Exploring Graphene Nanoribbons Using Scanning Probe Microscopy and Spectroscopy

Yen-Chia Chen

A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy

Physics

in the

Graduate Division

of the

University of California, Berkeley

Committee in charge:

Professor Michael F. Crommie, Chair Professor Alex Zettl Professor Oscar D. Dubon

Spring 2014 Exploring Graphene Nanoribbons Using Scanning Probe Microscopy and Spectroscopy

Abstract

Exploring Graphene Nanoribbons Using Scanning Probe Microscopy and Spectroscopy by Yen-Chia Chen Doctor of Philosophy in Physics University of California, Berkeley Professor Michael F. Crommie, Chair

Graphene nanoribbons (GNRs) are strips of graphene, featuring narrow widths at the nanometer scale. A GNR may be considered as a structure cut out of graphene, which is a two dimensional honeycomb lattice of sp2 carbon atoms. Cutting graphene in different ways may be understood as imposing different boundary conditions on graphene, and therefore the electronic structures of GNRs are dependent on their geometries. Fascinating properties of graphene nanoribbons ranging from width-dependent semiconducting energy gaps to localized edge magnetization are predicted in theory. These properties, together with their ultra-thin nature, give GNRs great potential in future electronic applications. This dissertation focuses on the fundamental relations between the geometry and the electronic structure of GNRs, and explores bottom-up strategies to synthesize GNRs via molecular self-assembly. Using scanning tunneling microscopy (STM) and spectrocopy (STS), chiral and ultranarrow armchair GNRs and width-modulated GNR heterojunctions were studied. The localized edge states in chiral GNRs derived from unzipping carbon nanotubes were explored and evidence is shown that these states are spin-polarized. We further modified the chiral GNR edges with hydrogen plasma, and determined both the terminal hydrogen-bonding structure and the edge electronic structure by combining STM and ab initio simulation. Bandgap tuning of bottom-up synthesized armchair GNRs was demonstrated via development of a new molecular building block. We find that the energy gap of wider N = 13 armchair GNRs is 1.4 ± 0.1 eV, 1.2 eV smaller than the bandgap of a narrower N = 7 armchair GNR. In addition, width-modulated GNR heterojunctions were obtained by fusing segments of two different molecular building blocks, and were characterized to possess electronic structure similar to type I semiconductor junctions. As an effort to develop an alternative route toward synthesis of GNRs, we imaged and studied single-molecule enediyne chemical reactions on metallic surfaces with non-contact atomic force microscopy (nc-AFM). This bond-resolved imaging technique allows us to extract an unparalleled insight into the chemistry involved in complex enediyne cyclization cascades on surfaces. i

Contents

Contents i

List of Figures iv

List of Abbreviations vi

Acknowledgments vii

1 Introduction 1 1.1 Why Graphene Nanoribbons? ...... 1 1.2 Basic Theory of Graphene Nanoribbons ...... 2 1.2.1 Graphene Bandstructure ...... 3 1.2.2 Armchair and Zigzag Graphene Nanoribbons ...... 4 1.2.3 Chiral Angles for Graphene Nanoribbons ...... 8 1.3 Theories of Magnetism in Graphene-Based Structures ...... 9 1.3.1 Hubbard Model and Lieb’s Theorem ...... 9 1.3.2 Single-Atom Vacancies in Graphene and Graphite ...... 10 1.3.3 Voids and Their Interactions ...... 10 1.3.4 Magnetism in Graphene Nanoribbons ...... 13 1.4 Scanning Tunneling Microscopy and Spectroscopy Principles ...... 14 1.4.1 The Bardeen Theory of Tunneling ...... 15 1.4.2 The Tersoﬀ-Hamann Model ...... 19 1.5 Atomic Force Microscopy Principles ...... 22 1.5.1 Operating Modes ...... 23 1.5.2 Amplitude-Modulation Atomic Force Microscopy ...... 24 1.5.3 Frequency-Modulation (Non-Contact) Atomic Force Microscopy . . . 25

2 Instrumentation 28 2.1 Low-Temperature STM ...... 28 2.1.1 UHV Chambers ...... 28 2.1.2 Cryogenics ...... 29 2.1.3 Vibration Isolation ...... 30 ii

2.1.4 STM Scanner ...... 30 2.1.5 STM Electronics and Software ...... 30 2.1.6 Modiﬁcations ...... 31 2.2 Room-Temperature STM ...... 33 2.3 qPlus Sensors for AFM/STM ...... 34 2.4 Knudsen Cells ...... 35 2.5 Quartz Crystal Microbalance ...... 37

3 Experimental Determination of Edge States of Chiral Graphene Nanorib- bons 38 3.1 Introduction ...... 38 3.2 STM and STS Characterization of Chiral Graphene Nanoribbons ...... 39 3.3 Hubbard Model Theory of Chiral GNRs ...... 43 3.4 Discussion ...... 46 3.5 Summary ...... 47

4 Modifying Graphene Nanoribbon Edge Terminations 48 4.1 Introduction ...... 48 4.2 Hydrogen Plasma-Etched GNRs ...... 49 4.3 Theoretical Calculations of Etched-Edge Free Energies and Corresponding STM Images ...... 51 4.4 Summary ...... 55

5 Bottom-Up Synthesis and Bandgap Tuning of Graphene Nanoribbons 56 5.1 Introduction ...... 56 5.2 Synthesis of 13-AGNRs ...... 57 5.3 STM dI/dV Measurement of 13-AGNRs ...... 60 5.4 Localized End-States ...... 62 5.5 Discussion ...... 64 5.6 Summary ...... 66

6 Molecular Bandgap Engineering of Bottom-Up Synthesized Graphene Nanoribbon Heterojunctions 67 6.1 Introduction ...... 67 6.2 Width-Modulated Graphene Nanoribbon Heterojunctions ...... 68 6.3 First-Principles Calculations for 7-13 GNR Heterojunctions ...... 71 6.4 Summary ...... 74

7 Imaging Single-Molecule Chemical Reactions 75 7.1 Introduction ...... 75 7.2 Imaging Enediyne Reactions on Ag(100) ...... 76 7.3 Thermodynamics of Reaction Routes ...... 81 iii

7.4 Summary ...... 83

Bibliography 84

A Dual-Crucible Evaporator 94 A.1 Parts List ...... 94 A.2 Construction Procedure ...... 96

