural relation between a graphene sheet and a nanotube. The vectors a1, a2 form a basis pair for the graphene lattice. The chiral vector Ch = n a1 + m a2 is specified by the ordered pair (n, m). By limiting the chiral angle θ to between 0º and 30º, every value of Chdefines a unique nanotube.

8

Like their physical structure, the electronic structure of nanotubes can be approximated

from the rolled-graphene-sheet model. Strictly speaking, graphene is a conductor since no

energy gap exists between the conduction and valence bands. Compared to typical metals,

however, graphene is a poor conductor owing to a vanishingly small bandwidth at the Fermi

energy, as seen in a plot of the first Brillouin zone (Fig. 2.9).

When the sheet is rolled into a closed cylinder, a periodic boundary condition is imposed

along the direction of the chiral vector. This results in quasi-one-dimensional electronic states

that are azimuthally quantized while remaining unconstrained in the axial direction. Thus, the

states of the nanotube are represented in reciprocal space by the intersection of the 2-dimensional

graphene Brillouin zone with a series of parallel lines representing the azimuthal subbands. It

follows that there are two distinct cases for the electronic structure of nanotubes (Fig. 2.10). If a

Fermi point is an allowed state of the nanotube, then the valence and conduction bands will

adjoin and the tube will exhibit metallic conduction. Otherwise, there will be an energy gap

between the bands, and the tube will be semiconducting. The chiral indices (n, m) can be used to

determine the type of any particular tube; when the quantity (n - m) is an integer multiple of 3 the

tube will have a (nominally) metallic density of states (DOS) (a derivation of this condition is

provided in Appendix A). An obvious consequence of this condition is that a third of all

conceptually possible tubes should be, to first order, metallic.

(5, 5) ‘Armchair ’

(7, 3) ‘Chiral’

(9, 0) ‘Zigzag’

Figure 2.8: Examples of different nanotube structures.

9

The energy spacing of the azimuthal subbands of a nanotube is directly related to its

diameter D [16]. In semiconducting tubes, the band gap is given by Egap = 2γ0ac-c /D, where γ0 is

a parameter representing the nearest-neighbor overlap integral in a tight-binding scenario (fits to

experimental results place γ0 ≈ 2.6-2.8 eV, while calculations for graphite give γ0 = 3.13 eV

[17, 18]). Gap widths for the most commonly observed tubes are ≈0.53 eV. In metallic tubes,

the first subband plateau spans a width of Emetallic = 6γ0ac-c /D around the Fermi energy, with

typical values being ≈1.6 eV. In both types of tubes the spacing between successive subbands is,

to first order, E = 3γ0ac-c /D (≈0.8 eV) [19]. The 1-dimensional nature of nanotube electronic

states results in the appearance of sharp resonance peaks (van Hove singularities) in spectral

measurements at the onset of each subband (Fig. 2.11).

kx

ky

K

ΓΓΓΓ

Allowed wavevectors for a (7, 3) tube

K'

kx

ky

K

ΓΓΓΓ

Allowed wavevectors for a (5, 5) tube

K'

Figure 2.10: Allowed electronic states (dashed lines) of two different nanotubes, superimposed upon the graphene Brillouin zone to illustrate the two distinct types of electronic behaviors. The (5, 5) tube is metallic (K/K' points are allowed states), while the (7, 3) tube is semiconducting (K/K' points forbidden).

kx

ky

K

ΓΓΓΓ

K'

Figure 2.9: Brillouin zone of a graphene sheet. Graphene is a zero gap semimetal with a Fermi surface consisting of six points.

10

While arguments based on “ rolling” (i.e. imposing periodic boundary conditions on) a

graphene sheet provide largely accurate results, there are a few important corrections to consider.

Surprisingly, Peierls instability in metallic nanotubes is not one of these corrections. Peierls

distortion in an ideal 1-dimensional metal is a static lattice distortion which lowers the overall

energy of the system [20]. A consequence of this distortion is the opening of a band gap at the

Fermi energy. However, the cylindrical shape of nanotubes makes the energy cost of forming

lattice distortions around the entire circumference high, resulting in a greatly suppressed band

gap that can be safely neglected to temperatures well below that of liquid helium [21].

One effect of forming a cylinder from a graphene sheet is the introduction of curvature

into the carbon lattice, which gives rise to a small relative angle between adjacent pz orbitals.

The deviation from ideal sp2 bonding results in a shifting of the Fermi points from their graphene

positions. This manifests as a small band gap on the order of 10 meV opening at the Fermi

energy in nominally metallic tubes [22]. However, it should be noted that in the case of the

metallic (n, n) armchair nanotubes, the perturbation in the location of the Fermi points happens

to occur along the direction of the allowed states of the tube, making this class of nanotube truly

metallic.

Another important interaction to consider is that between tubes within a bundle.

Nanotubes “stick” to one another via van der Waals attraction, much like the way individual

graphene layers bond together in graphite. Ropes consisting of many tubes preferentially align

Figure 2.11: Ab initio calculation of electronic structure for various metallic and semiconducting nanotubes (from ref. 19). The onset of each azimuthal subband is demarcated by a van Hove singularity.

11

into a close-packed triangular lattice. Interactions between adjacent tubes break local

symmetries, leading to band repulsion and a depletion of electron states near the Fermi energy in

armchair nanotubes. This is characterized by the appearance of a pseudogap in the electronic

DOS with a typical width on the order of 150 meV (Fig. 2.12) [23].

2.2 Scanning Tunneling Microscopy

Scanning tunneling microscopy was initially developed by Binnig and coworkers at the IBM

laboratory in Zürich in 1981 [24]. While the principles on which STM is based had been known

for some time, it was widely believed that the development of a practical instrument was

unfeasible. Not only was such an instrument possible, it performed far better than could be

reasonably expected. The STM demonstrated an imaging resolution an order of magnitude better

than initial predictions. It would take several years for theories to emerge that would shed light

on the origin of this technique’s remarkable spatial resolution.

Since the initial experiments of Binnig et al. [24, 25], the field of STM has experienced

rapid growth. Microscopes are currently available in several commercial models designed for

performing experiments on a variety of samples in many different environments. However, the

best instruments continue to be those built by the user. The details of the custom instrument used

in this thesis appear in Chapter 3; what follows is a description of the basic concepts and modes

of operation involved in STM.

Figure 2.12: Calculated electronic structure for a rope of (10, 10) armchair nanotubes (from ref. 23). Inter-tube interactions lead to a depletion of electronic states near the Fermi level.

12

2.2.1 Pr inciple of Operation

The fundamental physical phenomenon on which STM is based is the quantum mechanical

tunneling of electrons through a potential energy barrier. This process is a key prediction of

quantum theory and is described in detail in introductory quantum mechanics textbooks (for

example, see chapter 6 of E. Merzbacher, Quantum Mechanics, John Wiley & Sons, New York,

1998). For simplicity, consider the 1-dimensional case of an electron incident upon a localized

potential energy barrier (Fig. 2.13). In classical mechanics the outcome is straightforward; if the

height of the barrier exceeds the total energy of the electron, then the electron will be reflected.

In quantum mechanics, however, the electron is described by a spatially extended wavefunction

that satisfies Schrödinger’s equation. At the barrier interface, the wavefunction amplitude

decays exponentially into the classically forbidden region. If the barrier is not too wide or tall,

the wavefunction can penetrate completely through the barrier with a value significantly different

from zero, meaning that the electron will have some probability of appearing on the other side.

If it does, then the electron is said to have “ tunneled” through the barrier.

In the laboratory, this situation is realized when two conducting materials are brought in

close proximity to one another, separated by a narrow non-conducting region (vacuum or an

insulating material) (Fig. 2.14). This is known as a tunnel junction. In the absence of external

perturbations, electrons are just as likely to tunnel in either direction, resulting in zero net

transfer. Applying a voltage V across the junction breaks the symmetry of the barrier, making it

V > E

V > E

E

Classical

E

‘tunnel’

Quantum

Figure 2.13: Electron tunneling in one dimension. Classically, the energy barrier confines the electron to the left. In quantum mechanics, the electron has some probability of “tunneling” through the barrier and appearing on the right side.

13

easier for electrons to tunnel across in one direction. In macroscopic systems consisting of large

numbers of charge carriers, instead of the probability of individual electrons tunneling through

the barrier, the rate at which electrons tunnel is considered. This is referred to as the tunneling

current I.

The functional dependence of the tunneling current on the barrier parameters follows

directly from the exponential decay of a wavefunction in a classically forbidden region. The

width of the barrier is taken to be the separation distance W (in Å) between the conductors, and

its height is the work function (defined as the amount of energy required to eject an electron

from a material into vacuum) of the conductor on the high-bias side of the junction. In terms of

these parameters, the tunneling current I is proportional to V exp (-1.025 1/2 W). Accordingly,

for typical metals in which ≈ 4 eV, the tunneling current is reduced by a factor of ≈7.4 for each

angstrom increase in separation distance. This characteristic exponential dependence of the

tunneling current on the separation distance was experimentally verified fully a decade before

the advent of STM [26].

It was realized that the sensitivity of the current through a tunnel junction to the

separation distance can be used to obtain information concerning the microscopic structure of the

surface of conducting samples. This requires the creation of a junction with a controllable

separation distance using a localized probe. The ideal probe is a thin wire whose end has a

radius of curvature that is relatively small and uniform. Piezoelectric ceramics are used to

achieve sub-angstrom control of the tip position relative to the sample surface. Early attempts to

create a working device suffered greatly from instability induced by mechanical vibrations. The

Tip SampleBarr ier

EfeV

ϕϕϕϕtip

ϕϕϕϕsample

W

Figure 2.14: A one-dimensional tunnel junction. Biasing the junction with a voltage V creates a net flow of electrons across the barrier.

14

extreme sensitivity to small changes in probe position makes decoupling the instrument from

ambient environmental noise of paramount importance (in fact, STM tunnel junctions can serve

as ultra-sensitive vibration detectors).

Binnig and coworkers were the first to achieve acceptable working conditions by

magnetically levitating the head of their microscope on a superconductor. One of the first

images obtained with this instrument was of the (111) surface of silicon, published in 1983

(Fig. 2.15) [25]. This result represented a remarkable achievement, resolving a long standing

debate regarding the precise structure of this surface and heralding the arrival of a new

experimental technique with the ability to probe physics on an atomic scale.

A schematic diagram of a modern STM device is shown in figure 2.16. The tip position

is controlled by three mutually orthogonal piezoelectric transducers (in practice, a cylindrical

tube piezo with outer electrodes arranged into quadrants is used). The x-y piezos are computer

controlled, allowing rastering of the tip to acquire image scans over a square or rectangular area.

Depending on the mode of operation, the z piezo is either held fixed during scanning or

controlled by a feedback loop that attempts to maintain a constant tunneling current as the tip

changes location. Junction bias voltages (ranging from a few millivolts to several volts) are

applied to the sample, and a current amplifier is used to measure the current flowing across the

junction (usually tens of picoamps to several nanoamps). The microscope head, consisting of the

tip-sample assembly, is constructed to be as rigid as possible to inhibit uncontrolled relative

motion between the tip and sample. The head is buffered from the environment with some type

of vibration isolation, such as magnetically-dampened springs.

Figure 2.15: First glimpse of the atomic structure of a surface using STM (from ref. 25). This image resolved a long standing debate by revealing the 7x7 reconstruction of the silicon (111) surface.

15

2.2.2 Sur face Topography

The most common mode of operation for an STM is constant current imaging

(Fig. 2.17). In this mode, the tip is rastered across the sample as a feedback control loop

compares the measured tunneling current to a fixed setpoint value. If the measured current is

less than the setpoint, the loop responds by moving the tip closer to the sample. If the measured

current is greater, the tip is moved back. The computer records the change in tip displacement

Z as a function of position (x, y), which can be plotted as a topographic map of the surface

(Fig. 2.18). Generally, this type of measurement maps contours of constant integrated electronic

density; however, these contours often reflect the underlying atomic structure of the surface.

Modern instruments can routinely resolve structures of about 1 Å laterally and 1 pm

perpendicular to the surface.

I setpoint

Trajectory

Tip

Sample

Z0

Z0

∆∆∆∆Z

R(ωωωωt)

Figure 2.17: STM operating in the constant current imaging mode. This mode generates a topographic map ∆Z(R).

Tip

Sample

Controlled Env ironment

Vibration Isolation

Current Amplif ier

Piezo Voltage

Bias Voltage

System Control

Figure 2.16: Block diagram of an STM.

16

Occasionally, large features on a surface (such as step edges) can overwhelm the small

asperity features (such as corrugations associated with the atomic lattice) in the plotted image. In

this case, instead of plotting the data as a topographic map Z(x, y), it can be plotted as a

directional derivative map d[ Z(x, y)]/dx (hereafter shortened to dZ/dx). This has the effect of

“ flattening” the image to bring out the small asperity features (Fig. 2.19).

Another type of imaging mode is constant z imaging, in which the z piezo voltage is held

fixed while the tip is rastered across the surface. In this mode, the measurement variable is the

tunneling current, which changes as the separation distance and local electronic properties

change. An inherent danger in this type of measurement is that the tip may “crash” into objects

which protrude from the surface of the sample, such as a step edge. It has the advantage, though,

of allowing for much faster scanning speeds since the reaction time of the feedback loop does not

have to be accounted for.

2.2.3 Tunneling Spectroscopy

While its ability to produce beautiful atomic scale images of surfaces is what made STM a well-

known and widely-used technique, arguably the most important mode of STM measurement is

spatially-resolved scanning tunneling spectroscopy (STS).

Figure 2.18: A constant current image of a silicon (111) surface acquired using an Omicron STM (Center for Microanalysis of Materials, University of Illinois @ Urbana-Champaign). The image spans an area of 150 Å x 150 Å. The observed atomic contrast represents approximately 1 Å of tip height difference.

17

A starting point for interpreting STS measurements is the many-body model for current

across a 1-dimensional tunnel junction developed by Bardeen [27]. Adapting Bardeen’s

approach to the STM geometry begins by considering the wavefunctions of the independent tip

and sample systems (Fig. 2.20) and computing the overlap integral across a separation surface

between the two. Measuring energy relative to the Fermi energy (i.e. EF = 0), the resulting

expression for the tunneling current is

( ) ( ) [ ] [ ]∞

∞−

−−−= εεεεεπdMeVfeVf

eI TipSample 24 DDR

, (2.1)

where e is the electron charge, V is the bias voltage, R is a position vector on the surface, M is

the quantum mechanical tunneling matrix element, f(E) is the Fermi distribution function

describing the fractional occupancy of an electronic state with energy E at a given temperature,

and D[E] is the electronic local density of states (LDOS) in the sample or the tip as a function of

energy E.

For measurements acquired at low temperature, the Fermi distribution functions can be

approximated by step functions. This changes the indefinite integral into a definite one spanning

the energy range (0, eV). Considering that STM tips are typically chosen to be simple metals so

that their DOS near the Fermi energy is essentially constant, the expression (2.1) can be

simplified to

[ ] −∝eV

Sample dMeVI0

2 εεRD . (2.2)

Figure 2.19: Comparison of a topographic map (left) to a directional derivative map (right). The images are 256 Å x 512 Å acquired on a clean gold (111) surface. The derivative map brings out small asperity features at the expense of relative height information.

18

The final approximation to consider is one in which the matrix element M is independent

of energy near the Fermi level. While not a valid approximation in some systems, in many cases

it is not unreasonable. In this case, the matrix element can be removed from the integral, leaving

a definite integral over the LDOS of the sample. Applying the fundamental theorem of calculus,

the final relationship is obtained,

( ) [ ]eVVI Sample

RD∝εd

d, (2.3)

which states that the LDOS of the sample at energy eV is directly proportional to the differential

tunneling conductance dI/dV measured at bias voltage V. Thus, STS provides a method for

directly investigating the spatial distribution of a fundamental materials property (the LDOS) at

the surface of a conducting material.

In practice, tunneling spectra are measured in one of two ways. The simplest method is

to hold the tip position fixed and record the current as the bias voltage is swept across the range

of interest. The resulting I-V curve can then be differentiated by numerical means. A more

direct method of measuring the differential tunneling conductance is to apply a small sinusoidal

modulation to the bias voltage and use a lock-in amplifier to detect the in-phase current response

as the bias voltage is swept (again, with the tip position held fixed). Examination of the Fourier

TipSample

Bar

rier

Ef

eV

DDDDRSamp le[E] DDDDTip[E]

Figure 2.20: Conceptual illustration for interpreting tunneling spectroscopy measurements. The vertical axis is energy and the density of states for the sample (tip) is plotted on the far left (right). Shaded regions represent occupied electronic states at absolute zero.

19

series expansion for the time-varying current I[V(t)] reveals that this quantity, which is the

coefficient of the first harmonic component, is precisely dI(V)/dV.

2.2.4 Atomic Manipulation

It has been known from the inception of STM that interactions between the tip and surface can

be an important factor in tunneling experiments. Most often, attempts are made to operate the

microscope in a regime where tip effects have negligible impact on measurements. But the

possibility exists of operating in the other extreme - using tip interactions to alter the surface

environment in a controlled manner to investigate fundamental physics on an atomic scale.

STM manipulation of surface adsorbates is well established [28]. It is not unusual for

adsorbates which bond weakly to a surface to exhibit tip-induced lateral displacements during

imaging. There are numerous interactions that can lead to changes in adsorbate

position/orientation, such as van der Waals attraction, electric field effects, excitations from

inelastic tunneling, dipole-dipole interactions, and chemical bonding to the tip. These

interactions allow the STM to perform experiments not easily accessible to other techniques,

such as probing the interactions between adatoms as a function of separation distance [29] and

observing the step-by-step evolution of chemical reactions [30]. One experiment which

exemplifies the potential inherent in atomic manipulation is the nanofabrication of elliptical

“corrals” of cobalt adatoms on a copper surface, resulting in the spatial confinement of the

2-dimensional surface electronic states [31].