B Growth of Boron Nitride Thin Films on Cu(111) 98 B.1 System Setup and Growth Procedure ...... 98 B.2 STM Imaging ...... 100 iv

List of Figures

1.1 Graphene honeycomb lattice...... 3 1.2 Graphene bandstructure...... 4 1.3 Brillouin zone and bandstructures of AGNRs...... 5 1.4 Brillouin zone and bandstructures of ZGNRs...... 7 1.5 Chiral vector and chiral angle for GNR...... 8 1.6 Density of states of a 15-AGNR with two single-atom vacancies located in diﬀerent sublattices...... 11 1.7 Density of states in the vicinity of two triangular vacancies in a 15-AGNR. . . . 12 1.8 DFT-calculated Bandstructure and energy gaps of ZGNRs...... 14 1.9 Schematic of STM...... 15 1.10 Schematic of STM geometry in Tersoﬀ-Hamann model...... 20 1.11 Shifts in resonance frequency and steady-state amplitude in dynamic AFM. . . . 23 1.12 Schematic of an oscillating cantilever at its turnaround points...... 26

2.1 Overview of cryogenic UHV STM...... 29 2.2 STM scanner and stage...... 31 2.3 Addition of gate electrode to the STM...... 32 2.4 Schematic of a qPlus sensor...... 35 2.5 Schematic of a Knudsen cell...... 36 2.6 A dual-crucible evaporator ...... 36

3.1 Topography of GNRs from unzipping CNTs on Au(111)...... 40 3.2 STM characterization of partially unzipped carbon nanotube...... 41 3.3 Edge states of GNRs...... 42 3.4 Position and width-dependent edge-state properties...... 44 3.5 Theoretical band structure and density of states of a 20-nm wide (8, 1) GNR. . . 45

4.1 Eﬀect of hydrogen plasma treatment on GNRs deposited on a Au(111) substrate. 49 4.2 Atomically-resolved STM topographs of GNR edges...... 50 4.3 Thermodynamic stability of hydrogenated graphene edges calculated from ﬁrst principles...... 52 v

4.4 Comparison of line proﬁles derived from experiment and simulation for GNR zigzag and armchair edges...... 54

5.1 Synthesis of 7-AGNR...... 57 5.2 Synthesis of the precursor molecule to 13-AGNRs...... 58 5.3 Synthesis of 13-AGNRs...... 58 5.4 Images of 13-AGNRs and their precursor polymers...... 59 5.5 STM dI/dV spectroscopic measurement of 13-AGNR energy gap...... 61 5.6 Comparison of energy gaps in 7- and 13-AGNRs...... 62 5.7 Empty-state resonances in STM dI/dV measurement of 13-AGNR...... 63 5.8 Localized end-state of a 13-AGNR...... 65

6.1 Bottom-up synthesis of 7-13 GNR heterojunctions...... 69 6.2 STM dI/dV spectroscopy of 7-13 GNR heterojunction electronic structure. . . . 70 6.3 Comparison of experimental dI/dV maps and theoretically simulated LDOS for 7-13 GNR heterojunctions...... 71 6.4 Theoretical simulation of electronic structure of 7-13 GNR heterojunction. . . . 72

7.1 Bergman cyclization of enediyne...... 75 7.2 Proposed synthesis of GNR from isomerizing enediyne monomers...... 76 7.3 Synthetic route toward 1,2-bis((2-ethynylphenyl)ethynyl)benzene...... 77 7.4 Constant-current STM images of molecular reactant and products on Ag(100). . 78 7.5 Comparison of STM images, nc-AFM images, and structures for molecular reactant and products...... 79 7.6 STM and nc-AFM images of minority products...... 80 7.7 Proposed pathways for the cyclization of reactant...... 82

A.1 Dimensions for an aluminum oxide spacer...... 95 A.2 Dimensions for a Macor® thermal shield...... 95 A.3 A dual-crucible evaporator...... 97 A.4 Cell assembly...... 97

B.1 Borazine source container...... 99 B.2 Room-temperature STM image of Moir´epattern of BN monolayer ﬁlm on Cu(111).100 vi

List of Abbreviations

AFM Atomic Force Microscope or Atomic Force Microscopy AGNR Armchair Graphene Nanoribbon AM Amplitude Modulation CNT Carbon Nanotube DFT Density Functional Theory dI/dV Diﬀerential Conductance DOS Electronic Density of States ec Absolute value of the Electron Charge EF Fermi energy FM Frequency Modulation GNR Graphene Nanoribbon LDOS Local Density of States LT Low Temperature (around 77 K or lower) nc-AFM Non-Contact Atomic Force Microscope or Non-Contact Atomic Force Microscopy QCM Quartz Crystal Microbalance rms Root Mean Square RT Room Temperature STM Scanning Tunneling Microscopy or Scanning Tunneling Microscope STS Scanning Tunneling Spectroscopy UHV Ultrahigh Vacuum ZGNR Zigzag Graphene Nanoribbon vii

Acknowledgments

I am in debt to many people throughout the time the work for this dissertation was done. I have been fortunate to work with people who are great in science and fun to work with. This certainly has made the graduate life an enjoyable one. First of all I would like to thank my adviser Professor Mike Crommie for allowing me to work in his group. I really appreciate his generous support to his students as well as his motivating research style. There are people whom I directly worked with to thank. I learned a lot from them, and I enjoyed our time spent together in a B2-floor lab, which is almost like a bunker. They are postdocs Chenggang Tao, Dimas de Oteyza (who taught me a lot about research and project planning; with him I also went sailing for the first time in my life), Danny Haberer, graduate students Xiaowei Zhang, Zahra Pedramrazi (who wanted to convince me to watch Korean dramas), Chen Chen, and visiting scholar Juanjuan Feng. I also would like to thank former graduate student Ryan Yamachika (“Dr. Ryan”) here. Although we did not directly work together, I learned so much from him that it feels like we actually did. I also often got support from other members in the group. Ivan Pechenezhskiy always gave me helpful suggestions; he also taught me the Russian way of drinking vodka. Aaron Bradley helped our subgroup a lot on instrumentation, and often invited us for coffee. Alex Riss, Sebastian Wickenburg and Hsin-Zon Tsai were my collaborators for a non-contact AFM work. There are also numerous people in the group with whom I enjoyed chatting and exchanging ideas. To name some of them, Giang Nguyen, Dillon Wong, Chad Germany, Kacey Meaker, Yang Wang, Jairo Velasco Jr., and Miguel Moreno Ugeda. The work presented in this dissertation has involved extensive and stimulating collabo- ration with chemists, electrical engineers and theorists. Liying Jiao, Liming Xie and Profes- sor Hongjie Dai in the Chemistry Department at Standford University made the graphene nanoribbons from unzipping carbon nanotubes. Professor Felix Fischer and his group members Patrick Gorman, Francesca Toma among others developed organic molecules for self- assembled graphene nanoribbons. Patrick Bennett, Ali Madani and Professor Jeff Bokor measured transport properties of the molecular graphene nanoribbons we synthesized. The- orists Oleg Yazyev, Professor Rodrigo Capaz, David Strubbe, Sangkook Choi, Ting Cao and Professor Steven Louie helped us interpret our experimental data. Thank you all. Administrative support is also very important to the completion of this dissertation. In particular, Anne Takizawa and Donna Sakima in the Physics Department Office and Elaine Quiter, our group administrator assistant, helped me a lot along the way. I also would like to thank my cousin Servina, her husband Chester and their son Joseph for often inviting me to gather together for holidays; my friends Pei-Chen, Darren and Hsien- Ching for hanging out with me. It was so great to have some Taiwanese connections here so far away from home. Finally, I want to thank my family for their endless support throughout the years. 1