2.3 Previous STM Measurements of Fullerenes

Scanning tunneling microscopy has been a cornerstone technique in elucidating the physics of

fullerenes, especially carbon nanotubes. In turn, nanotubes are an ideal system for demonstrating

the versatility of STM. The ability to probe an isolated tube and correlate electronic

measurements to atomic structure and local environment provides a powerfully comprehensive

method for direct verification of theoretic predictions. This section sets the groundwork for the

results which will be presented in Chapters 4 and 5 by providing a brief survey of previous STM

experimental results on fullerenes, with a particular emphasis on measurements of single-wall

carbon nanotubes.

20

2.3.1 STM of Buckyballs

The bulk of STM experiments on C60 molecules involve investigations of epitaxial thin film

growth. A review spanning work up to 1996 can be found in reference 32. Understanding

growth modes and substrate bonding mechanisms is seen as an important step in developing

useful applications for fullerene solids. STM has been used primarily to track adsorption sites

and layer ordering as a function of substrate composition, base crystal growth plane, and

temperature. It has revealed vast differences in surface interactions across substrates, from van

der Waals or ionic bonding on metal surfaces to covalent carbide bonding on semiconductors. In

extreme cases, the presence of C60 on some metal surfaces leads to elaborate mass transport

reconstructions at the interface layer.

A few studies have obtained high resolution imaging that reveals intra-molecular

structures within individual fullerenes [33-35]. A key factor in acquiring such images is the

freezing of rotational freedom through surface interactions. Typically, observed features do not

directly reflect the atomic structure of the fullerene, but rather reveal the electronic state

symmetries of the molecule-substrate system. Among the various types of patterns seen in

images are three-fold symmetric, donut-like, and striped. Calculations have shown that a number

of factors determine the exhibited pattern, such as adsorption site, substrate bonding mechanism,

angular orientation of the fullerene cages, and tunneling bias polarity. This illustrates the

sensitivity of STM to electronic effects not necessarily related to molecular structure.

Recently, images resolving the individual C-C bonds (and thus the atomic structure) of

buckyballs were observed [36]. These were obtained by depositing C60 on top of a buffer layer

of alkylthiol, to which the fullerenes interact so weakly that their electronic structure remains

essentially unaltered from that of the free molecule.

While the results of spectroscopic measurements depend greatly on the interaction

between the fullerenes and the supporting substrate, it is not unusual for STM data to exhibit

peaks in the tunneling spectra near sample bias voltages of -0.8 V and 1.0 V, corresponding

closely with the respective energies associated with the hu HOMO and t1u LUMO orbitals of the

free molecule [37].

Other results merit mention in passing. On surfaces for which C60 does not form strong

chemical bonds, STM has been able to push individual molecules around or pick them up. Tip-

adsorbed buckyballs have been shown to improve imaging resolution on graphite, whose surface

21

is often difficult to image [38]. STM has also been used to stimulate polymerization in C60 films

via electron irradiation [39], and to differentiate C60 dimers and trimers from unpolymerized

buckyballs within the surface of an ordered film [40].

2.3.2 STM of Nanotubes

Carbon nanotubes have rapidly become a leading candidate for molecular electronic device

applications. Key to their development is a complete understanding of how individual nanotubes

react to various conditions and perturbations. STM is at the forefront of these investigations

because of its unique ability to directly correlate electronic properties to local environment.

Experiments have been performed probing interactions between nanotubes and substrates,

adsorbates, mechanical stress, structural defects, and even other nanotubes.

Initial attempts to identify the structure of individual nanotubes with STM [41] revealed

that although atomic-scale resolution was readily achievable, the relatively large height and

curved surface of the tube complicates the interpretation of the topographic images [42].

Nominally, one should be able to identify the chiral indices (n, m) of a given tube by measuring

its diameter and the chiral angle of its atomic lattice. This is not as straightforward as it might

seem. The cylindrical shape of the tube leads to significant distortion in the appearance of the

atomic lattice in topographic images. This distortion takes the form of a stretching of the lattice

perpendicular to the long axis of the tube, and is the result of lateral tunneling between the tube

and tip. Tube diameters appear exaggerated in images because of tip-shape convolution effects,

while the height profile routinely underestimates tube size, possibly the result of mechanical

deformation induced by tube-substrate or tube-tip interactions. Extrinsic factors such as twists or

bends in the tube can also contribute to tube misidentification.

Besides the geometric distortions, topographic measurements of tubes often reveal

unusual patterns that are not directly indicative of the underlying hexagonal atomic structure. A

similar situation exists in the imaging of planar graphite surfaces [43], though it is not clear to

what extent the two are related, if at all. Theoretical calculations indicate that scattering of

electrons from defects or tube ends can lead to asymmetric images which change pattern with

bias polarity and magnitude [44].

Experimental confirmation of fundamental nanotube properties was achieved with the

acquisition of spectroscopy measurements in conjunction with topographic imaging [17, 18].

22

Individual metallic and semiconducting nanotubes were clearly distinguished, and comparison of

measured spectra with expected band structure provided a complimentary method for verifying

the chiral indices determined from imaging. Plots of gap width in semiconducting tubes versus

tube diameter D followed closely the expected 1/D dependence. Sharp resonance peaks

appearing at the onset of each energy band confirmed the 1-dimensional nature of the electronic

structure, and the energy spacing between peaks was used to derive an empirical value for the

tight-binding nearest-neighbor overlap integral γ0 in close agreement with calculated values.

Measurements of some nominally metallic nanotubes revealed the existence of small

band gaps in the DOS on the order of 10 meV in width [45]. These arise from curvature effects

that reduce the pz orbital overlap of neighboring sites around the tube circumference. Tubes of

this type are more accurately described as small gap semiconductors. However, these gaps are

not observed in the (n, n) armchair tubes.

An important class of intrinsic defect in chemically pure tubes is topological defects, such

as the substitution of hexagons with pentagons and heptagons. These arise in response to

mechanical strain, and can affect transport properties through electron scattering. The presence

of pentagons in hemispherical end caps create localized electronic states measurable with STM

[46]. Computational models of possible end cap structures reveal that the energies of these local

states depend upon the spatial arrangement of the pentagons. This allows the STM to reveal

information about the atomic structure of an end cap despite not being able to directly image it.

Measurements have also determined that lattice defects can allow for a change in

chirality within a single tube [47]. Such multi-chiral tubes are termed intramolecular junctions,

and can be thought of as two tubes of different chirality being fused together with

pentagon/heptagon defects. These chemically-bonded composite structures have interesting

possibilities for use as electronic nanodevices, such as molecular rectifying P-N junctions formed

from adjoining metallic and semiconducting tubes together.

How nanotubes react to ambient environments is a key factor in their technological

development. Tubes deposited onto substrates are often bent, twisted, and tangled together.

STM measurements of mechanically deformed tubes reveal localized electronic states appearing

at high strain sites [48]. Since tubes are quasi-one-dimensional conductors, these states can have

significant consequences on electron transport by acting as scattering centers. Spectra acquired

on armchair nanotubes within bundles reveal a suppressed DOS near the Fermi energy [45].

23

Theory indicates that inter-tube coupling in ropes breaks the mirror symmetries of the armchair

lattice, leading to band repulsion and a depletion of electronic states in a region 150 meV wide

around the Fermi energy (this depletion zone is commonly referred to as a “pseudogap”).

Junctions formed from one tube lying across another have also been investigated [49].

Spectroscopy measurements show spatial fluctuations in the electronic band edge energies of the

upper tube. These are attributed to nonuniform charge doping from the substrate. Also,

localized electronic states are measured at the crossing point, which is the region of maximum

tube deformation. Imaging height profiles have been used to estimate an inter-tube contact force

of about 1 nN, which is an order of magnitude greater than the estimated force that an STM tip

exerts on a nanotube, and a tube-substrate bonding energy of 0.8±0.2 eV/Å.

While the strength of the substrate bonding makes manipulation of tubes with the STM

extremely difficult, tubes can be cut cleanly using controlled bias pulses [50]. This enables

experiments investigating finite-length effects in tubes. In metallic nanotubes, restricting the

length leads to quantum confinement effects in which the axial momentum assumes discrete

values with appreciable spacing between energy levels. This is similar to the “particle-in-a-box”

situation in elementary quantum mechanics, and is observable as a series of steps in I-V

measurements, or as a set of equally-spaced peaks in the DOS. As the length of a tube becomes

smaller, the energy spacing between levels increases to the point that spatial mapping of

individual electronic states becomes possible [51]. Curiously, the effects of length reduction on

spectral measurements of semiconducting tubes appear to be negligible [48], perhaps indicating

that the electron mean-free-path lengths are much shorter in these tubes than in metallic tubes.

Owing to their large aspect ratio, exceptional mechanical stability, and the small radius of

curvature at the end, nanotubes promise to be the ultimate tip for scanning probe microscopies.

Nanotube probes are already being utilized in atomic force microscopy to push the limits of

image resolution and depth profiling. However, their value for STM appears to be limited. It is

unlikely that nanotube tips will be able to improve upon the already sub-angstrom resolution of

STM, and their complex electronic structure presents a serious complication in spectroscopic

measurements. Still, investigations of STM nanotube tips continue, with atomically-resolved

images of a silicon surface having been achieved [52].

24

2.4 References [1] J. Robertson, Adv. Phys. 35, 317 (1986). [2] E. Osawa, Kagaku (Kyoto) 25, 854 (1970). (in Japanese) [3] H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, Nature 318, 162

(1985). [4] E. A. Rohlfing, D. M. Cox, and A. Kaldor, J. Chem. Phys. 81, 3322 (1984). [5] R. D. Johnson, G. Meijer, and D. S. Bethune, J. Am. Chem. Soc. 112, 8983 (1990). [6] R. D. Johnson, D. S. Bethune, and C. S. Yannoni, Acct. Chem. Res. 25, 169 (1992). [7] Tsuneyuki Group Homepage, http://www.issp.u-tokyo.ac.jp/labs/theory/stsune/gallery/

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G. A. Sawatzky, Int. J. Modern Phys. B 6, 3915 (1992). [9] A. Oshiyama, S. Saito, N. Hamada, and Y. Miyamoto, J. Phys. Chem. Solids 53, 1457

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B. Miller, J. M. Rosamilia, R. M. Fleming, A. R. Kortan, S. H. Glarum, A. V. Makhija, A. J. Muller, R. H. Eick, S. M. Zahurak, R. Tycko, G. Dabbagh, and F. A. Thiel, Nature 350, 320 (1991).

[11] A. M. Rao, P. C. Eklund, J.-L. Hodeau, L. Marques, and M. Nunez-Regueiro, Phys. Rev. B

55, 4766 (1997). [12] B. I. Yakobson and R. E. Smalley, American Scientist 85, 324 (1997). [13] C. Journet, W. K. Maser, P. Bernier, A. Loiseau, M. Lamy de la Chapelle, S. Lefrant,

P. Deniard, R. Lee, and J. E. Fischer, Nature 388, 756 (1997). [14] A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C. Xu, Y. H. Lee, S. G. Kim,

A. G. Rinzler, D. T. Colbert, G. E. Scuseria, D. Tománek, J. E. Fisher, and R. E. Smalley, Science 273, 483 (1996).

[15] J. Kong, A. M. Cassell, and H. Dai, Chem. Phys. Lett. 292, 567 (1998). [16] C. T. White and J. W. Mintmire, Nature 394, 29 (1998).

25

[17] J. W. G. Wildöer, L. C. Venema, A. G. Rinzler, R. E. Smalley, and C. Dekker, Nature 391, 59 (1998).

[18] T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, Nature 391, 62 (1998). [19] A. Rubio, Appl. Phys. A 68, 275 (1999). [20] R. E. Peierls, Quantum Theory of Solids (Oxford University Press, New York, 1955). [21] J. W. Mintmire, B. I. Dunlap, and C. T. White, Phys. Rev. Lett. 68, 631 (1992). [22] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 78, 1932 (1997). [23] P. Delaney, H. J. Choi, J. Ihm, S. G. Louie, and M. L. Cohen, Phys. Rev. B 60, 7899 (1999). [24] G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, Phys. Rev. Lett. 49, 57 (1982). [25] G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, Phys. Rev. Lett. 50, 120 (1983). [26] R. D. Young, J. Ward, and F. Scire, Phys. Rev. Lett. 27, 922 (1971). [27] J. Bardeen, Phys. Rev. Lett. 6, 57 (1960). [28] D. M. Eigler and E. K. Schweizer, Nature 344, 524 (1990). [29] W. Chen, T. Jamneala, V. Madhavan, and M. F. Crommie, Phys. Rev. B 60, R8529 (1999). [30] S.-W. Hla, L. Bartels, G. Meyer, and K.-H. Rieder, Phys. Rev. Lett. 85, 2777 (2000). [31] M. F. Crommie, C. P. Lutz, and D. M. Eigler, Science 262, 218 (1993). [32] T. Sakurai, X.-D. Wang, Q. K. Xue, Y. Hasegawa, T. Hashizume, and H. Shinohara, Prog.

Surf. Sci. 51, 263 (1996). [33] E. I. Altman and R. J. Colton, Phys. Rev. B 48, 18 244 (1993). [34] T. Hashizume, K. Motai, X. D. Wang, H. Shinohara, H. W. Pickering, and T. Sakurai,

J. Vac. Sci. Technol. A 12, 2097 (1994). [35] X. Yao, R. K. Workman, C. A. Peterson, D. Chen, and D. Sarid, Appl. Phys. A 66, S107

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[38] K. F. Kelly, D. Sarkar, S. Prato, J. S. Resh, G. D. Hale, and N. J. Halas, J. Vac. Sci. Technol. B 14, 593 (1996).

[39] Y. B. Zhao, D. M. Poirier, R. J. Pechman, and J. H. Weaver, Appl. Phys. Lett. 64, 577

(1994). [40] J. Onoe, T. Nakayama, M. Aono, and K. Takeuchi, Riken Rev. 33, 39 (2001). [41] M. Ge and K. Sattler, Appl. Phys. Lett. 65, 2284 (1994). [42] L. C. Venema, V. Meunier, Ph. Lambin, and C. Dekker, Phys. Rev. B 61, 2991 (2000). [43] D. Tománek, S. Louie, H. Mamin, S. Abraham, R. Thomson, E. Ganz, and J. Clarke, Phys.

Rev. B 35, 7790 (1987). [44] C. L. Kane and E. J. Mele, Phys. Rev. B 59, R12 759 (1999). [45] M. Ouyang, J.-L. Huang, C. L. Cheung, and C. M. Lieber, Science 292, 702 (2001). [46] P. Kim, T. W. Odom, J.-L. Huang, and C. M. Lieber, Phys. Rev. Lett. 82, 1225 (1999). [47] M. Ouyang, J.-L. Huang, C. L. Cheung, and C. M. Lieber, Science 291, 97 (2001). [48] T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, J. Phys. Chem. B 104, 2794 (2000). [49] J. W. Janssen, S. G. Lemay, L. P. Kouwenhoven, and C. Dekker, Phys. Rev. B 65, 115 423

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27

Chapter 3 Exper imental Two prerequisites for any experiment in condensed matter physics are a sample and an

instrument with which to measure it. The success or failure of an experiment is ultimately

determined before the first set of data is acquired. An investigator intending to observe one

physical property may end up with completely unrelated results if the groundwork for the

experiment is not adequately set. This includes both proper handling and preparation of samples,

and verifying that all instrumentation is in proper working order. The hours invested in

developing a reliable experimental procedure can eliminate weeks of wasted operational time.

This chapter opens with a detailed description of the homebuilt STM used in this thesis.

A discussion of the investigated nanotube materials follows, including details of how fullerene

peapods were synthesized. Next is an in-depth account of the procedures used in preparing

samples for measurement. The chapter concludes with a look at the general STM characteristics

of prepared samples.

Numerous STM images appear in this and subsequent chapters. Topographic maps and

directional derivative maps are used interchangeably, and are identified as needed. Color scales

denoting the displayed range of ∆Z are omitted; relevant height information is presented in the

form of line cuts through the data. Tunnel junction parameters are quoted as “V@A” , where V

represents the bias voltage applied to the sample and A is the junction setpoint current.

Spectra are acquired using lock-in amplifier detection of the AC response to a sinusoidal

bias modulation. After the tunneling junction is stabilized over the point of measurement, the

feedback loop is disabled and the voltage is swept across the range of interest. Results are

presented in units of conductance or in arbitrarily scaled units as appropriate.

Refer to Appendix B for further notes on data processing and presentation.

3.1 Instrumentation

Construction began in 1998 on a state-of-the-art STM (Figs. 3.1 and 3.2) based upon a system

developed by D. M. Eigler at IBM’s Almaden Research Center [1]. Built inside of an acoustic

28

enclosure to reduce the effects of external noise on measurements, this instrument is designed for

operation at liquid helium temperatures to provide long-term stability of tunnel junctions, and

utilizes an ultra-high vacuum (UHV) environment to reduce sample degradation from external

contaminants.

The room temperature portion of the instrument primarily consists of two UHV chambers

mounted on a dual deck optical table (Technical Manufacturing Corp.) that provides vibration

Analysis Chamber

Transfer Chamber

Load Lock

Optical Table

Dewar

Vacuum Pumps

Microscope Assembly

Pneumatic Suspension

Inline Shutter

Figure 3.2: Schematic illustrating various STM system components.

Figure 3.1: Low temperature, ultra-high vacuum STM.

29

decoupling from both the floor and the low temperature portion of the system. One of these

vacuum chambers (Fig. 3.3) is outfitted with a variety of apparatus for sample preparation and

surface characterization, including a Low-Energy Electron Diffractometer (Omicron Associates

Gmbh.), a Residual Gas Analyzer (Balzers), an Auger Spectrometer and an Ion Sputter Gun

(Physical Electronics Inc.). This analysis chamber can be isolated from the rest of the system

using a UHV gate valve. The smaller chamber (Fig. 3.4) acts as an atrium for samples being

Ion Pump

Evaporation Sources

Figure 3.4: Transfer Chamber. The evaporation sources are used for in situ dosing of samples with metal adatoms.