Chapter 1

Introduction

1.1 Why Graphene Nanoribbons?

Semiconductors are the foundation of modern electronics. In 1947 John Bardeen, Walter Brattain and William Shockley developed the first transistor via a semiconducting germa- nium block [1]. Since then transistors have become ubiquitous in almost every thinkable electronic device today. The size of the first transistor was on the millimeter scale; as of March 2014 a transistor can be as small as ∼ 20 nm (length of a gate electrode) and a single integrated chip can contain billions of transistors in it. As transistors become even smaller, controlling the electronic properties of transistors also becomes more and more challenging: any imperfection in transistor structure can have a huge effect on the performance of the transistor. For example, a rough interface between the gate electrode and the conduction channel in a metal-oxide-semicondutor field-effect transistor (MOSFET) can greatly suppress electronic transport through the channel. Conventional semiconductor devices are mostly based on silicon and III-V compounds and are fabricated generally via top-down methods (e.g., photolithography). As Moore’s Law is approaching its end [2], applying new semiconducting materials that are intrinsically on the nanometer scale may be the key to future electronics. Graphene nanoribbons (GNRs), strips of sp2 carbon atoms whose widths are on the nanometer scale, are a candidate material for future electronics. Predicted long before the successful isolation of graphene [3], a GNR can be imaged as a strip carved out of a sheet of graphene, and its electronic structure depends on how boundary conditions are imposed on the wavefuntions of graphene [4, 5]. The boundary conditions correspond to the width, orientation, atomic edge structure and edge functionalization of the GNR, and therefore all these factors crucially influence the electronic properties of the GNR. For example, the energy gap for an armchair-edged GNR is predicted to be, roughly speaking, inversely proportional to its width [6, 7]. Magnetism associated with sp2 carbon structures has also been predicted to exist in zigzag-edged GNRs, which may provide a new means toward spintronics [5, 8, 9]. If one can precisely control the geometrical structure of a GNR, she/he will be able to control CHAPTER 1. INTRODUCTION 2 the electronic properties of the GNR and use it in electronic/spintronic applications. Despite the immense potential, up-to-date experimental understanding of the relation between the geometrical and electronic structures of GNRs remains largely obscure, and fabricating GNRs having a defined geometry is still challenging . This dissertation will thus focus on the fundamental physics and controlled synthesis of graphene nanoribbons. For fundamental GNR studies, it is essential to develop methods that produce GNRs of a well-defined geometry, and it is critical to characterize both the geometrical structure (down to the atomic scale) and the electronic structure of the GNRs at the same time. For the former, both top-down and bottom-up methods have been attempted to produce GNRs with smooth edges and defined widths (via unzipping of carbon nanotubes (CNTs) and self-assembly of molecular precursors, respectively). For the latter, scanning tunneling microscopy (STM) and spectroscopy (STS) are employed to investigate locally both the geometrical and electronic structure of GNRs. In addition, single-molecule chemical reactions have been investigated jointly by STM and non-contact atomic force microscopy (nc-AFM) for alternative chemical routes toward synthesis of GNRs. The dissertation is structured as follows. Chapter 1 introduces basic theories for the electronic and magnetic properties of GNRs, and the principles of STM, STS and AFM. Chapter 2 gives brief descriptions of the instruments used in this dissertation; modifications to the STM systems are noted. Following chapters describe our work in GNR-related projects. Chapter 3 describes our study on chiral GNRs derived from unzipping CNTs and discusses the magnetic nature of the localized edge states in these GNRs. Chapter 4 nar- rates experimental modification of GNR edges by hydrogen plasma and theoretical thermodynamic calculations on the edge structures. Chapter 5 focuses on the bottom-up synthesis of N = 13 armchair GNRs from a newly developed molecular precursor, and the STS characterization of the bandgaps for those GNRs. Chapter 6 describes bandgap engineering of width-modulated GNR heterojunctions, which were synthesized from two different types of precursor molecules. Chapter 7 presents the idea of using Bergman cyclizations of enediynes for GNR synthesis, and describes our nc-AFM work on surface-supported, single-molecule enediyne reactions.

1.2 Basic Theory of Graphene Nanoribbons

As a GNR structure is based on graphene, one may try to understand the GNR bandstructure by imposing boundary conditions on graphene wavefunctions according to the GNR geometry. Speciﬁcally, if the GNR geometry is periodic along its long axis, the corresponding 1D GNR bandstructure may be predicted by projecting the graphene bandstructure onto the 1D Brillouin zone (which is a line segment in the momentum space). This technique, the so-called zone-folding technique, has been successfully applied on graphene-based one-dimensional carbon nanotubes (CNTs) [10]. Similar to CNTs, the GNR bandstructure changes depending on the crystallographic orientation of the longitudinal axis of the GNR, because the graphene bandstructure is projected onto a diﬀerent line in the momentum space. CHAPTER 1. INTRODUCTION 3

Some features in the GNR bandstructure such as zero-gap locations and width-dependent energy gaps can be predicted qualitatively by the zone-folding technique. Other features, such as 1D localized edge states in zigzag GNRs, cannot be derived from the graphene bandstructure. Tight-binding as well as density functional theory are therefore needed to give a more complete picture of the electronic structure of GNRs.