Residual Gas AnalyzerOptical

Pyrometer

LEED

Auger Spectrometer

Ion Sputter Gun

Figure 3.3: Analysis Chamber. A 6” UHV gate valve located behind the chamber allows for isolation from the rest of the system.

30

transferred into the low temperature region of the system. Also attached to this chamber is a

UHV-gateable quick-entry load lock (Fig. 3.5) that serves as the sample entry point. The load

lock can be evacuated from atmosphere to better than 1x10-7 torr in less than two hours.

Vacuum is generated with a variety of mechanical and non-mechanical pumps. During

microscope operation all mechanical pumps are shut down to reduce measurement noise, and

vacuum integrity is maintained by a pair of ion pumps (Physical Electronics Inc.) and the natural

cryo-pumping action of the low temperature region of the instrument. Pressure inside the room

temperature chambers routinely measures ≤5.0 x 10-10 torr, implying a pressure within the cold

microscope environment of better than 1.0 x 10-12 torr.

The STM is housed within the low temperature section of the system, located inside a 60

liter capacity liquid helium dewar (Kadel Engineering) suspended beneath the transfer chamber.

The dewar is affixed to an aluminum plate that is supported on pneumatic legs (Technical

Manufacturing Corp.) mounted on the main optical table. These legs provide an additional layer

of vibration isolation for the microscope. Within the dewar, a cylindrical insert isolates the UHV

microscope chamber from the liquid helium cryogen. The insert is filled with a low pressure of

helium gas to allow thermal coupling to the cold bath.

The microscope assembly (Fig. 3.6) resides within a UHV sealed Kovar jar (Larson

Electronic Glass). The jar is connected to the transfer chamber by a meter-long section of

tubing, with UHV sealed bellows providing mechanical decoupling. The jar and tube-line form a

Turbo Pump

UHV Gate

Figure 3.5: Load Lock. This is attached to the Transfer Chamberopposite the Analysis Chamber.

31

pendulum that is supported by a pneumatic suspension system. The suspension system is

comprised of three stainless steel welded bellows (Standard Bellows Co.) that provide a platform

for a yoke collaring the tube-line. The sealed bellows are attached to 1 L pressure reservoirs,

which can be independently adjusted to tune the vibration dampening. The suspension system

also doubles as a centering mechanism for the pendulum, and is adjusted to prevent mechanical

contact between the tube-line and the exchange gas insert.

The level of mechanical noise reaching the microscope from the external environment

can be monitored in situ using a pair of velocitometers (Geospace model HS-1) mounted halfway

down the tube-line. Tests conducted using various configurations of the vibration isolation

components have shown that the pendulum mechanism provides the primary means of

attenuating external vibrations. With the microscope under UHV and the insert can filled with

1-10 torr of helium exchange gas, the suspension performs best when the pressure reservoirs are

set to -13” Hg (vacuum pressure relative to atmosphere) of nitrogen gas. While the overall

performance of the pneumatic suspension is good, there are two weaknesses in the current design

that impact the operation of the microscope.

The first is a resonance mode of the suspension structure near 4 Hz. This is a relatively

slow vibrational mode that is compensated for by the feedback control loop during imaging, but

creates considerable problems in open-loop spectroscopic measurements. With the feedback

Jar

Shutter

Sample

Scanner

Figure 3.6: Microscope Assembly. The Kovar jar allows visual inspection of the assembly while under vacuum.

32

loop disabled, δI/I at the setpoint regularly ranges between 10-25%, indicating a variation in tip-

sample separation as large as 10 pm. Averaging provides some improvement in data quality, but

the periodic nature of the noise requires averaging over a time span on the order of the vibration

period, limiting the rate at which data can be acquired.

In addition to the difficulties stemming from the 4 Hz resonance, there is also a

mechanical instability in the suspension that creates problems. Ideally, the bellows which

support the tube yoke act like damped pistons (similar to the shock absorbers on a car).

However, they also have a limited sideways shear motion. Under operating conditions, the

pendulum tends to “ fall” off center laterally. This sometimes results in aperiodic shot noise that

can result in various types of junction failure, such as tip relocation (new tip apex formed at a

different location on the sample) and cut nanotubes. The source of this noise is believed to be

mechanical contact within the suspension between the tube yoke and the bellows supports. Over

time, this phenomenon has become increasingly troublesome as continued shearing has worn

down the bellows. As of this writing, modifications are underway to improve the performance of

the pneumatic suspension and alleviate these problems for future experiments.

The temperature of the microscope is maintained near 4 K through thermal coupling to a

liquid helium bath. With a 60 L dewar capacity, the STM can remain in continual operation at

this temperature for more than 4 days. Temperature is monitored using a Cernox sensor

(Lakeshore) mounted on the exterior of a 6” stainless steel flange connected to the jar. The large

mass of this flange makes it a good thermal anchor for the microscope assembly, which is

attached on the vacuum side. Conductive heat leak is minimized by using ultra-thin 10 mil

stainless steel tubing. Radiative heating of the microscope is reduced through the use of a series

of three line-of-sight shutters, including a custom built inline UHV shutter (Thermionics)

mounted about halfway down the tube-line.

The microscope head is an inverted Besocke design [2]. The scanner was purchased fully

assembled from RHK Technologies Inc. as a modification of that used in their commercially

available STM system. It is affixed to a linear-motion stage that is raised to engage samples for

measurement. Above the microscope stage is a box-shaped sample stage, which is designed to

rotate 180º to allow in situ dosing of sample surfaces using evaporation sources mounted on the

transfer chamber. The two stages are designed to mate rigidly.

33

A three-segment titanium ramp is enclosed within the sample stage. The walking surface

is hand polished using 1 micron alumina sludge to achieve the microscopic smoothness required

for reliable walking. A motion restrictor encircles the walking surface to limit lateral

displacement and prevent samples from contacting the sample stage. This restrictor limits the

accessible scan area of a sample to a circle about 1 mm in diameter.

Samples are loaded into custom-designed holders (Fig. 3.7) that accommodate the

insertion of a resistive-element UHV button heater (HeatWave) for annealing. Sample holders

plug into the ramp and are held in place using three standard spring-loaded ball plungers.

The STM tip is mechanically cut iridium wire that is prepared in situ using field emission

against a clean Cu(111) single crystal. Typical emission parameters are +200 V bias applied to

the tip, with currents generated on the order of 1 µA. The prepared tip is checked against the

clean copper surface for imaging resolution and stability.

Control electronics and software were purchased from RHK Technologies, and homebuilt

filters were added to the piezoelectric ceramic signal lines to reduce electrical noise. Tunneling

currents were measured using a DL Instruments model 1211 Current Preamplifier.

3.2 Samples

The nanotubes in these experiments are single-wall nanotubes (SWNTs) grown with pulsed laser

vaporization and acquired commercially from Tubes@Rice (since commercialized as Carbon

Nanotechnologies Inc.) in a toluene suspension. The fullerene heterostructures formed by the

encapsulation of C60 molecules inside of SWNTs (henceforth “peapods”) were provided by

Figure 3.7: Sample Holder. The top and bottom halves are separated by a ceramic spacer to provide electrical contacts used in the operation of a resistive element button heater located inside.

34

D. E. Luzzi and coworkers at the University of Pennsylvania Department of Materials Science

and Engineering. The exotic nature of these structures merits a review of the procedure used to

synthesize them.

3.2.1 Fabr ication of Carbon Peapods

Experimental demonstration that C60 molecules could occupy the interior of nanotubes was first

achieved in 1998 [3]. One of the natural byproducts of pulsed laser vaporization growth of

SWNTs is C60 fullerenes. This extraneous material is removed during the post-growth

purification process. However, transmission electron microscopy (TEM) measurements of

purified nanotube material revealed occasional tubes containing chains of buckyballs inside

them. But the overall yield of peapods was miniscule.

The first targeted fabrication of these hybrid structures was reported by Smith and Luzzi

in 2000 [4]. SWNT material is acid etched to open the ends and create holes in the sidewalls of

the tubes. After heating to 225ºC in vacuum to remove chemical residue, a drop of C60

suspended in N,N-Dimethyl Formamide [HCON(CH3)2] is added to the mix and dried in air.

The sample is then annealed for several hours during which time filling occurs (Fig. 3.8).

The details of the encapsulation mechanism are diagrammed in figure 3.9. During

annealing, C60 enters the vapor phase and permeates the material. Van der Waals attraction

causes buckyballs to stick to the nanotubes for some amount of time, during which they diffuse

along the outer wall. When an opening is encountered in a tube of sufficient size to

accommodate a buckyball (diameter > 12.8 Å), a strong attraction pulls the molecules into the

interior region of the tube. This attraction originates from the convex surface of C60 molecules

binding more strongly to the concave side of the curved nanotube surface [6].

Figure 3.8: High resolution TEM micrograph of a SWNT containing a self-assembled chain of C60 molecules (from ref. 5). Scale bar is 2 nm.

35

The minimum tube diameter requirement is a natural consequence of the high energy cost

associated with stretching the lattice of an undersized nanotube to accommodate a buckyball [7].

The SWNT material used in this synthesis is known to have a diameter distribution peaked

around 14 Å, making it a good choice for producing high yields of peapods with chains of C60

molecules well-confined to one dimension.

The efficiency of the filling process is sensitive to the annealing temperature. It is

necessary to heat the sample beyond 325ºC to achieve significant buckyball mobility. As the

temperature increases, the characteristic “sticking” time for C60 on nanotubes becomes smaller,

reducing the likelihood that any given molecule will encounter an opening in the tube wall.

Above 900ºC the damaged nanotubes repair themselves faster than they can be filled. The

samples used in these experiments were formed at 450ºC, followed by a final anneal at ≈ 600ºC

to allow nanotube walls to heal.

3.2.2 Preparation for Measurement

Rarely are as-fabricated fullerenes amenable to analysis with the STM (nanotubes grown using

chemical vapor deposition being a noteworthy exception). The importance of developing a

reliable means of transferring fullerenes from post-growth harvest to samples suitable for

experimentation cannot be overlooked.

C60 Vapor

‘Open’ Nanotube

Adhered C60Diffused C60

Encapsulated C60

Figure 3.9: Illustration of the peapod encapsulation mechanism. Upon annealing, C60 enters the vapor phase. Buckyballs will adhere to a nanotube for a short period of time, during which they can diffuse along the outer wall. When an opening is encountered, van der Waalsattraction “sucks” the C60 molecules inside, creating a peapod.

36

Several methods have been employed, but the most common technique utilizes

suspension of fullerene molecules in the organic solvent 1,2-Dicholorethane [(CH2Cl)2]. The

mixture is agitated ultrasonically to break up large clusters of nanotubes, and then is dripped or

spin-coated onto a substrate. The most common choice of substrate is gold, either as a film on

mica or glass, or as an unsupported foil. Gold has several properties that make it favorable for

STM measurements; it is relatively non-reactive and easy to prepare, it orders readily into (111)-

oriented crystallites possessing a distinct and easily-imaged atomic surface reconstruction, and it

exhibits a nearly uniform electronic structure that simplifies tunneling spectroscopy

measurements.

The procedure used to prepare samples in these experiments is similar to that described

above. Two different source materials were examined. Unfilled SWNTs were vacuum-filtered

from a toluene suspension using micron filter paper under ambient conditions to form a black

sludge, which was allowed to dry into a sooty paper. Peapods were received from the University

of Pennsylvania in the form of a thin, fragile buckypaper (Fig. 3.10).

An organic solvent is used as a delivery medium, but dimethyl formamide (DMF) is used

instead of dicholorethane to form a suspension. There is evidence indicating DMF attacks

nanotubes aggressively [7]. One hypothesis is that this aggressiveness facilitates the unraveling

of ropes, as well as aids in the removal of loose carbon impurities which often attach themselves

to nanotubes. At the very least, DMF does not prohibit preparation of samples suitable for study

with STM.

Figure 3.10: Peapod Buckypaper (as received). A small piece is shredded and mixed with organic solvent to form peapod suspensions for dosing.

37

Agitation in a 125 watt ultrasound (Branson model 2210) is used to disperse pieces of

fullerene paper in solvent. The use of ultrasound to aid in mixing fullerene suspensions is

common practice, but is also a step worth some consideration. Measurements have shown that

exposure to ultrasound radiation creates varying amounts of structural damage in carbon

nanotubes, depending on the type of solvent and exposure time [9]. Consequently, one attempts

to strike a balance between adequately mixing the suspensions and maintaining the integrity of

the nanotubes. Fresh mixtures are initially agitated for about an hour, followed by 15-20 minutes

of agitation immediately prior to dispensing onto substrates.

Atomic force microscopy (AFM) is used to empirically determine suitable solution

concentrations and dosing levels. This technique easily resolves nanotubes on gold surfaces

under ambient conditions (Fig. 3.11), making it an excellent diagnostic tool for these

experiments. There are several important parameters affecting the delivery of fullerenes to the

substrate that must be taken into account.

The concentration of fullerenes in suspension plays a critical role in dosing. In addition

to determining the amount of material delivered per fluid volume, concentration level also affects

the spatial distribution of fullerenes on the substrate. Graphitic van der Waals attraction exists

between nanotubes, as evidenced by their propensity for forming bundles. Nanotubes in

Figure 3.11: Atomic force microscopy image of a gold thin film dosed with SWNTs. Individual nanotubes are clearly visible on the surface. The image is 10 µm x 10 µm recorded with a Digital Instruments Nanoscope in contact mode.

38

heavy concentrations tend to entangle more, leading to highly uneven dispersal on the substrate.

Resulting samples have micron-sized fullerene macroclusters (which are difficult to measure

with STM because of their convoluted structure) separated by vast unoccupied areas of the

surface (which makes locating tubes on the surface more time consuming).

Differences in concentration can be gauged not only by the visible tint of the suspension,

but also by how long it takes fullerene material to condense into macroscopic clumps. When the

mixture density is high the rate at which tubes become enmeshed increases, resulting in the rapid

formation of a miasmic fullerene network. This network eventually comprises the majority of

fullerenes in suspension, and the fluid solvent returns to its premixed colorless appearance

(Fig. 3.12). Excessively dense mixtures begin to coagulate immediately upon removal from

ultrasound, while overly dilute solutions have a very faint tint and require days to condense.

Experience has shown that good suspensions will remain well mixed for at least 5 minutes, with

large scale coagulation occurring 20-40 minutes after removal from ultrasound. From the results

of AFM and STM measurements, the best mixing ratio for the peapod material was determined

to be a 3 mil x 5 mil swath of paper shredded into 50 pipette drops of DMF.

Less evident than solution concentration, the means of fluid delivery also had an effect on

the quality of dosing. For AFM study 4 mm x 4 mm gold thin films on mica were affixed to

ferric disks using general purpose bonding adhesive. Fluid was dripped onto the surface using a

pipette and then blown dry using nitrogen gas. There are several variables involved in this

process.

Figure 3.12: Peapod suspension in DMF after sitting undisturbed for several hours. Note the dark, cloudy condensation that has settled at the bottom of the vial.

39

Using fluid drops of smaller volume resulted in more efficient delivery of nanotubes,

possibly due to the larger surface-to-volume ratio in the drop. Of course, allowing the drops to

sit for longer periods of time before drying with nitrogen gas resulted in heavier dosing, but it

also increased the density of (presumably carbonaceous) contaminants. Drops that were allowed

to dry completely in air left behind an optically detectable residue layer that was difficult to

image with contact AFM, indicating a soft nature. Finally, the kinetics of the dripping action had

a noticeable effect on dosing. Tilting the substrate and allowing fluid drops to flow over the

surface appeared to be a more efficient means of delivery than applying static drops directly onto

the surface.

Substrates used in the STM experiments are gold thin films, typically 2000-3000 Å thick,

grown on mica. These substrates are prepared in vacuum prior to dosing. Preparation entails

argon ion sputtering using 1.5 keV ions at a rate of ≈1.5 µA for 15 minutes followed by

annealing to 150-200ºC for 20 minutes. This procedure is cycled as needed to produce a clean,

locally-ordered surface as determined with STM (Fig. 3.13).

Prepared substrates are removed from the system through the load lock and immediately

dosed under ambient conditions. To recreate the fluid-flow dosing mechanism, a metal probe is

(b)(a)

Figure 3.13: Pair of images showing typical surfaces of clean gold substrates. (a) Image spans 150 nm x 150 nm acquired at 1 V @ 375 pA. Bending points of the herringbone ridges are decorated with individual adsorbates, and a slip dislocation runs from top to bottom on the right side. (b) Derivative map (dZ/dx) spans 100 nm x 100 nm acquired at 1 V @ 375 pA. This image also exhibits decoration of the herringbone ridge bending points, as well as Friedel oscillations emanating from the step edge on the right side.

40

used to make a small notch in the film along the edge of the sample holder aperture far from the

accessible scan area. This allows fluid to drain from the surface into the holder, after which

nitrogen gas is used to facilitate drying. Typically, 6-8 drops are applied to the sample, which is

then returned to the load lock for reintroduction to the system. Total exposure to ambient

conditions is 10-15 minutes, and another 1-2 hours is required to evacuate the load lock before

samples can be transferred into the UHV portion of the instrument.

An important final step before insertion into the low temperature sample stage is an

annealing under vacuum to not more than 150ºC for 15-20 minutes to outgas atmospheric

contaminants and remove residual DMF, which has a boiling point of 153ºC at atmosphere.

Measurements performed on samples using different annealing times and temperatures indicate

that surface contamination is significantly reduced by this process. An unusual side-effect of

annealing is the appearance of nanotubes partially buried below the surface of the gold

(Fig. 3.14). The potential impact of this on STM measurements is discussed in the next section.