1.2.1 Graphene Bandstructure Depicted in Fig. 1.1 is a graphene honeycomb lattice. The graphene honeycomb lattice consists of two hexagonal sublattices A and B, with a lattice constant a = 2.46 A.˚ The ﬁlled and empty circles are drawn to indicate atom sites in the sublattices A and B, respectively. The rhomboid around those two circles represents a graphene unit cell. Two high-symmetry crystallographic directions—armchair and zigzag—are drawn (in principle any non-reconstructed graphene edge is composed of armchair or zigzag segments). The unit vectors for graphene are √ ! √ ! 3a a 3a a a = , , a = , − . (1.1) 1 2 2 2 2 2

Figure 1.1: Graphene honeycomb lattice. The honeycomb lattice consists of two hexagonal sublattices A and B with a lattice constant a = |a1| = |a2| = 2.46 A.˚ The rhomboid (shaded blue) indicates a unit cell in the honeycomb lattice. The green and red lines are drawn to show a zigzag and an armchair lines, respectively.

The corresponding reciprocal unit vectors are 2π 2π 2π 2π b1 = √ , , b2 = √ , − . (1.2) 3 a a 3 a a CHAPTER 1. INTRODUCTION 4

Figure 1.2: Graphene bandstructure obtained with ﬁrst-principles calculations. (A) The bands painted red in the diagram cross at the K point at the Fermi energy and exhibit linear dispersion relations. The labels indicate the symmetries of the bands. Data extracted from Ref. [11]. (B) Schematic of graphene Brillouin zone and Dirac cones at K and K0 points.

Fig. 1.2A depicts the resulting bandstructure of graphene. At the corners of the Brillioun zone (K and K0 points), the conduction and valences touches each other at the Fermi energy (EF ), giving a zeo-bandgap semimetal structure. Interestingly, the energy-momentum dis- 0 persion relation is linear near EF , which can be described as “cones” apexed at the K and K points (see Fig. 1.2B). This dispersion relation is signiﬁcantly diﬀerent from a conventional semiconductor bandstructure, where the dispersion relation is usually parabolic. In anal- ogy to relativistic physics, the linear E vs. k relation implies that a low-energy electron in graphene can be described as a “massless fermion” traveling at a speed of ∼ 108 cm/s [12]. One can therefore study relativistic physics in a bench-top condensed matter experiment using graphene.

1.2.2 Armchair and Zigzag Graphene Nanoribbons Here we begin our discussions on the electronic structure of GNRs of the two high-symmetry types: armchair and zigzag GNRs. The former have edges of the armchair shape, and the latter have zigzag edges (this deﬁnition for GNRs is opposite to that for carbon nanotubes; armchair CNTs have armchair termini and the longitudinal axes are in the zigzag direction, whereas zigzag CNTs have zigzag termini and the longitudinal axes are in the armchair direction). CHAPTER 1. INTRODUCTION 5

Figure 1.3: Brillouin zone and bandstructures of AGNRs. (A) A Na = 11 AGNR. The width Na is deﬁned against the number of carbon dimer rows across the width. The rectangle shows a unit cell of the AGNR. (B) 1D Brillouin√ zone of an AGNR (the red line segment). The length of the Brillouin zone is da = 2π/ 3a, where a is the graphene lattice constant. (C) Bandstructures of 4-, 5- and 6-AGNRs. The bandstructures are calculated with nearest- neighbor tight-binding theory. Data extracted from Ref. [4].

Fig. 1.3A illustrates an Na = 11 AGNR (11-AGNR). The number Na refers to the number of carbon dimer rows across the width of the AGNR. The rectangle√ indicates a unit cell for the AGNR, and the structure repeats itself with a period of 3a long the longitudinal axis of the AGNR. For an infinitely long AGNR, the 1D translational symmetry allows√ crystal momenta to be well defined, and the size of the 1D Brillouin zone is da = 2π/ 3a (see the red segment in Fig. 1.3B). The bandstructure of an AGNR may therefore be roughly CHAPTER 1. INTRODUCTION 6 understood as the 2D graphene bandstructure projected onto the AGNR’s 1D Brillioun zone. For example, the K and K0 points in the graphene Brilloiun zone will be projected onto the k = 0 point in the AGNR’s Brilloiun zone, so the lowest conduction band and the highest valence bands of the AGNR may “touch” at k = 0. Indeed, nearest-neighbor tight-binding calculations predict that for AGNRs with widths of Na = 3M + 2 (M is a positive integer), no energy gap exists between the conduction and valence bands; in contrast, AGNRs with widths of Na = 3M or Na = 3M + 1 exhibit a nonzero bandgap at k = 0 and they are semiconductors (Fig. 1.3C) [4]. Interestingly, first-principles density functional theory (DFT) calculations have predicted that all the AGNRs—including those with Na = 3M + 2—are all semiconductors, distinctively different from the results of tight-binding calculations [7]. The DFT calculations are based on relaxed AGNR structures, in which the distances between carbon atoms may differ from those in a perfect, non-distorted graphene lattice. This distortion affects the hybridization of carbon orbitals and changes the energy gaps. Generally speaking, AGNRs are categorized into three families according to their widths (Na = 3M, 3M +1 and 3M +2), and the energy gaps of AGNRs within the same family scale inversely with their widths. The energy gap, however, does not decrease monotonically when (disregarding AGNR families) Na increases. For the same M, the energy gap ∆ is largest in the Na = 3M + 1 AGNR, and smallest in the Na = 3M + 2 AGNR. In other words, ∆3M+1 > ∆3M > ∆3M+2 [7]. In the case of ZGNRs, the width Nz is defined as the number of zigzag lines from one edge to the other. As depicted in Fig. 1.4A, the longitudinal axis of the ZGNR is rotated 90° from that of the AGNR shown in Fig. 1.3 (imagine these two GNRs are cut from the same sheet of graphene). Therefore, the 1D Brillouin zone of the ZGNR is rotated 90° as well (Fig. 1.4B). The structure of the ZGNR repeats itself with a period of a, so the length of its Brillouin zone is dz = 2π/a. As has been demonstrated for AGNRs, the bandstructure of a ZGNR can be roughly predicted by projecting the graphene bandstructure onto the 1D ZGNR Brillouin zone. A gapless feature is thus expected to reside at k = ±dz/3 = ±2π/3 (here we set a = 1 for simplicity) in ZGNR bandstructure, onto which the K and K0 points in the graphene Brillouin zone are projected. Tight-binding calculations on ZGNRs, however, tell a different story. Fig. 1.4C shows the bandstructure of 4-, 5- and 6-ZGNRs. In the 4-ZGNR case the lowest conduction band and the highest valence band are degenerate at the zone boundary, k = π. Both bands appear rather flat near the zone boundary, and remain degenerate while moving toward the zone center (k = 0). The degeneracy then lifts at around k = 3π/4, before reaching the supposed gap-closing wavenumber k = 2π/3. Similar results are also found for the 5- and 6-ZGNRs. Nakada et al. [4] show that when Nz gets larger, the wavenumber where the degeneracy lifts approaches k = 2π/3: the lowest conduction band the the highest valence band become flatter as Nz increases. Eventually the degeneracy lifts at k = 2π/3 at large Nz(> 30), and the flat bands occupy 1/3 of the Brillouin zone. This flat-band feature cannot be derived from the graphene bandstructure. The zero-energy states at the zone boundary are found to be highly localized at the zigzag edges, and their amplitude decays exponentially away from the edges. Because of their highly localized distribution near the edge, these states are called CHAPTER 1. INTRODUCTION 7

Figure 1.4: Brillouin zone and bandstructures of ZGNRs. (A) A Nz = 6 ZGNR. The width Nz is deﬁned against the number of zigzag lines across the width. The rectangle shows a unit cell of the ZGNR. (B) 1D Brillouin zone of a ZGNR (the red line segment). The length of the Brillouin zone is dz = 2π/a, where a is the graphene lattice constant. (C) Bandstructures of 4-, 5- and 6-ZGNRs. The bandstructures are calculated with nearest-neighbor tight-binding theory. Data extracted from Ref. [4].

“edge states” in a ZGNR. The high local density of states (LDOS) implies strong repulsive interactions between electrons, and magnetic ordering are predicted to emerge from the edge states, causing the opening of a bandgap even for ZGNRs [5, 8, 9]. Subsection 1.3.4 will further discuss the magnetism in ZGNRs. CHAPTER 1. INTRODUCTION 8

1.2.3 Chiral Angles for Graphene Nanoribbons The high-symmetry armchair and zigzag line segments can be combined to form complex edge geometry in GNRs. For a GNR with a periodic structure whose edges are neither armchair nor zigzag, one may call it a “chiral” GNR. Drawn in Fig. 1.5 is a chiral GNR, whose edges mix armchair and zigzag segments. The boxed region indicates a unit cell of the chiral GNR. For the periodic GNR geometry, the translational unit vector T = na1 + ma2 = 3a1 + a2 describes how the GNR structure repeats translationally in space. We call T the chiral vector of the GNR, and define (n, m) as the chirality of the GNR. In addition, the chiral angle is defined to be the angle θ between T and the closest zigzag orientation. This definition implies 0 ≤ θ ≤ 30. Mathematically θ and (n, m) are related by the equation: √ 3m tan θ = . (1.3) 2n + m Note that this definition of chiral vector is best for the case when n = 1 or m = 1. If n ≥ 2 and m ≥ 2, (n, m) can correspond to multiple different edge geometries. Also notice that this definition is different from that for CNTs, where the circumferential unit vector is defined as the chiral vector [10].

Figure 1.5: Chiral vector and chiral angle for GNR. The GNR is chiral if its edges are neither armchair nor zigzag. The rectangle indicates a unit cell of the GNR. The chiral vector T = 3a1 + a2, and therefore the chirality (n, m) = (3, 1). The chiral angle θ is the angle between T and the closest zigzag orientation (in this case, the direction of a1). CHAPTER 1. INTRODUCTION 9

1.3 Theories of Magnetism in Graphene-Based Structures

An extensively studied aspect in graphene research is defect-related magnetism. Unlike conventional magnetism arsing from d- or f-orbitals, magnetism in graphene and related materials is associated with the pz (or π) orbital in carbon atoms. When studying magnetism, the Hubbard model is often used to include electron-electron (repulsive) interactions. Although ab initio calculations such as density functional theory may oﬀer self-consistent results, the Hubbard model sometimes provides deeper insight into the eﬀect of electron-electron interactions on carbon magnetism [11]. In this section we will discuss the magnetic structure of voids in graphene based on the Hubbard model. We will also discuss the magnetic ordering and gap-opening schemes in GNRs (in particular, ZGNRs).

1.3.1 Hubbard Model and Lieb’s Theorem The Hubbard model is widely used to study magnetism in graphene and related π electron systems. The Hubbard model Hamiltonian (considering only nearest-neighbor hopping) is

X † † X H = −t (ciσcjσ + cjσciσ) + U ni↑ni↓, (1.4) hi,ji,σ i

† where < i, j > are nearest-neighbor pairs, and ciσ and ciσ create and annihilate an electron † of spin σ at the site i, respectively. niσ = ciσciσ is the occupation number of electron at the site i. Compared with the tight-binding model, the additional second term introduces Coulomb repulsion between electrons occupying the same site. This term implies that it will cost more energy (U > 0) to fill a second electron into a state that has been singly occupied. This may result in energy-split, spin-polarized states. An important theorem on the magnetism of the half-filled (or non-doped) Hubbard model is Lieb’s theorem, which relates the imbalance in sublattice sites in a bipartite lattice to the total spin S in the ground state [13]. A lattice is bipartite if it can be divided into two sublattices A and B, and non-zero hopping can only occur between different sublattices. Assume there are in total N(A) sites in the sublattice A and N(B) in the sublattice B. In the repulsive case (U > 0) Lieb’s theorem warrants that in the Hubbard model for a half-filled bipartite lattice, the ground state has total spin 1 S = |N(A) − N(B)|. (1.5) 2 Therefore, if there is an imbalance in the two sublattices, a non-zero net spin is expected. Lieb’s theorem is valid for the Hubbard model for bipartite lattices in any dimensions; also, a bipartite “lattice” does not have to be periodic—what matters is how hopping connects different sites. Graphene-based structures described by the Hubbard Hamiltonian in Eq. 1.4 are therefore bipartite lattices. Below we will apply Lieb’s theorem to examine the magnetism in vacancies in graphene as well as the magnetism in GNRs. CHAPTER 1. INTRODUCTION 10

1.3.2 Single-Atom Vacancies in Graphene and Graphite Let us ﬁrst apply Lieb’s theorem on single-atom vacancies in graphene and examine the associated magnetism. In a supercell in a single layer of graphene, there are equal numbers of atoms in each sublattices, namely N(A) = N(B) = N/2. Applying Lieb’s theorem discussed above we obtain 1 S = [N(A) − N(B)] = 0, (1.6) 2 which means there is no net magnetic moment. However, introducing a single-atom vacancy will have directly change the net magnetic moment. Suppose a vacancy is created on a site in the sublattice B, or N(B) = N(A) − 1, we obtain 1 1 S = [N(A) − N(A) + 1] = . (1.7) 2 2

The total spin magnetic moment in the system is thus 1µB. As long as there are unequal numbers of vacancies or other kind of defects, e.g. hydrogen chemisorptions that are bound to carbon atoms, in the two sublattices, a net spin magnetic moment is expected to emerge. For STM/STS studies on single-atom defects on graphite or graphene, see, for example, Refs. [14, 15].