3.3 STM Character ization of Samples

After annealing, samples are lowered halfway down the microscope tube-line on a liquid-

nitrogen-cooled manipulator and allowed to cool for 30-60 minutes. Samples are then inserted

into the microscope stage and left overnight to thermally equilibrate at liquid helium

temperature. It is important that samples be given sufficient time to cool, otherwise thermal drift

in the piezoelectric ceramics will prohibit measurement.

Buried Tubes

Figure 3.14: STM image showing bundles of SWNTs on gold after annealing. The lower rope appears to submerge below the surface. Image is 64 nm x 32 nm acquired with 1.5 V bias applied to the sample at 100 pA tunneling current, displayed as a derivative (dZ/dx).

41

-150

-100

-50

0

50

100

-1 -0.5 0 0.5 1

Cu

rren

t (p

A)

Sample Bias (V)

0.00

0.05

0.10

0.15

0.20

dI/d

V (

nA/V

)

Figure 3.16: Point spectra on a bare gold surface. The image spans 50 Å x 50 Å acquired at 1 V @ 100 pA. Spectral plots were acquired at the image center and averaged over 8 sweeps. Differential conductance was measured using a 5 mVrms bias modulation. The onset of the surface states occurs at ≈ -450 mV.

0

0.4

0.8

1.2

0 10 20 30 40 50 60 70

Rel

ativ

e H

eig

ht

(Å)

Lateral Displacement (Å)

Figure 3.15: High resolution image of gold spanning 100 Å x 75 Å acquired at 700 mV @ 375 pA exhibiting resolution of individual atomic sites. The displayed section shows an average interatomic separation of 2.43 Å, with a height corrugation of 0.1 – 0.3 Å.

42

3.3.1 Substrate Character ization

The bare (111) surface of gold possesses an unusual reconstruction known as a herringbone

pattern, characterized by sets of parallel ridges (Fig. 3.13). These ridges mark the boundary

between two distinct atomic orderings of the surface. The ideal spacing between ridges within a

pair is 25 Å, and 38 Å between pairs [10]. Since gold is a noble metal with excellent conduction

properties, individual atomic positions are difficult to resolve. But with a carefully conditioned

tip and stable tunneling conditions the structure of the surface is revealed (Fig. 3.15). Point

spectroscopy measurements indicate a relatively constant DOS in the vicinity of the Fermi

energy, with the exception of a sharp step-like drop near -450 meV denoting the band edge for

the 2-dimensional electronic states that reside on this surface (Fig. 3.16).

After dosing, the surface becomes coated with carbonaceous residue. Coverages range

from approximately 0.5 to more than a full monolayer. While the presence of carbon is not

prohibitive, it does add a level of complication since carbon structures can adhere to the STM tip.

Imaging resolution is not as much of a concern as is the appearance of anomalous features in

spectroscopy. An example of this is evident in figure 3.17, which shows an image of a fully

covered surface. The measured point spectrum is distinctly different from that observed on clean

gold, displaying several peaks and a narrow gap-like feature at low bias. Care must be taken to

ensure spectral measurements accurately reflect the properties of the object being investigated.

0

1

2

3

4

5

0 100 200 300 400 500

Rel

ativ

e H

eigh

t (Å

)

Lateral Distance (Å)

-2 -1 0 1 20

2

4

6

8

10

dI/dV (arb

)

Sample Bias (V)

Figure 3.17: Carbonaceous over-layer on a gold surface. Image spans 473 Å x 218 Å acquired at 1.5 V @ 250 pA. The measured spectrum is distinctly different from that acquired on clean gold.

43

3.3.2 Imaging and Spectroscopy of Nanotubes

On average, nanotubes disperse on the substrate with a density of a few bundles per square

micron. The affinity between tubes in liquid suspension makes the sighting of isolated single

tubes rare. Typical ropes consist of six or fewer tubes (Fig. 3.18), though bundles consisting of a

dozen or more tubes are not uncommon (Fig. 3.19).

Compared to most objects studied with STM, nanotubes possess an extremely large

height profile, with a typical tube diameter being 14 Å. This complicates imaging significantly.

Usually, only the last few angstroms of an STM tip are directly involved in the tunneling

process. While this still holds for images acquired along the apex of a nanotube, images across

the width of the tube involve a nanometer or more of the tip, which can have a complicated

geometry. Simply adsorbing a small atomic cluster to the tip is not sufficient to ensure faithful

imaging; one must also eliminate extraneous spurs near the apex (which is difficult to do in

practice). The most common artifact in topography is multiple imaging of a tube, which makes a

single tube appear to be a bundle. This effect makes it difficult to state with certainty the number

of distinct tubes in any given bundle, though the artifact can often be identified from the

remarkable similarity in atomic structures between “adjacent” tubes (Fig. 3.20). Tip

conditioning can also reveal this effect, as multiple tubes will suddenly revert to a single tube

upon a change in tip structure.

Gold Surface

Carbon Impurities

Nanotube Bundle

Unimageable Bundle

Figure 3.18: Image of typical nanotube bundles. Image spans 500 Å x 500 Å acquired at 1.5 V @ 100 pA.

44

Figure 3.20: Demonstration of a multiple image artifact. The left image spans 59 Å x 27 Å acquired at 2.5 V @ 100 pA; the right is 59 Å x 109 Å acquired at 2.5 V @ 250 pA. What appears to be at least two nanotubes is actually a single tube imaged multiple times.

Figure 3.21: Atomic resolution image of a nanotube bundle. Image spans 237 Å x 109 Å acquired at -1.25 V @ 300 pA.

Figure 3.19: Image of an exceptionally large bundle of tubes. Image spans 512 Å x 512 Å acquired at 1.5 V @ 250 pA.

45

Atomic resolution is readily achieved on most nanotubes (Fig. 3.21), though occasional

tubes appear featureless under typical imaging conditions (Fig. 3.22). This indicates high spatial

uniformity of charge density in these tubes, which invariably are metallic. The converse relation

is not true; not all metallic tubes appear smooth. Tubes are best imaged along the apex where the

tangent plane is parallel to the image plane. Tip interactions along the side of a tube tend to be

erratic, often resulting in distinctive directional scan asymmetries (Fig. 3.23).

Metallic and semiconducting tubes are easily distinguished by spectroscopy (Fig. 3.24).

For semiconducting tubes, the measured gap width provides a lower bound on the diameter. In

this example, the conductance signal dips below the limit of detectability from -390 to 450 meV,

resulting in a lower bound on the tube diameter of 8.8 (10.6) Å for values of γ0 = 2.6 (3.13) eV.

The spectrum for the metallic tube exhibits a (pseudo)gap 150-200 meV wide near zero bias,

which is discussed in more detail in section 4.2.

A byproduct of the annealing step in the sample preparation procedure is the partial

embedding of nanotubes into the gold surface (Fig. 3.25). Similar images have been attributed to

ragged tube edges resulting from acid etching [11]. While it is known that tubes are routinely

etched during purification and processing, the appearance of exposed edges in these samples is

considered unlikely since the dangling bonds of open-ended tubes are chemically active and

should attract the contaminants that pervade these samples (see Figs. 3.18, 3.22, 4.3, 4.5 and

-1.5 -1 -0.5 0 0.5 1 1.50.00

0.05

0.10

0.15

0.20

dI/dV (n

A/V

)

Sample Bias (V)

Figure 3.22: Image of a “featureless” nanotube (with a multiple imaging artifact). Image spans 200 Å x 200 Å acquired at 1 V @ 100 pA. The associated point spectrum (averaged over 8 sweeps) reveals the metallic nature of this tube.

46

0.00

0.20

0.40

0.60

0.80

1.00

dI/d

V (

nA/V

)

-1000 -500 0 500 1000Sample Bias (mV)

-300-200-100

0100200

-1000 -500 0 500 1000

Cur

rent

(pA

)

Sample Bias (mV)

Figure 3.24: Pair of nanotubes, one semiconducting (left) and one metallic (right). Image acquired at 1.25 V @ 300 pA with boundary spanning 64 Å x 27 Å. Associated spectra averaged over 16 sweeps.

Scan Direction Scan Direction

Axial Sections

0

1

2

3

4

5

0 10 20 30 40 50 60Rel

ativ

e H

eigh

t (Å

)

Lateral Distance (Å)

Cross Sections

0

5

10

15

20

30 40 50 60 70 80Rel

ativ

e H

eig

ht (

Å)

Lateral Distance (Å)

Figure 3.23: Example of erratic tunneling and directional asymmetry in simultaneously acquired images along the side of an isolated nanotube. Images acquired at 2 V @ 500 pA, with boundary spanning 138 Å x 56 Å. Sections across the tube axis (left) and along the tube axis (right) are plotted for both the image acquired in the forward (red) and reverse (blue) scan directions. Note the unusually large tube diameter in the cross section; this is an example of how tip-width convolution affects the apparent width of nanotubes in STM images (see section 2.3.2).

47

4.26 for examples consistent with this scenario). Additionally, substrate-tube attraction should

lead to a flattening of an exposed ragged tube edge, altering the regularity of the lattice under

imaging. This is not seen in measurements, which indicate that the lattice extends with minimal

distortion into the surface.

This embedding effect may benefit STM of nanotubes in bundles by providing a direct

path to the substrate for current to drain, as opposed to traversing through other tubes in the

bundle and coupling their electronic properties into spectral measurements. Preliminary

measurements near the embedding region reveal an effect in the tube’s electronic structure

similar to rectification in semiconductor-metal contacts [Fig. 3.25(c)]. Investigations of tube

properties are best performed away from these areas.

3.4 References [1] D. M. Eigler and E. K. Schweizer, Nature 344, 524 (1990). [2] J. Frohn, J. F. Wolf, K. Besocke, and M. Teske. Rev. Sci. Instrum. 60, 1200 (1989). [3] B. W. Smith, M. Monthioux, and D. E. Luzzi, Nature 396, 323 (1998).

(a) (b)

0.0

0.5

1.0

1.5

-2 -1 0 1 2

dI/d

V (n

A/V

)

Sample Bias (V)

(c)

42 Å

128 Å

Figure 3.25: Partially buried nanotubes. (a) Image spans 500 Å x 500 Å acquired at 1.5 V @ 100 pA. (b) Image acquired at -1.5 V @ 250 pA with boundary spanning 56 Å x 82 Å. (c) Point spectra acquiredat different displacements from the submergence point of a tube.

48

[4] B. W. Smith and D. E. Luzzi, Chem. Phys. Lett. 321, 169 (2000). [5] B. W. Smith, M. Monthioux, and D. E. Luzzi, Chem. Phys. Lett. 315, 31 (1999). [6] L. A. Girifalco, M. Hodak, and R. S. Lee, Phys. Rev. B 62, 13 104 (2000). [7] S. Okada, S. Saito, and A. Oshiyama, Phys. Rev. Lett. 86, 3835 (2001). [8] M. Monthioux, B. W. Smith, B. Burteaux, A. Claye, J. E. Fischer, and D. E. Luzzi, Carbon

39, 1251 (2001). [9] K. L. Lu, R. M. Lago, Y. K. Chen, M. L. H. Green, P. J. F. Harris, and S. C. Tsang, Carbon

34, 814 (1996). [10] W. Chen, V. Madhavan, T. Jamneala, and M. F. Crommie, Phys. Rev. Lett. 80, 1469 (1998). [11] T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, J. Phys. Chem. B 104, 2794 (2000).

49

Chapter 4 Unfilled Single-Wall Nanotubes This chapter is divided into four sections. The first section describes general phenomena

associated with STM measurements of single-wall nanotubes. Next, the appearance of

pseudogaps in the electronic structure of metallic nanotubes in bundles is investigated. A

discussion of adsorbate-related phenomena follows, and the chapter concludes with the STM

characterization of defects in the atomic lattice of a nanotube.

Details concerning data presented in this chapter can be found in the introduction to

Chapter 3 and in Appendix B.

4.1 General Properties of SWNTs

This section covers a number of nanotube properties commonly observed in STM measurements.

Much of what is presented stands in confirmation of previously obtained results, and validates

the methodology used in subsequent experiments.

4.1.1 Bias Dependent Imaging

It is known that many materials (notably semiconductors) exhibit pronounced changes in STM

imaging as the junction bias is varied. This effect is intrinsic to the imaging mechanism. To first

order, STM images consist of a summation of electronic states between the Fermi energy and the

tunneling bias voltage. If the majority of these states possess a particular spatial distribution, the

resulting image will reflect this. As the bias voltage is varied, the numbers and types of states

contributing to the image also changes. The most pronounced variation in imaging often occurs

when the polarity of the junction is inverted and the STM switches from probing occupied states

to unoccupied ones (or vice versa). In many materials these states lie in different energy bands,

which can exhibit different (sometimes complimentary) spatial distributions.

The same holds true for nanotubes. In previous work it has been noted that the full

hexagonal symmetry of the atomic lattice is not always present in images of nanotubes [1, 2].

While tip-nanotube interactions may account for some of these effects (known to be the case for

50

graphite [3]), calculations indicate that even in ideal tunnel junctions the coherent superposition

of electronic states propagating in opposite directions on the tube can result in image

asymmetries [4]. In particular, the occupied/unoccupied azimuthal subband edge state pairs in

semiconducting tubes possess complimentary spatial distributions whose sum displays the full

hexagonal structure of the lattice. But these effects are not limited to just semiconducting tubes,

as demonstrated in the nanotube in figure 4.1.

Spectroscopy reveals a metallic DOS with the onset of the second occupied and

unoccupied subbands occurring near -1.14 V and 0.52 V respectively, for an estimated tube

diameter of 13.35 Å (γ0 = 2.6). The lack of spectral symmetry with respect to the Fermi energy

is due to charge transfer from the substrate; the observed band shift of 310 meV is consistent

with similar observations in reference 1, and is equivalent to the difference in work function

between Au(111) (5.31 eV [5]) and nanotubes (5 eV [6]).

High resolution images acquired at various bias voltages are shown in figure 4.2.

Pronounced changes in topography are observed at low bias (between ±500 mV), with the most

dramatic effect occurring when bias polarity is reversed. The image acquired at +25 mV exhibits

a ring-like structure, while at -25 mV the pattern shifts emphasis to the spiral bond chains. As

voltage is increased and more states contribute to the image, anisotropy becomes suppressed and

the full hexagonal structure begins to appear; this is especially evident in the positive bias images

where the second subband is encountered at 0.52 V.

-40

-20

0

20

4060

80

-1.0 -0.5 0.0 0.5 1.0

Cu

rrent (p

A)

Sample Bias (V)

0.00

0.05

0.10

0.15

0.20

dI/dV (n

A/V

)

Figure 4.1: Metallic nanotube. Image spans 64 Å x 128 Å acquired at 1.25 V @ 100 pA. Point spectra acquired 16 Å apart averaged over 8 sweeps each.

51

Figure 4.2: Series of images displaying pronounced bias dependent effects. Images span 16 Å x 64 Å acquired at a fixed junction impedance of 2.5 GΩ (excepting second from right, acquired at 7.5 GΩ). From left to right: -1.20 V @ 480 pA; -1.00 V @ 400 pA; -0.50 V @ 200 pA; -0.25 V @ 100 pA; 0.25 V @ 100 pA; 0.50 V @ 200 pA; 0.75 V @ 100 pA; 1.00 V @ 400 pA.

0.0

0.2

0.4

0.6

-500 0 500

dI/d

V (n

A/V

)

Sample Bias (mV)

(a)

(b)

(c)

Figure 4.3: Bundle of nanotubes, some of which terminate. (a) Image spans 100 Å x 100 Å acquired at 250 mV @ 2 nA. (b) Point spectra acquired on two different tubes, each averaged over 8 sweeps andexhibiting metallic conduction. (c) Image of the end region of the central tube, spanning 20 Å x 40 Å acquired at 250 mV @ 2 nA. Arrows highlight enhanced electronic density resulting from coherent backscattering from the end region.

52

4.1.2 End Caps

The terminal points of nanotubes are conceptually equivalent to the surfaces of 3-dimensional

crystals, and should exhibit analogous characteristics. For instance, coherent backscattering

from the end creates periodic enhancements in electron density observed in high resolution

images [Fig. 4.3(b)], reminiscent of Friedel oscillations [see Fig. 3.13(b)]. These enhancements

are most easily imaged at low bias voltages (Fig. 4.4).

Discontinuity in the lattice structure at the end of a tube, particularly the presence of

pentagonal rings that are necessarily present in tubes with closed ends, can lead to the formation

of localized electronic states [7]. An example of this is shown in figure 4.5, where peaks are

observed in the gap region at the end of a semiconducting tube. This is illustrative of the effect

topological perturbations have in general on the electronic structure of nanotubes, as will be

discussed in detail in section 4.4.

4.1.3 Strained Nanotubes

Nanotubes are bound to the gold surface by a rather substantial van der Waals attraction,

estimated to be about 0.8 ±0.2 eV/Å [8]. The strength of this attraction can stabilize structural

distortions in tubes, such as bends or twists [9]. It is rare to encounter an image of a nanotube

Figure 4.4: Bias dependence in images of the end region of the nanotube pictured in figure 4.3(c) (right tube). Images span 40 Å x 40 Å acquired at 2 nA. Top row left to right: -750 mV, -500 mV, -250 mV. Bottom row right to left: 250 mV, 500 mV, 750 mV.

53

(STM or otherwise) that does not exhibit at least some small bend, and often times extreme

mechanical strain (see Fig. 3.11). The fact that tubes can obtain such convoluted configurations

without breaking apart is a testament to their inherent mechanical strength.

The prevalence of strain makes it a subject of paramount importance in the development

of nanotube technologies, and the topic has been well addressed theoretically [10-12]. Figure 4.6

shows a nanotube in a bundle with a bend of about 6º. The tube appears to have an armchair

structure, and spectroscopy confirms its metallic nature (Fig. 4.7). Far away from the bent

portion of the tube, tunneling spectra appear normal, with a characteristic 150 mV wide

pseudogap around 0 V. Within the bend region, though, a peak appears at low bias. A similar

feature is observed in spectroscopy of tubes exhibiting high-angle bends [13].

The effects of strain are also evident in crossed tube junctions (Fig. 4.8). Conceptually,

the only differences between tubes lying on top of one another in parallel (as in a bundle) and

perpendicularly (crossed junction) are the length of the inter-tube interaction, and the additional

strain imposed upon the top tube in the second orientation due to substrate attraction.

Spectroscopic studies of these junctions reveal two distinguishing features: a localized low-bias

state near the apex of the junction (the point of maximal deformation), and significant bending of

the electronic band edges across the junction [8]. The first effect is consistent with the

0.0

1.0

2.0

3.0

4.0

5.0

6.0

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

dI/dV

(nA

/V)

Sample Bias (V)

(d)

(c)

(b)

(a)

Figure 4.5: Localized electronic states at the end of a nanotube. (a) Image spans 500 Å x 500 Å acquired at 500 mV @ 500 pA. (b)-(c) Images span 100 Å x 100 Å acquired at 750 mV @ 500 pA. Image centers are 108 Å apart. (d) Point spectra illustrating the localized electronic states found at the end of the nanotube. Both spectra averaged over 8 sweeps.

54

measurement in figure 4.7. The second effect can be accounted for, at least partially, by spatial

variation in charge transfer stemming from the loss of substrate contact at the crossing.

However, small variations in the positions of band edges along the length of a tube lying flat on a

surface or in a bundle are not uncommon in these samples (Fig. 4.9). This supports the view that

band-bending accompanies the lattice strain that occurs when a nanotube conforms to the shape

of the substrate surface, or when substrate interactions “ flatten” the circumference of a tube.

An important consequence of strain in nanotubes is the formation of Stone-Wales defects

involving rotations of carbon-carbon bonds to form heptagon-pentagon pairs [10]. This is the

primary topic of section 4.4.

Figure 4.6: Nanotubes under strain. Left image spans 250 Å x 500 Å acquired at 750 mV @ 250 pA. Right image spans 128 Å x 128 Å acquired at 1.25 V @ 250 pA. There is a 5º-7º bend in the middle tube.

0.0

0.2

0.4

0.6

0.8

-1 -0.5 0 0.5 1

dI/dV

(nA

/V)

Sample Bias (V)

Figure 4.7: Strain-induced localized electronic state. Image spans 32 Å x 128 Å acquired at 1.267 V @ 250 pA. Spatially-resolved spectra are averaged over 4 sweeps each and offset in increments of 0.25 nA/V for clarity. Arrow denotes a localized state centered at 56 meV.

55

4.1.4 STM Induced Cutting

While the strong bonding between nanotubes and the gold substrate precludes using the STM

probe to perform controlled manipulations, it has been demonstrated that tubes can be readily

dissected into smaller sections using voltage pulses (see section 2.3.2 and Fig. 4.10). While the

propensity for nanotubes to break apart at high bias opens the door to investigations of finite size

effects in tubes, it also limits the range of parameters that can be explored experimentally. In

particular, measurements involving bias voltages approaching 3 V tend to result in damaged

tubes (Fig. 4.11).

Figure 4.8: Crossed bundles. Image acquired at 500 mV @ 500 pAwith boundary spanning 541 Å x 707 Å.

-1.5 0 1.75Sample Bias (V)

Scale

(nA

/V)

0.7

0.0

Po

sitio

n (Å

)

96

0

Figure 4.9: Color intensity plot of spectral measurements revealing spatial variation of the band edges (arrows) in a semiconductingnanotube. Image spans 24 Å x 96 Å acquired at 1.75 V @ 300 pA. Spectra acquired in 0.75 Å increments along tube axis (dotted line).

56

4.1.5 Discussion

This section provided an introduction to various aspects of nanotubes that are not the central

topic of this thesis, but which nonetheless are of general importance in interpreting the results of

the following sections. The majority of measurements presented thus far stand in confirmation

of results obtained by other researchers and establishes the validity of the methods used in these

experiments.

(c)(b)(a)

Figure 4.10: Image of a bundle before (a) and after (b) being cut by a voltage pulse. Images span 200 Å x 200 Å acquired at 250 mV @ 500 pA. (c) High resolution image of one of the newly formed end caps, spanning 50 Å x 50 Å acquired at 100 mV @ 250 pA.

0

2

4

6

8

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

dI/d

V (n

A/V

)

Sample Bias (V)

(b)

(c)

(a)

Figure 4.11: Image of a bundle before (a) and after (b) attempting a measurement using a 3 V sample bias. Images span 100 Å x 100 Å acquired at 1 V @ 1 nA. (c) Spectrum acquired prior to cutting, averaged over 8 sweeps.

57

4.2 Tube-Tube Interactions and Pseudogaps in Metallic Nanotubes

The occurrence of zero-bias pseudogaps in metallic nanotubes was introduced in section 2.3.2

(see figure 2.12). In this section, a spectroscopic study of this phenomenon is presented. The

underlying cause of pseudogaps in nominally metallic nanotubes is thought to be electronic

coupling between adjacent tubes in bundles, similar to the coupling between individual planes in

graphite. This coupling disrupts the mirror symmetries of armchair nanotubes, leading to band

repulsion [14, 15]. The result is a depletion of low-energy electronic states, which appears in

spectral measurements as a dip centered on the Fermi energy.

This effect is demonstrated in figure 4.12. The isolated tube in part (a) of the figure

exhibits no pseudogap; actually, this interpretation of the data is not quite so clear, as there are

ambiguous low-bias features in the spectra. But these features are not as well defined as the

pseudogaps observed in other measurements, and likely reflect the presence of carbonaceous

contaminants. In any event, the pseudogap in part (b) is unmistakable. This depletion is not a

true gap in that states still exist at these energies.

0.0

0.2

0.4

0.6

0.8

-1.5 -1 -0.5 0 0.5 1 1.5Sample Bias (V)

0.0

0.1

0.2

-1.5 -1 -0.5 0 0.5 1 1.5

dI/d

V (n

A/V

)

Sample Bias (V)

(b)(a)

Figure 4.12: Metallic nanotubes with associated spectra. (a) Image spans 256 Å x 256 Å acquired at 1.5 V @ 250 pA. (b) Image acquired at 250 mV @ 500 pA with boundary spanning 71 Å x 55 Å. Associated point spectra are each averaged over 2 sweeps.

58

Of interest in these experiments is whether the STM probe itself contributes to the

suppression of conductivity, such as through field-induced charge depletion or some other

mechanism. Also investigated is the spatial variation (or uniformity) of pseudogaps, which

reveals information about the length scale of inter-tube interactions.

4.2.1 Spectral Character ization of Pseudogaps

To investigate the possibility of tip-induced contributions to this effect, the armchair tube

in figure 4.13 (possessing a 173 mV wide pseudogap) was subjected to a series of spectroscopic

measurements at a single point with varying junction impedance values. Lowering the

impedance decreases the tip-nanotube distance, leading to a corresponding increase in the

magnitude of any tip-related effects. Of course, the measured differential tunneling conductance

dI/dV scales with junction impedance (Fig. 4.14), so spectra must be normalized against the

voltage-dependent impedance I(V)/V before they can be compared to one another [16] (see

Appendix B for details concerning the normalization procedure).

Measurements of the pseudogap ranging over 3.5 decades of junction impedance are

displayed in figure 4.15. For impedance values greater than 10 GΩ the signal at low bias is

extremely weak, and the pseudogap is washed out by noise. Below 10 GΩ the pseudogap is

evident in the normalized spectra between ±100 mV, with the onset of the depleted region

denoted by a decrease in the signal. The most prominent features are a set of three peaks within

the pseudogap region. It is likely that these are signatures of localized states arising from defects

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

dI/d

V (a

rb)

Sample Bias (V)

0.0

2.0

4.0

6.0

-250 -125 0 125 250Sample Bias (mV)

173 mV

Figure 4.13: Armchair nanotube exhibiting a pseudogap. Image spans 28 Å x 56 Å acquired at 200 mV @ 100 pA. Point spectra are averaged over 4 sweeps each.

59

0

5

10

15

20

25

-200 -100 0 100 200

(dI/d

V)/(

I/V)

Sample Bias (mV)

0

5

10

15

20

-200 -100 0 100 200

(dI/d

V)/

(I/V

)

Sample Bias (mV)

4 GΩΩΩΩ

2 GΩΩΩΩ

800 MΩΩΩΩ

400 MΩΩΩΩ

8 GΩΩΩΩ

20 GΩΩΩΩ

40 GΩΩΩΩ

20 MΩΩΩΩ

13.3 MΩΩΩΩ

10 MΩΩΩΩ

8 MΩΩΩΩ

40 MΩΩΩΩ

80 MΩΩΩΩ

200 MΩΩΩΩ

Figure 4.15: Measurements of a pseudogap as junction impedance is varied (offset in increments of 3 for clarity). Spectra are averaged over 4 sweeps each and normalized. Junction bias is 200 mV for all curves.

0

5

10

15

20

25

30

35

40

-200 -150 -100 -50 0 50 100 150 200

dI/d

V (

nA/V

)

Sample Bias (mV)

Figure 4.14: Measurements of a pseudogap as junction impedance is varied. Spectra are averaged over 4 sweeps each acquired at 200 mV bias voltage. Junction impedances in MΩ are 800 (black), 400 (red), 200 (blue), 80 (green), and 40 (orange).

60

or strain. It is noteworthy that the presence of these features does not inhibit the formation of the

pseudogap. The spectra remain unchanged to below 20 MΩ, when the various features appear to

attenuate and the overall spectra become flattened. The tip is expected to be within a few

angstroms of the tube in this regime, exerting substantial force upon the carbon lattice. A natural

consequence of this is the appearance of strain-induced states at low bias (as demonstrated in

section 4.1.3) that partially “ fill-in” the pseudogap. However, even in these spectra the

pseudogap onset is still observable, though much less prominent. The fact that the pseudogap

persists with little change in width in a situation where tip-tube interactions appear to be quite

strong is evidence that this effect is not induced or altered by the STM tip.

The spatial character of pseudogaps was investigated on the tube featured in figure 4.16.

Spectra were acquired at regular intervals along the tube axis (Fig. 4.17). As in the previous

experiment, peaks are observed at various energies within the depleted region. The localized

nature of these states is evident in the data. The pseudogap itself does not change substantially,

though the presence of low-bias peaks makes accurate determination of the gap width from point

to point difficult. What is clear, though, is that the pseudogap is present along the entire

investigated length of tube. Again, it is notable that the presence of various local states along the

tube does not significantly alter the character of the pseudogap.

0.00

0.04

0.08

0.12

-1.5 -1 -0.5 0 0.5 1 1.5

dI/d

V (n

A/V

)

Sample Bias (V)

0.0

0.2

0.4

-200 0 200Sample Bias (mV)

(c)

(b)(a)

Figure 4.16: Metallic nanotube in a bundle. (a) Image spans 64 Å x 64 Å acquired at 1.5 V @ 100 pA. (b) Same area at 250 mV @ 100 pA. (c) Point spectra of second tube from the left, averaged over 8 sweeps.

61

4.2.2 Discussion

These experiments demonstrate that pseudogaps are robust and persistent. The lack of distinct

spatial variation in the measured width suggests that the local details of inter-tube interactions

are irrelevant, and that only the average effect determines the nature of the pseudogap. For

instance, if a metallic nanotube is bundled next to different nanotubes at various locations along

its length, the resulting pseudogap will nonetheless appear uniform over the entire tube.

Importantly, this also means that either a tube has a pseudogap or it does not. If an inter-tube

interaction is sufficient to break the symmetry of a nanotube and create a pseudogap, it will do so

along the entirety of the tube. It should not be possible to create a situation in which a metallic

tube features a pseudogap on one end and no pseudogap on the other. An example supporting

this conjecture is observed in section 4.3.

0

2

4

6

8

-200 0 200

dI/dV

(nA

/V)

Sample Bias (mV)

Figure 4.17: Pseudogap measured as a function of position. Image spans 32 Å x 128 Å acquired at 250 mV @ 100 pA. Point spectra are averaged over 8 sweeps, acquired in 8 Å increments along the axis.

62

4.3 Interactions with Adsorbates

Whether in the form of impurities or dopants, extrinsic materials can significantly influence

nanotube properties. Two particular situations are investigated in this section. The effects of the

native contaminants that pervade these samples are examined briefly. The majority of this

section is devoted to measurements performed on a nanotube sample dosed with cobalt, which is

a transition metal element possessing a large magnetic moment.

4.3.1 Common Adsorbates

Figure 4.18 is of a nanotube with an adsorbate displaying behavior characteristic of most of the

adsorbates observed in these samples. It is conjectured that this object is a carbon-based

molecule or atomic cluster, as those are by far the most common types of impurity in nanotube

samples. But since STM is rarely able to provide direct information on the chemical makeup of

an object, it cannot be demonstrated unequivocally that this is the case.

Spectroscopy reveals semiconducting behavior typical of nanotubes. The adsorbate itself

appears as an amorphous lump that masks the lattice of the underlying tube. Close inspection

also reveals a disruption in the periodicity of the nearby region (Fig. 4.19). This indicates

scattering of electrons in the tube, reminiscent of the effect observed near tube ends (see

Fig. 4.3). This interpretation is also consistent with the subtle shifts in the observed lattice near

the adsorbate as the bias voltage is varied (Fig. 4.20).

-1.0

-0.5

0.0

0.5

1.0

-1.5 -1 -0.5 0 0.5 1 1.5

Cu

rren

t (n

A)

Sample Bias (V)

0.0

0.5

1.0

1.5

2.0

dI/d

V (n

A/V

)

Figure 4.18: Nanotube with an adsorbate. Image spans 64 Å x 128 Å acquired at 250 mV @ 2 nA. Spectra are averaged over 2 sweeps.

63

Point spectra over the adsorbate does not reveal any distinguishing features, with the

most notable effects being an enhancement in the DOS from 100-300 mV, and the appearance of

a broad peak around 550 mV (Fig. 4.21). However, as previously demonstrated, the spatial

variation in the electronic structure of tubes commonly observed in these samples may also

account for these changes (see Fig. 4.9). Further investigation is required to establish a definite

correlation between these adsorbates and any spectral features. What is clear is that the

fundamental electronic properties of the nanotube remain largely unaltered. As the next

experiment demonstrates, this is not always the case with adsorbates.

Figure 4.20: Bias dependence of images near an adsorbate. Images span 32 Å x 64 Å acquired at 2 nA. Sample biases are -350 mV (left) and 350 mV (right).

Figure 4.19: Topographic (left) and derivative (right) maps showing the disruption of the regular lattice pattern near an adsorbate. Image spans 48 Å x 48 Å acquired at 250 mV @ 2 nA.

64

4.3.2 Cobalt Dosing of Nanotubes

Dosing of a nanotube sample with cobalt was performed in situ using a homebuilt evaporator.

The low temperature of the sample inhibits atomic diffusion, resulting in a uniform coverage of

individual adatoms (Fig. 4.22).

Cobalt is an interesting dopant owing to its relatively large magnetic moment. The

presence of isolated magnetic moments in metals induces the formation of an electron spin-

screening cloud at low temperatures, a response known as the Kondo effect [17]. The

characteristic feature is the appearance of a many-body quantum state near zero bias. This

Kondo resonance has been observed with STM spectroscopy on several metallic surfaces,

including the (111) surfaces of copper [18], gold [19], and silver [20] (Fig. 4.23).

Previous efforts have been made to observe the effects of cobalt adsorbates on nanotubes

[21]. Spectral resonances near zero bias were measured on adsorbate clusters at 5 K. Individual

cobalt adatoms were not observed, though, which complicates the situation since the magnetic

moments within a cluster will couple together, leaving the overall net moment in question.

0.00.51.01.52.02.50

8

16

24

32

40

48

56

64

Relative Height (Å)

Lat

eral

Dis

tan

ce (

Å)

0.0

0.5

1.0

1.5

2.0

-500 0 500

dI/dV

(nA/V

)

Sample Bias (mV)

Figure 4.21: Spectra acquired at various displacements from an adsorbate. Image spans 32 Å x 64 Å acquired at 250 mV @ 2 nA. Spectra are averaged over 8 sweeps and offset in increments of 0.2 nA/V for clarity, acquired using a 741 mV @ 2 nA junction (except for the spectrum in green, acquired at 980 mV @ 2 nA).

65

14

18

22

26

30

-100 0 100Sample Bias (mV)

(c)

8.2

8.6

9.0

9.4

9.8

-80 -40 0 40 80Sample Bias (mV)

(b)

0.50

0.60

0.70

-100 0 100

dI/d

V (

nA

/V)

Sample B ias (mV)

(a)

Figure 4.23: Kondo resonance of cobalt on various surfaces. (a) Image on Au(111) spans 100 Å x 100 Å acquired at 100 mV @ 500 pA. Spectrum averaged over 8 sweeps. (b) Image on Cu(111) spans 80 Å x 80 Å acquired at 100 mV @ 1 nA. Spectrum averaged over 8 sweeps. (c) Image on Ag(111) spans 75 Å x 75 Å acquired at 100 mV @ 1 nA. Spectrum averaged over 2 sweeps acquired using a 110 mV @ 1.5 nA junction.

Figure 4.22: Gold surface dosed with cobalt atoms at low temperature. Image spans 500 Å x 500 Å acquired at 500 mV @ 500 pA. The single spots are individual adatoms, while the miasmic features are attributed to carbonaceous contamination.

66

A possible explanation for the lack of isolated adatoms is that dosing was carried out at 100 K,

which may not be low enough to prevent aggregation.

While isolated cobalt atoms image prominently on metal surfaces (Fig. 4.24), similar

features were not observed on any of the tubes examined in the dosed sample. This is clearly at

odds with the coverage displayed in figure 4.22. Two possible explanations are considered. The

first is that the STM tip may “sweep” adsorbed cobalt atoms off of tubes during imaging. This is

consistent with the fact that cobalt atoms on metal surfaces are easily moved with the STM.