1.3.3 Voids and Their Interactions Suppose there are multiple voids in a graphene-based structure, how will the interaction between the voids change the magnetic structure? Generally speaking low-energy (E ∼ 0) states in such a system are the most relevant to spin polarization because electron-electron repulsion can result in spin-polarized occupied and unoccupied states near EF . We will thus examine how the E ∼ 0 states evolve with the distance between the voids when the on-site Coulomb repulsion (U = 0) is temporarily “turned off”, and turn the repulsion back on (U > 0) to see how this results in spin-split states (following the treatment of Ref. [16]). Since we are interested in the low-energy states near EF , a semiconducting N = 15 AGNR is chosen to be the model system into which voids will be introduced. The density of states for the defect-free 15-AGNR is zero in the low-energy regime and therefore we can observe the low-energy states associated with the voids without interference from the AGNR states. Fig. 1.6A inset shows two single-atom vacancies created in the 15-AGNR. The two vacancies are located on different sublattices. Now let’s set U = 0 first and observe how the vacancies interact with each other. To help discussion on the interactions between voids, we introduce the local sublattice imbalance number:

NI (i) = NvacA − NvacB, (1.8)

where i is the “label” of the void, NA and NB are the numbers of missing atoms in sublattices A and B in a single void, respectively. Take the two single-atom vacancies in the 15-AGNR for example. The vacancy on the left is in sublattice B, and the vacancy on the right is in CHAPTER 1. INTRODUCTION 11

Figure 1.6: Density of states and energy splitting due to wavefunction hybridization in a 15- AGNR with two single-atom vacancies located in diﬀerent sublattices. No on-site Coulomb repulsion is considered (U = 0). (A) Density of states for the structure depicted in the inset. The vacancy on the left sits on the sublattice B whereas the one on the right sits on the sublattice A. The distance d between the vacancies is 6.35a, where a = 2.46 A˚ is the graphene lattice constant. The energy splitting between the lowest unoccupied state and the highest occupied state is denoted as ∆. (B) ∆ plotted as a function of the distance between the two vacancies. The y-axis is in log scale. Data extracted from Ref. [16].

sublattice A. Therefore, NI (left) = −1 for the vacancy on the left and NI (right) = +1 for the vacancy on the right. According to the results of Inui et al. [17], there will be at least

min X NZ = NI (i) (1.9) i zero-energy (spin-degenerate) states in the single-particle spectrum. If the two voids are far apart, they can be considered non-interacting with each other and treated as independent min voids. Therefore, each void is associated with at least NZ = |NI (left)| or |NI (left)| = 1 zero-energy state. However, as the two voids move closer, the hybridization between their local electronic states becomes stronger. The originally zero-energy states hybridize through the hopping terms in Eq. 1.4 (U is still set to 0) and form a bonding-antibonding pair: CHAPTER 1. INTRODUCTION 12 the energy splitting ∆ between the bonding-antibonding pair is positively correlated to the degree of hybridization. As shown in Fig. 1.6B, the energy splitting decays exponentially with the distance between the voids, signifying a lower degree of hybridization. Note that the hybridization is made possible because the non-interacting wavefunctions associated with the voids locate on diﬀerent sublattices [17]. If both the voids have NI ’s of the same sign, the associated zero-energy wavefunctions are on the same sublattice and will not hybridize in the bipartite lattice (by deﬁnition there is no hopping between sites on the same sublattice).

Figure 1.7: Density of states in the vicinity of two triangular vacancies in a 15-AGNR. (A) The vacancy on the left has two more atom sites in sublattice A than in sublattice B, and therefore local sublattice imbalance NI = +2. The vacancy on the right has NI = −2. (B) Distance-dependent density of states of the structure depicted in (A). Data extracted from Ref. [16].

We now consider pairs of larger voids. Fig. 1.7A depicts two triangular voids, whose sublattice imbalance are NI (left) = +2 and NI (right) = −2. One thus expect two localized zero-energy states associated with each of the voids. When the voids are d = 4.04a away from each other, two of the localized states hybridize, forming a bonding-antibonding pair with energies at about ±0.14 eV; the other two states remain at zero energy, implying little participation in hybridization (green curve in Fig 1.7B). The degeneracy at E = 0 is lifted practically only when the two voids are merged together (see blue curve in Fig. 1.7B). This is because the distribution of the localized states are highly directional, and they hybridize in different ways. The survival of zero-energy states often can be seen in larger voids or defect lines such as in ZGNRs. Now let’s turn the on-site Coulomb repulsion back on (set U > 0). For an isolated single- atom vacancy in graphene, there is one singly-occupied, zero-energy spin-degenerate state if no Coulomb repulsion is considered. In the case of U > 0, however, it costs energy to fill in another electron and the spin degeneracy is lifted. The localized zero-energy states in Fig. 1.7 are also expected to split into spin-polarized states. In contrast to the bonding-antibonding energy splitting due to hybridization of wavefunctions resided in different sublattices, the CHAPTER 1. INTRODUCTION 13 energy splitting due to Coulomb repulsion is most significant for highly localized states. An example for the energy splitting scheme is the spatially localized edge states in a ZGNR.