However, such an interaction is typically accompanied by noticeable responses in the tunneling

current or tip height, which was not observed in this sample.

A second possibility is that the topographic signature of cobalt on a carbon lattice is

much less pronounced than that on metal surfaces. Examination of figure 4.22 shows that

individual adsorbates are clearly resolved on the bare gold surface, but are not evident in the

areas covered with carbonaceous materials. In fact, single cobalt adsorbates could not be

distinguished on any dressed surfaces, no matter how large an area was spanned. A possible

explanation of this enigmatic fact is that cobalt may incorporate into carbon-based surfaces,

masking them from easy detection with the STM.

Calculations for cobalt adatoms on graphite indicate that adatoms preferably bond at the

hexagonal centers 1.52 Å above the graphene plane [22]. However, the curvature of the

0.0

0.4

0.8

1.2

0 10 20 30 40 50 60 70Rel

ativ

e H

eig

ht (

Å)

Lateral Displacement (Å)

Figure 4.24: Single cobalt atom on silver [from Fig. 4.23(c)].

67

nanotube wall can significantly alter bond geometry. For example, calculations show that nickel

preferably bonds to the hexagonal centers in graphite, but on armchair nanotubes prefer to sit

above carbon atoms [23]. Cobalt should be similar to nickel in bond character [24], and may

position itself in such a way as to be partially masked by the regular carbon lattice.

Figure 4.25 shows a single nanotube protruding from a bundle on the cobalt-dosed

sample. Spectra acquired at a random location along the tube reveals a metallic DOS (Fig. 4.26).

Note that a pseudogap is evident in the data despite the fact that the tube is locally isolated in the

vicinity of the measurement. This supports the conjecture in section 4.2.2 that pseudogaps are

essentially uniform along the length of a tube.

An interesting feature of the spectrum is the presence of a second, smaller gap near zero

bias. While it is tempting to assert that this is a Kondo resonance, the shape and width more

closely resemble a curvature-induced gap (see section 2.1.2) than the Kondo resonances

observed on tubes dosed with cobalt clusters. The presence of this gap is consistent with

atomically resolved images revealing that this tube is chiral, since armchair nanotubes are not

expected to develop curvature-induced gaps.

Aside from the gap structure, what makes this tube notable is the unusual defect

displayed in figure 4.27. This defect is topographically characterized by an unusually

pronounced site in the electronic lattice (which may indicate a cobalt adatom) accompanied by a

bright band around the circumference. This feature exhibits strong electron scattering, as

0

5

10

15

20

0 20 40 60 80 100

Rel

ativ

e H

eig

ht (

Å)

Lateral Displacement (Å)

Figure 4.25: Protruding nanotube. Image spans 100 Å x 400 Å acquired at 500 mV @ 2 nA.

68

10

20

30

40

50

-100 -50 0 50 100

dI/d

V (

nA

/V)

Sample Bias (mV)

0

5

10

15

20

-400 -200 0 200 400Sample Bias (mV)

Figure 4.27: Image of an unusual defect found on the nanotube in figure 4.25, along with spatially resolved point spectra revealing novel electronic behavior. Image spans 64 Å x 16 Å acquired at -50 mV @ 2 nA, and is flattened for clarity. Spectra are averaged over 8 sweeps acquired using a 98 mV @ 2 nA junction (left panel) and a 497 mV @ 2 nA junction (right panel).

-0.5

0.0

0.5

1.0

1.5

-500 0 500

Cur

rent

(nA

)

Sample Bias (mV)

0

5

10

15

dI/d

V (

nA/V

)

0.0

0.4

0.8

-200-100 0 100 200

Sample Bias (mV)

5

15

25

-100 0 100

Figure 4.26: Spectral measurement revealing metallic conduction and various low-bias gap structures in the tube featured in figure 4.25. Image spans 48 Å x 192 Å acquired at 50 mV @ 2 nA. Differential conductance measurements are averaged over 8 sweeps, current is averaged over 4 sweeps. Spectra were acquired using a 497 mV @ 2 nA junction, except for inset of far right frame, which was acquired using a 98 mV sample bias. Note that the apparent spectral asymmetry results from the onset of the negative bias azimuthal subband being beyond the range of measurement.

69

evidenced by the electronic interference patterns in the image. Spectroscopy reveals further

unusual behavior in the form of a spatially varying resonance peak that shifts down in energy and

increases in magnitude as the tip is moved closer to the band. This is prominently seen in

differential conductance maps in which the lock-in amplifier signal is recorded simultaneously

with topographic information (Fig. 4.28). As bias voltage is reduced, the resonance peaks

flanking the defect band move inwards, eventually converging at voltages approaching -200 mV.

4.3.3 Discussion

The features described here have not previously been observed in regular nanotubes, and may be

due to the presence of cobalt at the defect center. A similar effect was observed in an experiment

Figure 4.28: Bias dependent imaging of an unusual defect, along with simultaneously acquired differential conductance maps showing resonance peak positions as a function of bias. Images (left column) span 64 Å x 16 Å acquired with a 2 nA setpoint current, flattened for clarity. Conductance maps (right column) are acquired by applying a 1 mVrms modulation to the bias and recording the in-phase response as a function of position using a lock-in amplifier. Sample bias voltages (top to bottom) are: -300 mV, -200 mV, -150 mV, -100 mV, -75 mV, -50 mV, -25 mV, and +150 mV.

70

involving nanotubes containing encapsulated metallofullerenes (Fig. 4.29) [25]. Specifically, C82

endofullerenes containing single gadolinium atoms were inserted into single-wall nanotubes.

Because C82 is slightly larger than the typical diameter of a nanotube, the filling ratio was very

sparse. Near isolated metallofullerenes (identifiable from the resultant strain on the

encapsulating nanotube), differential conductance maps revealed resonance peak structures

strikingly similar to the results presented in this work. In that experiment, the peaks appeared at

positive sample bias and converged as the voltage was lowered to about 750 mV. While the

authors attributed the behavior to band shifting caused by lattice strain, the similarity to the data

acquired on the cobalt-dosed nanotube leads to the conjecture that the effect is a direct

consequence of the presence of a net magnetic moment on the nanotube (gadolinium being a

lanthanide element possessing a significant magnetic moment). An understanding of the

mechanism of the effect is lacking at this time. Possibilities include a 1-dimensional Kondo

effect or a resonance due to spin-flip scattering contributions to the tunneling conductance.

These preliminary results indicate that further investigation is merited. Additionally, STM

experiments involving low temperature cobalt dosing of a graphite surface would help clarify the

mystery of the “hidden” cobalt in these samples.

Figure 4.29: Topographic image (a) and energy-resolved differential conductance maps (b-e) of a metallofullerene peapod (from ref. 25).Blue arrows denote possible gadolinium metallofullerene sites. All images are 76 Å long, and bias voltages for dI/dV maps are (top to bottom): 1.4 V, 1.2 V, 1.0 V, and 0.8 V.

71

4.4 Stone-Wales Defects

While it has been demonstrated that nanotube properties can be altered by the presence of

extrinsic dopants, even nominally pristine tubes can experience significant perturbations

stemming from intrinsic defects within the atomic lattice. Among the most important of these

are bond rotations known as Stone-Wales transformations. This section presents the first direct

STM imaging of this important class of defect.

4.4.1 Theory

When a nanotube experiences strain, the bonds between carbon atoms are stretched from

equilibrium, increasing the overall energy of the atomic lattice. A portion of this increase can be

alleviated through atomic reorganization. One such mechanism is the rotation of a carbon-

carbon bond by 90º, which transforms four hexagons into a pair of heptagons and a pair of

pentagons (Fig. 4.30). Calculations indicate that this process, known as a Stone-Wales

transformation, becomes energetically favorable in tubes experiencing as little as 5% tensile

deformation [26]. As a primary mechanism of strain relief, these structures (also referred to as

5-7-7-5 defects) play a dominant role in the mechanical properties of nanotubes.

Theoretical modeling indicates that these defects possess distinguishing characteristics

that should make them easily identifiable with STM (Fig. 4.31) [26, 27]. Pentagonal rings create

localized electronic states that increase the density of electrons over the defect. Since STM

imaging essentially maps contours of electron density, these rings should appear prominent.

Furthermore, the localized states associated with the pentagons should be identifiable as peaks in

differential tunneling conductance spectra.

Figure 4.30: Illustration of a Stone-Wales transformation (from ref. 26).

72

Indirect observations of Stone-Wales defects have been reported [28, 29]. These

observations are based on the necessity of having this type of defect at kink sites and

intramolecular junction transition points. Direct STM identification has not previously been

reported. The data in this section represents the first known direct observation and

characterization of a Stone-Wales defect with STM.

4.4.2 STM Character ization of a Stone-Wales Defect

Figure 4.32 shows nanotubes in a bundle, one of which exhibits a pair of defects. In contrast to

adsorbate defects, which tend to mask the nanotube lattice, these defects display a rich structure

and appear to be an integral part of the tube. The first defect resembles a pair of rings, with one

ring located along the tube apex and the companion ring somewhat above and off to the side

(making it appear slightly compressed in the image). This double-ring structure is in excellent

agreement with predictions for the STM imaging signature of 5-7-7-5 defects [26]. The apparent

height of these rings is about 1 Å (Fig. 4.33), which equates to about an order of magnitude

increased conduction in these regions.

Figure 4.31: Simulated STM image of a Stone-Wales defect on a (10, 10) armchair nanotube under 10% tensile strain imaged at 0.5 V sample bias (from ref. 26). The distinguishing feature is a pair of prominent rings corresponding to the pentagons of the 5-7-7-5 geometry.

73

4 5 6 7

0

5

10

15

L1030539la 3:09:28 PM 12/23/2002

Relative Height (Å)

Lateral D

istance (Å)

4

5

6

7

0 2 4 6 8 10 12Rel

ativ

e H

eig

ht (

Å)

Lateral Distance (Å)

Figure 4.33: Line sections highlighting the pronounced apparent height of the defect featured in the top right panel of figure 4.32. The blue section line runs through the centers of both rings, while the red cuts only the apical ring.

Figure 4.32: Images of topological defects. Left image spans 64 Å x 128 Å, right images span 32 Å x 32 Å, all acquired at 1.25 V @ 100 pA.

74

The second defect has a somewhat different appearance, resembling a series of axially

oriented “ ridges” . This is not entirely unlike what is observed in the first defect, as a similar

ridge appears on the periphery of the apical ring. This leads to speculation that the structure of

the second defect is consistent with a 5-7-7-5 defect located closer to the side of the tube, where

the double-ring structure would be highly distorted in STM images.

Both defects were characterized spectroscopically using spatially-resolved point

measurements along the tube apex. Over the first defect, two distinct effects were observed

(Fig. 4.34). A suppression of the filled-state band edge near -1 V occurs within 4 Å of the ring

center, and directly over the center region a peak at 750 mV appears. This peak is consistent

with the expectation of localized electronic states over the pentagonal rings [26], though these

particular results are different from calculations indicating localized states should appear within

the filled-state band near -750 mV sample bias. While a feature in that energy range is present in

some of the spectra acquired within 4 Å of the defect center, it is less definite than the peak

observed over the center. The differences between measurement and calculation may be

attributable to the different parameters involved. Calculations were considered for a single

0.0

0.2

0.4

0.6

0.8

1.0

-1 -0.5 0 0.5 1

dI/dV

(nA

/V)

Sample Bias (V)

Figure 4.34: Spectra acquired at various displacements from the defect featured in the top right panel of fig. 4.32. Spectra are averaged over 8 sweeps and offset in increments of 0.075 nA/V for clarity, acquired using a 1.25 V @ 100 pA junction.

75

defect on an unsupported (10, 10) armchair nanotube, whereas measurements were performed

on a chiral nanotube in a bundle interacting with a substrate.

Results obtained for the second defect (Fig. 4.35) are in good agreement with those from

the first, supporting the hypothesis that this is also a 5-7-7-5 defect. The localized state at 750

mV is much less distinct than in the first measurement, which is consistent with the actual defect

being positioned off the tube apex.

4.4.3 Discussion

These results represent the first known direct observation of a Stone-Wales defect with STM,

and are in general agreement with theoretical predictions. The distinguishing feature is a

prominent double-ring structure likely associated with the formation of pentagons within the

atomic lattice. These rings are coincident with localized electronic states appearing in spectral

measurements as a peak in the unoccupied electronic states at 750 mV.

As a primary strain-relief mechanism, Stone-Wales defects should play a key role in the

mechanical properties of nanotubes. Additionally, the perturbation induced in the local

electronic structure indicates significant coupling between mechanical stress and electronic

0.0

0.2

0.4

0.6

0.8

1.0

-1.5 -1 -0.5 0 0.5 1 1.5

dI/dV

(nA

/V)

Sample Bias (V)

Figure 4.35: Spectra acquired at various displacements from the defect featured in the top right panel of fig. 4.32. Spectra are averaged over 8 sweeps and offset in increments of 0.075 nA/V for clarity, acquired using a 1.25 V @ 100 pA junction.

76

properties, in agreement with measurements performed on bent nanotubes. The implications of

this coupling are far reaching. Unusual conduction properties have been observed in nanotubes

in high-strain configurations; a fascinating example of this is single-electron transistor behavior

observed in room temperature measurements performed on single-wall nanotubes with multiple

kinks induced along the axis using an AFM probe [30]. In accordance with the results presented

here, the kink sites should contain pentagon-heptagon pairs that form localized electronic states

on the tube walls. These states could provide a strong barrier to electron transport, effectively

converting the section of the tube between the kink sites into a quantum dot.

The primary obstacle in STM investigations of 5-7-7-5 defects is the difficulty involved

in creating defects in an orientation accessible to the probe. Kinks induced with AFM probes

have high strain sites along the sides of the tube, where the resultant deformation in atomic

lattice is hidden from observation (much like the second defect observed in this experiment).

Given that these are strain-related features, the possibility exists of being able to induce a Stone-

Wales transformation using the STM, either through direct mechanical interaction or through

some activated electronic process. Investigations along these lines have yet to bear fruit. Once

in place, another intriguing property of these defects is their mobility along the tube wall.

Calculations indicate that in tubes of certain chirality, the position of the bond rotation will be

“ fluid” . By “sliding” the two pentagon-heptagon pairs of a 5-7-7-5 defect in opposite directions

along a tube axis, an intramolecular junction should be formed [26].

4.5 References [1] J. W. G. Wildöer, L. C. Venema, A. G. Rinzler, R. E. Smalley, and C. Dekker, Nature 391,

59 (1998). [2] W. Clauss, D. J. Bergeron, M. Freitag, C. L. Kane, E. J. Mele, and A. T. Johnson, Europhys.

Lett. 47, 601 (1999). [3] D. Tománek, S. Louie, H. Mamin, S. Abraham, R. Thomson, E. Ganz, and J. Clarke, Phys.

Rev. B 35, 7790 (1987). [4] C. L. Kane and E. J. Mele, Phys. Rev. B 59, R12 759 (1999). [5] Handbook of Chemistry and Physics, 69th Edition, CRC Press (1988). [6] M. Shiraishi and M. Ata, Carbon 39, 1913 (2001).

77

[7] P. Kim, T. W. Odom, J.-L. Huang, and C. M. Lieber, Phys. Rev. Lett. 82, 1225 (1999). [8] J. W. Janssen, S. G. Lemay, L. P. Kouwenhoven, and C. Dekker, Phys. Rev. B 65, 115 423

(2002). [9] W. Clauss, D. J. Bergeron, and A. T. Johnson, Phys. Rev. B 58, R4266 (1998). [10] M. Buongiorno Nardelli, J.-L. Fattebert, D. Orlikowski, C. Roland, Q. Zhao, and

J. Bernholc, Carbon 38, 1703 (2000). [11] A. Rochefort, Ph. Avouris, F. Lesage, and D. Salahub, Phys. Rev. B 60, 13 824 (1999). [12] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 78, 1932 (1997). [13] T. W. Odom, J.-L. Huang, P. Kim, and C. M. Lieber, J. Phys. Chem. B 104, 2794 (2000). [14] P. Delaney, H. J. Choi, J. Ihm, S. G. Louie, and M. L. Cohen, Phys. Rev. B 60, 7899 (1999). [15] A. Rubio, Appl. Phys. A 68, 275 (1999). [16] J. A. Stroscio and R. M. Feenstra, in chapter 4 of Scanning Tunneling Microscopy, edited

by J. A. Stroscio and W. J. Kaiser, Methods in Experimental Physics, Vol. 27 (Academic Press, San Diego, 1993).

[17] A. C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press,

Cambridge, 1997) and references therein. [18] H. C. Manoharan, C. P. Lutz, and D. M. Eigler, Nature 403, 512 (2000). [19] T. Jamneala, V. Madhavan, W. Chen, and M. F. Crommie, Phys. Rev. B 61, 9990 (2000). [20] M. A. Schneider, L. Vitali, N. Knorr, and K. Kern, Phys. Rev. B 65, 121 406 (2002). [21] T. W. Odom, J.-L. Huang, C. L. Cheung, and C. M. Lieber, Science 290, 1549 (2000). [22] D. M. Duffy and J. A. Blackman, Phys. Rev. B 58, 7443 (1998). [23] M. Menon, A. N. Andriotis, and G. E. Froudakis, Chem. Phys. Lett. 320, 425 (2000). [24] A. N. Andriotis, M. Menon, and G. E. Froudakis, Appl. Phys. Lett. 76, 3890 (2000). [25] J. Lee, H. Kim, S.-J. Kahng, G. Kim, Y.-W. Son, J. Ihm, H. Kato, Z. W. Wang, T. Okazaki,

H. Shinohara, and Y. Kuk, Nature 415, 1005 (2002).

78

[26] D. Orlikowski, M. Buongiorno Nardelli, J. Bernholc, and C. Roland, Phys. Rev. B 61, 14 194 (2000).