1.3.4 Magnetism in Graphene Nanoribbons Magnetism in GNRs are often associated with zigzag edges. The carbon atoms at each zigzag edge belong to the same sublattice and implies a local sublattice imbalance which is often related to a local magnetic order (Subsection 1.3.3). Among all different types of GNRs, zigzag GNRs are the most theoretically studied type for magnetism. In an ideal ZGNR, one edge consists of carbon atoms all on the sublattice A whereas the other edge consists of carbon atoms all on the sublattice B. Overall, both sublattices have the same amount of carbon atoms, and the total spin is expected to be zero according to Lieb’s theorem. However, Lieb’s theorem does not rule out the existence of local spin moments even for S = 0. In Section 1.2 we have seen that zero-energy flat bands exist in a ZGNR bandstructure calculated by tight-binding methods; electron-electron interactions can, however, drastically change the bandstructure. The flat-band states at the zone boundary (k = π) are highly localized at the edges while states at around k = 2π/3 extend across the width (see Section 1.2). When electron-electron repulsion is taken into account for the ground state of a half- filled ZGNR (e.g., in a U > 0 Hubbard model or in first-principles DFT simulations), the high density of states in the flat bands become energetically unfavorable. Therefore, the degeneracy at the zone boundary is lifted and the localized edge states are turned spin- polarized in the ground state—reminiscent of Hund’s rules in atoms [16]. Each edge is predicted to have a ferromagnetic order, and the edges are coupled antiferromagnetically (i.e., spin-up at one edge and spin-down at the other. See Fig. 1.8A) [5, 7, 8]. Fig. 1.8B 1 shows that an energy gap ∆Z opens at the zone boundary. Since this gap-opening mechanism 1 does not depend on the interactions between edge states, ∆Z is not expected to scale strongly with the width, as depicted in Fig. 1.8C. In contrast, on-site repulsion contributes less to the gap opening in delocalized states because there are fewer electrons at each site to repulse each other. For more delocalized states, gap-opening results from hybridization of mid-gap states on different sublattices in the “bulk” of a ZGNR. This is similar to bonding-antibonding pairs in molecular orbitals (in the Hubbard model, the hybridization is due to the t terms in the Hamiltonian, and therefore it mixes states on different sublattices [16, 17]). The gap opened 0 through this mechanism, ∆Z , is then expected to scale with the degree of hybridization between otherwise degenerate mid-gap states. Filled circles sketched in Fig. 1.8C indicate 0 that ∆Z roughly scales inversely with GNR width. This makes sense, for the overlap between the mid-gap states becomes smaller as the distance between the edges becomes larger. Note that although the results shown in Fig. 1.8 are based on DFT calculations, the gap-opening schemes can be well explained based on the Hubbard model. In chiral GNRs sublattice imbalance also arises. Nakada and co-workers have predicted that low-energy localized states can exist at short zigzag segments in GNRs [4], and evidence for the existence of localized states has also been observed experimentally at graphite step CHAPTER 1. INTRODUCTION 14

Figure 1.8: DFT-calculated bandstructure and energy gaps for ZGNRs. (A) Contour plot for spin density of a 12-ZGNR. Red (blue) contours present spatial distribution of up-spin (down-spin) states. (B) Bandstructure of a 12-ZGNR. Energy gaps result mainly from 0 1 wavefunction hybridization and on-site repulsions are labeled ∆Z and ∆Z , respectively. (C) 0 1 Width dependence of ∆Z and ∆Z . Reprinted ﬁgure with permission from Y.-W. Son et al., “Energy gaps in graphene nanoribbons”, Phys. Rev. Lett. 97, 216803 (2006). Copyright 2006 by the American Physical Society. edges [18–20] and GNRs [21–23]. Considering that the arguments for ZGNR magnetism are also valid in chiral GNRs, similar behaviors are also expected in chiral GNRs: energy gaps due to hybridization should vary with widths, and localized edge states are spin-split due to electron-electron interactions (magnetism in chiral GNRs will be further discussed in Chapter 3). In contrast, the edges of armchair GNRs do not break the symmetry between the sublattices and there is no local imbalance in sublattice atoms. Therefore, no local spin moments are expected in AGNRs.

1.4 Scanning Tunneling Microscopy and Spectroscopy Principles

This section will introduce the principles of scanning tunneling microscopy and spectroscopy, which are the main techniques used to inspect the physical properties of GNRs in this dissertation. In quantum mechanics electrons are allowed to tunnel through an energy barrier due to their wave nature. This tunneling phenomenon is the basic idea behind STM. In an STM, a metallic tip is brought very close to a conducting sample surface (distance usually < 1 nm). As shown in Fig. 1.9, a voltage bias (Vtip) is applied between the the tip and the sample. If the distance between the tip and the sample is small enough, electrons will CHAPTER 1. INTRODUCTION 15 be able to tunnel through the vacuum from one side to the other. The tunneling current is then converted to a voltage and used in a feedback circuit in the STM electronics. In the constant-current mode of operation, the feedback circuit will maintain a set value of the tunneling current by changing the voltage applied on the z-piezo that controls the tip- sample distance. If the detected current is greater (smaller) than the set value, the tip will be moved away from (toward) the sample. The x- and y-piezos will move the tip parallel to the sample surface. Scanning over a region of the sample surface and record the corresponding tip height, a real-space image of the surface can be obtained. A complementary technique

Figure 1.9: Schematic of STM.

to STM is STS. Instead of real-space imaging, differential tunneling conductance dI/dV is recorded in STS. By turning the feedback off, recording the dI/dV signal while sweeping the sample-tip bias, one may inspect energy-resolved local electronic structures of the sample. In order to better understand the principles of STM and STS, the Bardeen theory of tunneling will be first introduced below, followed by the Tersoff-Hamann model for STM. The main conclusion of the Tersoff-Hamann model is that, at a low bias, the tunneling current is proportional to the local density of states of the sample at the center of the tip curvature. The model requires minimum knowledge about the tip and is widely used to interpret STM and STS results for the local electronic structure of samples.