[27] V. Meunier and Ph. Lambin, Carbon 38, 1729 (2000). [28] M. Ouyang, J.-L. Huang, C. L. Cheung, and C. M. Lieber, Science 291, 97 (2001). [29] L. C. Venema, J. W. Janssen, M. R. Buitelaar, J. W. G. Wildöer, S. G. Lemay, L. P.

Kouwenhoven, and C. Dekker, Phys. Rev. B 62, 5238 (2000). [30] H. W. Ch. Postma, T. Teepen, Z. Yao, M. Grifoni, and C. Dekker, Science 293, 76 (2001).

79

Chapter 5 Nanotube Peapods

This section focuses on STM studies of a recently synthesized fullerene hybrid molecule

consisting of C60 molecules encapsulated within the hollow interiors of single-wall nanotubes.

The structure and fabrication of these peapod fullerenes is discussed in section 3.2.1. In much

the same way as the formation of endohedral fullerenes, the insertion of materials into the cores

of nanotubes represents a pathway for tailoring tube properties for specific functionality.

Previous investigations of filled nanotubes have focused primarily on tubes incorporating metal-

based filling materials, such as cobalt [1], silver [2], and chromium [3]. The experiments in this

chapter are the first to examine the electronic structure of nanotubes containing complex

fullerene molecules. A focal point of these experiments is how the electronic behavior of the

composite molecule relates to that of the constituent components. As will be demonstrated, the

combination of different fullerene types leads to novel behavior that is something more than just

“ the sum of the parts” .

5.1 STM Imaging of Peapods

With few exceptions, STM is exclusively a surface probe technique. Thus, the presence of

interior buckyballs must be inferred from their influence upon the host nanotube. The first

indication of novel effects in peapod samples was the appearance of a periodic modulation in the

apparent height along the apex of a tube (Fig. 5.1). This modulation takes the form of “crests”

measuring 30-50 pm relative to the tube surface, large in comparison to the 10 pm corrugation

typically observed on the atomic lattice of a nanotube. This feature is distinct from similar

effects induced by the presence of adsorbates (see Fig. 4.21), most notably in its periodicity over

large length scales. Crests were often seen to extend over hundreds of angstroms, with typical

spacing on the order of 10.5 ±1.0 Å. This is in excellent agreement with TEM images of

peapods showing that individual tubes can have substantial fractions of their interior space filled

by close-packed C60 chains with intermolecular spacing of ∼10 Å [4].

80

The most unusual property of this feature is its dependence on bias polarity, with the

majority of crests (≥ 90%) observable only with positive bias voltages greater than ∼1 V

(Fig. 5.2). Images acquired using negative bias polarity show only the lattice associated with the

underlying atomic structure of the nanotube. This leads to the conclusion that the crests reflect

the presence of interior C60 molecules, and furthermore that these molecules do not measurably

alter the atomic structure of the encapsulating nanotube. This is in agreement with theoretical

calculations predicting peapod formation is most favorable when it does not lead to structural

distortion of the fullerenes [5]. Further experimental evidence supporting this hypothesis was

obtained by performing bias-dependent imaging on a tube featuring a partial array of crests

(Fig. 5.3). Crests appear prominently in positive-bias STM topographs down to 1 V, where they

quickly fade to reveal the underlying tube structure. In comparison, images acquired over an

-40

0

40

0 20 40 60 80 100

Hei

gh

t (p

m)

Posit ion (Å)0 20 40 60 80 100

Posit ion (Å)

Figure 5.2: Images acquired using positive (left) and negative (right) bias polarity. The identifying characteristic of peapods is theappearance of a periodic enhancement in conduction (which manifests in images as an array of “crests”) under positive sample bias. Images acquired at ±1.5 V @ 700 pA with boundaries spanning 118 Å x 29 Å.

Figure 5.1: Nanotube on a peapod sample exhibiting novel features (arrows). Images acquired at 1.75 V @ 250 pA with boundaries (from left to right) 557 Å x 224 Å, 165 Å x 175 Å, and 122 Å x 84 Å.

81

0.00

0.04

0.08

0.12

0.16

-1.5 -1 -0.5 0 0.5 1 1.5

dI/dV

(nA

/V)

Sample Bias (V)

Figure 5.4: Peapod exhibiting metallic conduction. Images span 32 Å x 128 Å acquired at -1.8 V @ 300 pA (left) and 1.8 V @ 300 pA (right). Point spectrum averaged over 7 sweeps (each sweep averaged 16 times), acquired using a 1.8 V @ 300 pA junction.

Filled Section Unfilled SectionPos it ive Bias Negative Bias Pos itive Bias Negative Bias

2.50 V

2.00 V

1.50 V

1.00 V

0.75 V

0.50 V

1.25 V

1.75 V

2.25 V

Figure 5.3: Bias-dependent imaging performed on a partially filled peapod (featured in figure 5.1). Images in the left columns are acquired over a filled section of the tube, while the images on the right were acquired over an unfilled section as a control experiment. Images are flattened, with boundaries span 54 Å x 20 Å.

82

area devoid of crests exhibit little change with bias voltage, and show a lattice structure closely

resembling that in images acquired over the crested region using negative sample bias. These

effects are observed to occur in both metallic (Fig. 5.4) and semiconducting (Fig. 5.5) nanotubes.

5.2 Tunneling Spectroscopy of Peapods

Point spectroscopy reveals distinct differences in the local electronic structure over and in

between crest sites (Fig. 5.5). Between crests, spectral measurements resemble those expected

for unfilled nanotubes. Over the crests, prominent new features appear in the unfilled (positive

bias) state structure in the form of peaks in the differential conductivity. Typically, these peaks

occur in pairs, with a major peak near +1 V followed by a minor peak a few hundred millivolts

higher.

The correspondence between imaging crests and spectral peaks is demonstrated directly

through bias-dependent imaging coupled with simultaneously acquired differential conductivity

maps (Fig. 5.6). As the crests in the image fade, the differential conductivity at that location

experiences a sharp spike in intensity. These characteristics are also evident in differential

conductivity measurements plotted over space and energy (Fig. 5.7), where the spectral peaks are

seen to exhibit the same periodicity as the crests in imaging. Notable is the lack of discernable

change in the filled (negative bias) state structure with position. The relatively small fluctuations

seen in spectral plots are attributable to the 30-50 pm difference in tip height between on- and

off-site locations; normalization of the data removes this artifact.

0.0

0.4

0.8

1.2

-2 -1 0 1 2d

I/dV (n

A/V

)Sample Bias (V)

Figure 5.5: Point spectra acquired over (red) and in between (blue) crests on the peapod featured in figure 5.2. Points are spaced 6 Å apart along the tube apex. Spectra are averaged across 16 samples, acquired using a 2.5 V @ 700 pA junction.

83

Spectral data acquired at higher biases reveals a second pair of peaks beyond +2 V

(Fig. 5.8). Presently, there is not enough data in this energy range to say with certainty the

nature of these features. As discussed in section 4.1.4, measurements in this voltage range are

difficult to obtain because of the potential for field-induced damage to the nanotubes. Also, the

relatively large voltages significantly distort the tunneling barrier, resulting in rapidly increasing

contributions to the current that makes identification of peaks difficult. As demonstrated in

figure 5.8, normalization of the data is necessary for peaks to be clearly distinguished. Further

investigation is required to determine if these features appear consistently across different

peapods.

The combination of results from tunneling spectroscopy and topographic imaging leads

to the conclusion that the double-peak features in the spectra reflect a modification in the local

electronic structure caused by the interaction of the C60 molecules with the encapsulating

1.26 V

1.23 V

1.19 V

1.11 V

1.03 V

0.99 V

0.96 V

0.65 V

Sample Bias Topography dI/dV Map

Figure 5.6: Topographs (left column) and simultaneously measured differential conductance maps (right column) of a peapod at various bias voltages. Images acquired at 500 pA with boundaries spanning 85 Å x 34 Å. Differential conductance maps were measured using lock-in detection of the AC current response to a 5 mVrms modulation applied to the bias.

84

nanotube. A consequence of this modification is the spatially periodic enhancement in tunneling

conduction above ∼1 V, which manifests as crests in STM images. The filled electronic states of

the nanotube are unperturbed by the interaction with C60, making peapods indistinguishable from

unfilled nanotubes in negative bias STM measurements.

An important clue concerning the nature of the C60-nanotube interaction is provided by

measurements on peapods exhibiting spatial variation in band edge energy (see section 4.1.3).

Spectroscopy reveals that the double-peak energy is tied to the band edge onset energy of the

nanotube (Fig. 5.9). This indicates that these features are the consequence of coupling between

the electronic structures of the constituent fullerenes, as opposed to simply resulting from direct

tunneling into the valence states of the C60 molecules.

5.3 STM Induced Motion of Encapsulated C60

Calculations indicate the spatial variation in the binding energy of a C60 molecule adhered to the

exterior of nanotube is small (≈0.1%) [6]. While the total binding energy is larger for a molecule

on the interior surface due to increased contact area, the relative spatial variation should remain

the same. This suggests that buckyballs can be mobile inside peapods, a conjecture verified by

time-lapse TEM imaging demonstrating spontaneous motion of C60 molecules at room

temperature (Fig. 5.10) [7].

-1.0 0 1.8Sample Bias (V)

Po

sitio

n (Å

)

112

0

Scale (nA/V)

0.5

0.0

1.2

0.0-1.75 0 1.75

Sample Bias (V)

Position

(Å)

128

0

Figure 5.7: Intensity plot comparing spectroscopy measurements on the peapod in figure 5.2 with an unfilled semiconducting nanotube (not pictured). Arrows denote major (white) and minor (black) peaks in the differential conductivity. Spectra are averaged across 16 samples, acquired in 0.22 Å increments using a 1.8 V @ 700 pA junction (left) and in 0.5 Å increments using a 1.75 V @ 500 pA junction (right).

85

Sca

le (nA/V

)

0.6

0.0-1.5 0 1.5

Sample Bias (V)

Po

sition (Å

)

182

0

Figure 5.9: Spectral plot of a peapod exhibiting band edge bending. Simultaneously recorded image spans 32 Å x 182 Å acquired at 1.5 V @ 300 pA. Spectra are averaged across 16 samples, acquired in 0.5 Å increments.

9

0

Scale (nA/V)

0.64

0.00

nA

/V

arb0 3.5

Sample Bias (V)0 2.6 3.5

Sample Bias (V)

Po

sition (Å

)

111

0

Normal ized

Figure 5.8: Spectral plot of a peapod acquired at positive bias up through 3.5 V. The plot on the right is normalized to accentuate features appearing at high bias near 2.2 and 2.6 V. Image acquired at 1.5 V @ 700 pA with boundary spanning 29 Å x 116 Å. Spectra are averaged across 16 samples, acquired in 0.22 Å increments using a 3.5 V @ 700 pA junction.

86

The STM experiments are performed at 4 K, which should inhibit spontaneous diffusion

of C60 molecules. However, it was discovered during the course of these experiments that the

STM tip can be used to activate motion (Fig. 5.11). The precise mechanism by which this occurs

is as yet undetermined, but procedurally this is accomplished by rapidly moving the tip across

the peapod in a direction perpendicular to the tube axis. This has the effect of bringing the tip in

close range of the tube before the feedback loop can respond, resulting in a “shock” interaction

that may involve momentary structural deformation of the tube.

Figure 5.10: Time-lapse TEM images showing spontaneous diffusion of buckyballs inside a nanotube at room temperature (from ref. 7). Images are acquired in 30 second intervals. Scale bar is 2 nm.

Negative Bias

Figure 5.11: Successive topographs demonstrating changes in crest position on a peapod resulting from interaction with the STM tip. Images are flattened, acquired at 2 V @ 250 pA (except far right, acquired at -2 V) with boundaries spanning 141 Å x 176 Å.

87

Scale

(nA/V

)

1.28

0.00-0.75 0 2.00

Sample Bias (V)

Po

sition (Å

)

88

0

Figure 5.13: Spectral plot obtained on the peapod in figure 5.12 after removal of the crests from the imaged region via interaction with the STM probe, acquired using the same measurement parameters.

Scale (nA

/V)

1.28

0.00-0.75 0 2.00

Sample Bias (V)

Position

(Å)

88

0

Figure 5.12: Spectral plot for the peapod in figure 5.6. Image acquired at 2 V @ 500 pA with boundary spanning 28 Å x 95 Å. Spectra are averaged across 16 samples, acquired in 0.17 Å increments using a 2 V @ 500 pA junction.

88

The ability to alter the structure of a peapod leads to an interesting experiment. A

spectral measurement of a peapod is plotted in figure 5.12. After acquisition of this data, the C60

molecules were moved away from the area using the STM. The measurement was then repeated

on the now unfilled section of tube (Fig. 5.13). Comparison of the two measurements yields

information concerning the extent of C60-nanotube interactions. For instance, while the double-

peak spectral feature is clearly tied to the buckyballs, the variation of the band edge energy

appears inherent to the nanotube and is unaffected by the presence (or absence) of C60.

5.4 Theory

Initial calculations indicated unusual electronic behavior should be expected in peapod structures

[5]. Recently, a theoretical framework in which to interpret STM measurements has been

developed [8, 9]. The key feature is a symmetry-selective coupling between the electronic states

of C60 and the azimuthal subbands of the nanotube. Electrons can transit between quantum states

of the nanotube and the buckyballs only when those states have the same energy and adhere to

certain angular momentum selection rules (note that the angular momentum quantum number of

the tube states is NOT the same thing as the azimuthal subband index - a subband can be

composed of states containing an admixture of different angular momenta [9]). Since the

electronic structure of nanotubes varies greatly depending on tube diameter and chirality (see

section 2.1.2), it is expected that peapods will also exhibit a wide range of electronic

characteristics, perhaps not all of which are easily identified with STM.

To model the results presented in this chapter, a calculation for a peapod consisting of a

periodic array of buckyballs encapsulated inside a semiconducting nanotube having a diameter of

13.2 Å was performed. In this situation, the t1u valence orbitals of the C60 molecules reside in the

same energy range as the onset of the third azimuthal subband of the nanotube. Computation of

the tunneling amplitudes indicates that mixing of these electronic states is strong, particularly for

a (12, 8) or a (13, 6) nanotube. This mixing results in the formation of a narrow (∼0.2 eV) C60-

derived electronic band near the subband edge, separated from the remaining nanotube states by

a hybridization gap. The periodic nature of the encapsulated fullerenes leads to the formation of

complimentary standing wave patterns on either side of this gap, which is expected for electrons

residing in a periodic potential.

89

In the occupied electronic states, the hu orbitals of C60 overlap the second azimuthal

conduction subband. The tunneling amplitudes in this case indicate that electron transitions are

symmetry forbidden, and no hybridization occurs.

The expected electronic structure for this model is shown in figure 5.14. The primary

feature is the large enhancement in the density of states over the C60 sites near the edges of the

t1u-derived band. A hybridization gap separates this band from the remaining states of the third

azimuthal tube subband, which also exhibits a modulation at the band edge, but shifted in phase

by a half-period. For comparison, a section of the data from figure 5.11 is also plotted in

figure 5.14. There is noticeable similarity between the two.

The physics involved in this model can be reduced to the case of two buckyballs

encapsulated within a nanotube (Fig. 5.15) [9]. In this situation, the C60 molecules interact with

the electronic structure of the tube to form bound states in the nanotube wall. In turn, the

nanotube acts as a conduit for coupling the bound states together, which mix to form high and

low energy configurations, similar to bonding/antibonding pairs. These states scatter electrons

propagating on the tube wall, inducing oscillations in electron density at higher energies. As

expected from self-interference due to coherent backscattering, the oscillation wavelength

becomes shorter with increasing energy. At some energy the wavelength becomes comparable to

the spacing between buckyballs. At this energy, the C60 molecules act as an electronic Fabry-

Perot resonator, resulting in an accumulation of electron density between the sites.

Figure 5.14: Comparison of the calculated electronic structure of a semiconducting peapod with a 13.2 Å diameter (left, from ref. 9) and a corresponding section from the experimentally measured differential conductivity map in figure 5.12. In the calculation, the energy of the C60t1u orbitals is taken to be 1.3 eV.

0.8 eV 1.8 eV

Computation

a

Measurement

0.8 eV 1.8 eV

9.7

Å

90

5.5 Discussion

The identifying feature of peapods in STM images is the appearance of a periodic array of crests,

which reflect the presence of interior C60 molecules and the modification in electronic structure

they induce. Theory indicates that this modification is not simply the addition of C60 states to the

nanotube, but results from coupling between the constituent fullerenes. Thus, the properties of

the composite material are different from the properties of the individual constituents summed

together. This demonstrates the possibility of engineering novel electronic behavior in

composite fullerene systems. Future investigations on peapods formed from metallofullerenes

[10] and polymerized chains of C60 molecules [11] should yield further unique effects.

All of the data presented in this chapter shows C60 molecules in chains. This is the case

generally; isolated molecules were not observed or did not have identifiable signatures. TEM

imaging indicates a propensity for buckyballs to form chains. This is expected, since fullerenes

are mutually attracted to one another by van der Waals interactions [6].

An interesting point to consider is the angular orientation of the C60 molecules. As stated

in section 2.1.1, in solid form buckyballs rotate freely at room temperature. As they are cooled

the rotational motion freezes out and the molecules preferentially align with their neighbors. It

seems reasonable that this would also occur in peapods, provided that they are not rapidly

quenched. However, determination of this appears to be beyond to capability of STM at present.

Figure 5.15: Local density of states for a pair of C60 molecules encapsulated inside a nanotube (from ref. 9). In the calculation the nanotube subband onset energy is 1.1 eV and the energy of the C60 t1uorbitals is 1.3 eV.

91

5.6 References [1] S. Liu and J. Zhu, Appl. Phys. A 70, 673 (2001). [2] Z. L. Zhang, B. Li, Z. J. Shi, Z. N. Gu, Z. Q. Xue, and L.-M. Peng, J. Mater. Res. 15, 2658

(2000). [3] F.-X. Zha, D. L. Carroll, R. Czerw, A. Loiseau, H. Pascard, W. Clauss, and S. Roth, Phys.

Rev. B 63, 165 432 (2001). [4] B. Burteaux, A. Claye, B. W. Smith, M. Monthioux, D. E. Luzzi, and J. E. Fischer, Chem.

Phys. Lett. 310, 21 (1999). [5] S. Okada, S. Saito, and A. Oshiyama, Phys. Rev. Lett. 86, 3835 (2001). [6] L. A. Girifalco, M. Hodak, and R. S. Lee, Phys. Rev. B 62, 13 104 (2000). [7] B. W. Smith, M. Monthioux, and D. E. Luzzi, Chem. Phys. Lett. 315, 31 (1999). [8] D. J. Hornbaker, S.-J. Kahng, S. Misra, B. W. Smith, A. T. Johnson, E. J. Mele, D. E. Luzzi,

and A. Yazdani, Science 295, 828 (2002). [9] C. L. Kane, E. J. Mele, A. T. Johnson, D. E. Luzzi, B. W. Smith, D. J. Hornbaker, and

A. Yazdani, Phys. Rev. B 66, 235 423 (2002). [10] J. Lee, H. Kim, S.-J. Kahng, G. Kim, Y.-W. Son, J. Ihm, H. Kato, Z. W. Wang, T. Okazaki,

H. Shinohara, and Y. Kuk, Nature 415, 1005 (2002). [11] T. Pichler, H. Kuzmany, H. Kataura, and Y. Achiba, Phys. Rev. Lett. 87, 267 401 (2001).

92

Chapter 6 Summary

While the physics of nanotubes is well understood at a fundamental level, these experiments

demonstrate that interaction with ambient environments can profoundly affect nanotube

behavior. Significant changes in locally probed electronic properties arise from structural strain,

coupling to other nanotubes and extrinsic dopants, and lattice defects.

Inter-tube interactions suppress the low-bias conductivity of armchair nanotubes due to

symmetry-breaking effects. This suppression is robust, unaffected by lattice strain induced by

STM tips and local variations in electronic structure typical of substrate supported nanotubes.

Measurements performed on a nanotube sample dosed with the magnetic element cobalt

have lead to the observation of unusual defect that exhibits a tunneling resonance that shifts

location as the bias voltage is varied. This resonance closely resembles data acquired on

gadolinium metallofullerene peapods. A common link between the two experiments is the

magnetic nature of the elements involved. This phenomenon requires further investigation.

The first direct STM measurement of a Stone-Wales defect is reported. Theory indicates

that this type of defect plays a central role in the electromechanical properties of perturbed

nanotubes, and may be at the center of several intriguing and potentially important effects

observed in other experiments.

The first STM characterization of all-carbon nanotube peapods is reported. Analysis of

the data indicates that electronic coupling between the constituent fullerenes results in novel new

behavior. This demonstrates the potential for engineering new fullerene macromolecules with

properties tailored for specific functionalities.

Several avenues of nanotube research remain open. While progress has been achieved

concerning the effects that various dopants have on nanotube behavior, interactions with

substrates other than gold are largely unknown. The unusual physics of fullerene

heterostructures such as peapods and intramolecular junctions merit continued exploration.

Controlled growth processes and microassembly techniques are topics with immense

technological impact. STM has proven to be a cornerstone technique in elucidating the physics

of nanotubes, and will continue at the forefront of fullerene research for the foreseeable future.

93

Appendix A

Derivation of the (n-m) = 0(mod 3) Condition Geometric arguments can be used to extract a condition on the chiral indices (n, m) that will

indicate whether a given nanotube is metallic or semiconducting. Figure A.1 shows a diagram of

the graphite lattice with basis vectors a1 and a2. Using the Cartesian coordinate system defined

in the figure,

( ) ( )312

01 02001 ,a;,xa

aaa === (A.1)

where a0 = 3 ac-c = 2.46Å is the graphite lattice constant (in this appendix, coordinates in

parenthesis are understood to be in the appropriate Cartesian basis). It follows that the wrapping

vector Ch can be expressed as

( )mmna

mn 3220

21h ,aaC +=+= . (A.2)

Since a1 is coincident with the x-axis, it follows trivially that the chiral angle (as defined in

section 2.1.2) is given by

mn

m

+=

2

3tan 1-θ . (A.3)

a1

a2

x

y

Figure A.1: Diagram of the graphene lattice in real space. The Wigner-Seitz primitive cell is outlined in red, and a1 and a2 denote lattice basis vectors.

94

Noting that the length of the wrapping vector is the circumference of the nanotube, we have the

relation

[ ] 21

220h mnmnaD ++== Cπ (A.4)

where D is the diameter of the nanotube.

The cylindrical shape of the nanotube forces the electron states around the circumference

to satisfy a boundary matching condition. The smallest allowed wavevector in that direction is

simply the reciprocal wrapping vector

h (unlike the “particle-in-a-box” problem, a half

wavevector is not allowed – the first circuit around the circumference will be annihilated by the

opposite-phased second circuit). The reciprocal space basis vectors are defined as

132

132

321

321 22

aaa

aab;

aaa

aab

ו×

=ו

×= ππ (A.5)

where in this case a3 is taken to be the out-of-plane unit vector. The calculation is simplified by

realizing that the triple vector products in the denominators are equivalent; the resulting vectors

in kx, ky coordinates are

( ) ( )203

213

3

2

0

2

0

1 ,b;,baa

ππ =−= . (A.6)

Figure A.2 shows a diagram of the reciprocal lattice and the resulting first Brillouin zone

constructed from the perpendicular bisectors of the lines joining the nearest neighboring points in

the various directions. As mentioned in section 2.1.2, the Fermi points of graphene are located at

the corners of this hexagon. The coordinates for K and K ' are

( )

=′=3

11

201

3

4

00

,aa

ππK;,K . (A.7)

To write an expression for

h, the axis intercepts of the “plane” (a line in two

dimensions) defined by Ch with respect to the real space basis lattice a1, a2 must first be

determined. The geometry for this is diagrammed in figure A.3. The calculation of the

coefficients u, v is straightforward, yielding

mn

mnmnv

mn

mnmnu

22

22

2222

+++=

+++= ; . (A.8)

95

The expression for

h is then

( )( )mmnmnmnavu

3211

220

21h ,bbC +++

=+= π . (A.9)

Noticing the similarities between expression (A.9) and expressions (A.2) and (A.4), this can be

recast as

h

hh

2

CC

CD

= (A.10)

where it is understood that Ch retains its original form, but mapped onto the reciprocal space

Cartesian axes.

θθθθ60º

u a1

v a2

C h

x

y

Figure A.3: Calculating the reciprocal wrapping vector coefficients.

b1

b2

kx

ky ΓΓΓΓ K

K'

Figure A.2: Reciprocal lattice of graphene with basis vectors b1 and b2. The first Brillouin zone boundary is marked in red, with Fermi points located at the vertices.

96

The allowed states of the nanotube are a series of parallel lines in reciprocal space

defined by integer multiples of

h. A nanotube will exhibit metallic conduction when one of

these states crosses a Fermi point. In this appendix, only the condition for the specific point K to

be an allowed state will be considered; the reader can verify independently that the derived

condition holds for all Fermi points (i.e. if one point is an allowed state, all points are allowed).

The problem is diagrammed in figure A.4. Lines denoting allowed states pass through

the origin with chiral angle relative to the ky-axis and interline spacing |

h|. It follows that

these lines intersect the kx-axis at a regularly spaced set of points ηq, where η is an integer. The

interval q is determined from the relation

( ) ( )mna

mn

mD

qq +

=

+

==2

4

2

3tancos

2cos

01-

h πθC

. (A.11)

The tube will be metallic when ηq = K for some η, or

( ) ( ) 3) (mod02323

4

2

4

00

=+≡=+=+

mnmnamna

ππ (A.12)

The final equality is trivially equivalent to the desired expression n - m = 0(mod3); simply

subtract -3n = 0(mod 3) and multiply by -1=1(mod 3).

q

ky

K

ΓΓΓΓ 3a0

4ππππ, 0)(

|

h |θθθθ

Figure A.4: Geometric considerations in determining the condition for metallic conduction of a nanotube.

97

Appendix B

Notes on Data Acquisition and Processing

While it is common practice to digitally enhance STM images for public display, post-processing

of images in this thesis has been kept to a minimum to ensure the integrity of the results. The

only alteration in most images is the digital subtraction of a plane in order to orient terraces or

nanotubes parallel to the image plane. Images of nanotubes that are described as “ flattened”

have had the average value of each scan line parallel to the tube axis subtracted individually, in

effect compressing the curved surface of the nanotube onto a plane in order to accentuate the fine

details of the lattice. Digital filtering of images has not been employed. As a result, the images

presented (especially those with very small asperity, such as in figure 4.24) exhibit noticeable

noise, which provides a measure of imaging resolution. Under good tunneling conditions

relative height differences on the order of a few picometers can be resolved. Lateral resolution is

difficult to estimate on surfaces lacking high crystalline order, and as a rule varies over time as

the tip and sample interact. This issue is especially difficult to address in experiments involving

nanotubes, which interact with a greater portion of the tip than is typical (see section 3.3.2).

In June of 2001, for reasons unknown, the voltage-distance scaling constant along one

direction of the piezo tube scanner inexplicably changed by a factor of two. Unfortunately, this

aberration was not detected until April of 2002, and as a result images acquired during this

period are directionally anisotropic. These images have been mathematically remapped to

restore uniformity, and are easily identifiable as the corrected topographs take the form of

parallelograms.

Structural and thermal effects in the piezoceramic components can lead to “drifting” of

the tip over time. While potentially a source of image distortion, the rate of lateral drift under

typical operating conditions has been measured to be on the order of 1 Å per hour. More

troublesome is drift perpendicular to the sample when the feedback control loop is disabled

during spectroscopic measurements. This results in a skewing of the resulting data, as evidenced

in figure B.1. Generally, drift rates under open loop conditions are characterized by a 20%

98

change in tunneling current over a span of ∼3 minutes, though the particular rate at any given

time depends greatly on the recent history of the piezoelectric ceramics. The protocol for high

resolution data acquisition is to allow the piezos to equilibrate a few hours before measurement

and avoid large changes in scanner positioning.

Over the course of these experiments two different STM control/acquisition packages

from RHK Technologies were employed. While the imaging capability of these systems is

essentially identical, there are a few differences in spectral acquisition that should be noted. The

system used for experiments up through the initial observations of peapods performed spectral

measurements using a dual forward/backward bias sweep mode, where the bias voltage is

ramped from the starting value to the end value, then ramped in reverse back to the starting

value. This method has the advantages of providing a measure of perpendicular tip drift and of

eliminating large, sudden changes in bias voltage which can potentially alter tip structure or

damage nanotubes. However, the maximum number of data points that could be measured in a

sweep using this setup was 256, which is less than ideal as it unnecessarily limits voltage

resolution in wide bias spectral scans. The more recently employed system eliminates this

constraint, and the measurement resolution is limited only by the bit resolution of the analog-to-

digital converter, which is 4.88 mV. Unfortunately, the newer system does not utilize the

forward/backward mode of acquisition, which is occasionally a source of experimental difficulty.

A general feature of lock-in amplifiers is the use of output filtering. In essence, the

output signal is integrated over a window determined by a user-selected time constant. This

2.0

2.5

3.0

3.5

4.0

-100 -50 0 50 100

Lock

-in O

utpu

t (V

)

Sample Bias (mV)3

60 m

V

Figure B.1: Example of the effects of tip drift on spectra acquired in the forward/backward sweep mode. Bias voltage is swept positive to negative (red curve) then back to positive (blue curve).

99

attenuates signal fluctuation due to input noise. The downside of this is the creation of lag time

in the response of the signal to change. This lag is evident in spectra acquired using the

forward/backward sweep mode (Fig. B.2). Since the lag time is equivalent in either sweep

direction, it can be compensated for by shifting the forward and backward sweeps equally so

their features coincide. In unidirectionally acquired spectra signal lag is compensated for by a

time delay before the reading the lock-in output at each bias increment.

The signal resolution in spectral measurements depends on detection sensitivity setting of

the lock-in amplifier and the gain value of the electrometer. The absolute output resolution of

the lock-in amplifier is illustrated in figure B.3, which shows the measured signal for figure 4.11,

consisting of 4 pairs of forward/backward sweeps (8 curves). The variation in raw signal

between sweeps is about 10-20%. Averaging the sweeps together, decreases the error bar

accordingly. For spectra acquired in the forward/backward mode, averaging is done primarily

over multiple sweeps. In the unidirectional setup, averaging is performed point-wise. This is a

less desirable averaging method as it increases the sweep time substantially, aggravating data

skew due to tip drift. However, the discontinuous voltage jump that accompanies the end of a

unidirectional sweep makes running a statistically significant number of sweeps a risky

proposition.

A difficult aspect of lock-in measurements is determining the correct phase relation

between signal and response. Phase errors result in the admixing of a small amount of capacitive

response into the signal. Generally, this has two results; a scaling down of the measurement

0.0

0.5

1.0

1.5

2.0

2.5

-1.5 -1 -0.5 0 0.5 1 1.5

Lock

-in O

utp

ut (

V)

Sample Bias (V)

93 mV

Figure B.2: Spectra displaying marked directional asymmetry from time lag in the signal response of the lock-in amplifier. Spectra are averaged over 4 sweeps each, swept right-to-left (red) and left-to-right (blue).

100

by a constant factor, and shifting of the “zero signal” level to a non-zero value. This second

effect is evident in figure B.4, where the differential conductance within the gap region of a

semiconducting tube is measured to be a value slightly less than zero. In most cases, offset

errors on semiconducting tubes are observed to be on the order of 15-30 mV (on a 10 V full-

scale output). For the most part, these small errors are not compensated for in presented data. In

a few cases curves have been arbitrarily shifted by setting the minimum measured value equal to

zero; in these cases the displayed units are listed as arbitrary.

In order to make comparisons between spectra acquired at disparate junction impedances

(as in figure 4.15) they must first be normalized against the voltage-dependent impedance

0.0

0.5

1.0

1.5

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

Lo

ck-in

Out

put (

V)

Sample Bias (V)

Figure B.4: Spectrum of a semiconducting nanotube averaged over 2 sweeps acquired using a 1.25 V @ 300 pA junction. The measured signal in the gap region displays a large offset from zero of -150 mV.

0

1

2

3

4

5

6

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2L

ock-

in O

utp

ut (

V)

Sample Bias (V)

Figure B.3: Individual spectra (8 in all) whose average constitutes the spectrum in figure 4.11. The signal width exhibits a 10-20% variation from curve to curve.

101

I(V)/V. The most straightforward method is to simultaneously measure I and dI/dV as the bias

voltage is swept. However, in cases when it is not possible or practical to do so, the next best

method is to calculate I(V) from numerical integration of dI/dV (with the integration constant set

to force I-V through the origin). Comparisons of spectra normalized using both methods are in

good agreement (Fig. B.5). Ideally, the integration should yield the setpoint current value at the

-60

-40

-20

0

20

40

60

-200 -100 0 100 200

Cur

ren

t (p

A)

Sample Bias (mV)

Figure B.6: Current response associated with the spectrum from figure B.5. Black curve is the measured signal and the red curve is obtained via numerical integration.

0.0

1.0

2.0

-200 -100 0 100 200

(dI/d

V)/

(I/V

)

Sample Bias (mV)

0.0

0.1

0.2

0.3

dI/d

V (n

A/V

)

Figure B.5: Differential conductance spectrum of a pseudogap averaged over 16 sweeps acquired using a 200 mV @ 50 pA junction (top panel) and the associated normalized spectrum (bottom panel). The black curve is normalized against the measured current response and the red curve is normalized via numerical integration. The offset is the result of a small positive error in the measured current response (the measured current changes polarity near -4 mV bias, indicative of a small stray voltage on the signal line or in the electronics).

102

junction bias voltage, though in practice the value differs by as much as 20% (Fig. B.6). This

results from error in the lock-in phase relation; constant offsets in dI/dV are equivalent to

“ tilting” of the integrated I-V response by a constant slope. In theory, one could use the

integrated I-V curve to determine the offset error in the measured dI/dV. For the purpose of

normalization this is unnecessary, as arbitrary offsets do not affect the final outcome, with the

caveat that all spectral values are required to be nonnegative (in fact, for spectra containing band

gaps it is advisable to add a small arbitrary offset to keep the integrated current nonzero and

prevent the normalized spectra from “blowing up” in the gap).

A final consideration for spectroscopy is the possible influence instrument measurement

parameters have on the resulting data. This was checked by comparing data acquired as part of

the pseudogap versus junction impedance measurement in section 4.2.1. In order to span such a

wide range of junction impedances, data had to be acquired at 3 different electrometer gain

settings. At each setting a baseline spectrum was acquired using a 200mV @ 100 pA junction.

The normalized results are plotted in figure B.7, and are largely identical. The most noticeable

difference is that the data acquired at the lowest current gain is scaled down slightly, which is not

surprising due to the weakness of the signal under these conditions. The conclusion is that

spectral measurements are independent of specific instrument settings, provided the detection

sensitivity is properly matched to the signal level.

0

2

4

6

8

-200 -100 0 100 200

(dI/d

V)/

(I/V

)

Sample Bias (mV)

Figure B.7: Demonstration that normalized spectral measurements are generally independent of the electrometer gain setting. Spectra are averaged over 4 sweeps each acquired using a 200 mV @ 100 pAjunction. Electrometer gain settings (in A/V) are 10-8 (black), 10-9 (red), and 10-10 (blue).

103

Vita

Daniel Jay Hornbaker was born in Minneapolis, Minnesota in 1973. He earned his B.S. in

Mathematics with a second major in Physics from Michigan State University, graduating magna

cum laude in December of 1996. Beginning graduate study in Physics at the University of

Illinois at Urbana-Champaign in the fall of 1997, he received his M.S. in October of 2000 and

completed his Ph.D. in May of 2003.