1.4.1 The Bardeen Theory of Tunneling Bardeen’s theory of tunneling was originally used to understand the tunneling phenomena in metal-insulator-metal (MIM) junctions (at low temperature, one or both sides of the metals turn into superconductors) [24]. Many concepts developed through the study of MIM CHAPTER 1. INTRODUCTION 16 tunneling junctions were later utilized to explore the tunneling phenomena in STM and STS [25]. For a MIM junction, quantum mechanics demands the system to satisfy ∂ψ Hψ = ih¯ . (1.10) ∂t Bardeen’s theory treats an MIM junction as if there are two nearly independent subsystems. One subsystem contains the insulator (potential barrier) and the metal on the one side, while the other subsystem contains the insulator and the metal on the other side. Each subsystem has a well-defined Hamiltonian in its region. To help discussion on the tunneling phenomena in STM later, we will call the metals the sample and the tip. The Hamiltonian Hs is good for the sample and the barrier, and Ht is good for the tip and the barrier. Although Bardeen’s theory of tunneling is often referred to as a first-order perturbation theory, the “perturbation” is not applied on one Hamiltonian for the whole system. In- stead, the original Hamiltonian and the perturbation Hamiltonian belong to two different subsystems. Bardeen’s theory of tunneling is based on several assumptions [26]: 1. Tunneling is weak and first-order approximations are sufficient to describe the system. 2. Sample and tip states are nearly orthogonal (little overlap in space). 3. Electron-electron interactions can be ignored, allowing description of tunneling phenomena using single-electron Hamiltonians. 4. Occupation probabilities for sample and tip states are independent of each other. They do not change even if tunneling occurs. This assumption is valid if both the tip and the sample contain huge numbers of electrons and can be treated as infinite reservoirs of electrons. 5. Both the sample and the tip are in electrochemical equilibrium. Bardeen then define the Hamiltonians for the sample and the tip subsystems h¯2 H ψ = − ∇2ψ(r) + V (r)ψ(r), (1.11) s 2m s h¯2 H φ = − ∇2φ(r) + V (r)φ(r), (1.12) t 2m t

where Vs(r) ∼ 0 in the tip whereas Vt(r) ∼ 0 in the sample. Now let’s assume at time t = 0 there is an occupied sample state ψl with energy El, and see how this state tunnels into the tip. ψl satisﬁes the time-dependent Schr¨odingerequation ∂ψl −iElt/¯h Hsψl = ih¯ ∂t , and evolves into e ψl at time t in the isolated sample subsystem. If tunneling is weak (Assumption 1) the wavefunction evolves largely in the same way as in the isolated sample subsystem with small contributions from the tip states added:

−iElt/¯h X −iEkt/¯h ψl(t) = e ψl + ak(t)φke , (1.13) k CHAPTER 1. INTRODUCTION 17

where φk’s are bound states for the tip Hamiltonian, Htφk = Ekφk. Plugging Eq. 1.13 into Eq. 1.10, and using the relations Hsψl = Eψl and Htφk = Ekφk, we obtain

X dak(t) X ih¯ φ e−iEkt/¯h = (H − H )ψ e−iElt/¯h + a (t)(H − H )φ e−iEkt/¯h. dt k s l k t k k k

Taking the inner product with φj, to the ﬁrst order

daj(t) ih¯e−iEj t/¯h = e−iElt/¯hhφ |(H − H )|ψ i. dt j s l

With the boundary condition aj(0) = 0, integrating the equation above gives

e−i(El−Ej )t/¯h − 1 aj(t) = hφj|H − Hs|ψli. El − Ej The tunneling matrix element is hereby deﬁned as

M(ψl, φj) = hφj|H − Hs|ψli, (1.14)

and one can express the probability amplitude of the φj state in the tip in terms of the tunneling matrix element as

2 2 2 4 sin [(El − Ej)t/2¯h] p(ψl, φj, t) ≡ |aj(t)| = |M(ψl, φj)| 2 . (1.15) (El − Ej) Deﬁning the function 2 4 sin [(El − Ej)t/2¯h] g(t) ≡ 2 . (1.16) t(El − Ej) and using the mathematical identity

Z ∞ sin2 ax 2 dx = 1, −∞ πax

2π one can see that for t h/¯ ∆E = |El − Ej|/h¯, g(t) → ¯h δ(El − Ej). Namely, if the tunneling process is slow compared with the uncertainty in timeh/ ¯ ∆E, Eq. 1.15 can be rewritten as 2π p(ψ , φ , t) = |M(ψ , φ )|2 t g(t) → |M(ψ , φ )|2 t δ(E − E ). (1.17) l j l j h¯ l j l j This implies elastic tunneling, meaning a state in the sample can only tunneling into a state in the tip of the same energy. Integrating p(ψ, φj, t) over energy and count the tip states whose energy values are the same as the original sample state (El), we arrive at 2π p(ψ , t) = |M(ψ , φ )|2 ρ (E )t, (1.18) l h¯ l j t l CHAPTER 1. INTRODUCTION 18

where ρt(El) is the density of states of the tip at energy El. Note that the tunneling matrix element is assumed to be nearly unchanged for different final tip states. We may consider it as an average value here. Now let’s first consider the low-temperature, low bias limit for tunneling. A small bias Vtip between the tip and the sample is applied. Suppose both the densities of states of the tip and the sample do not vary appreciably in the range of energy |ecV | (where ec is the absolute value of the electron charge) near the Fermi energy EF , the tunneling current out of the tip is

EF ≤El≤EF +ecVtip 2π 2 1 X 2 Itip ∼ ec Vtip ρt(EF ) × |M(ψl, φj)| (1.19) h¯ ec Vtip l 2π ∼ e2 V ρ (E )ρ (E ) |M(E )|2 . (1.20) h¯ c tip t F s F F The tunneling conductance is then

EF ≤El≤EF +ecVtip 2π 2 1 X 2 Gtip ∼ ec ρt(EF ) × |M(ψl, φj)| (1.21) h¯ ec Vtip l 2π ∼ e2 ρ (E )ρ (E ) |M(E )|2 . (1.22) h¯ c t F s F F At ﬁnite temperature and for a wider range of bias, the occupation probability follows the Fermi-Dirac distribution, and the densities of states and the tunneling matrix element vary with energy. Therefore the tunneling current is Z ∞ 2πec Itip = [f(EF − ecVtip + ) − f(EF + )] h¯ −∞ X 2 × ρt(EF + ) |M(El)| δ(EF − ecVtip + − El) d, (1.23) l

−1 where f() = (1 + exp[( − EF )/kBT ]) is the Fermi-Dirac distribution function. If kBT is smaller than the energy resolution of measurement, f() eﬀectively becomes a step function. Assuming the amplitude of the tunneling matrix element does not change signiﬁcantly in the interested energy interval, the tunneling current is proportional to the convolution of the densities of states of the sample and the tip:

Z eVc Itip ∝ ρs(EF − ecV + )ρt(EF + ) d (1.24) 0 The Bardeen matrix element defined in Eq. 1.14 can be expressed in a more symmetric form. This is reasonable since there is no fundamental difference between the sample and the tip in the tunneling theory. To begin the derivation we first choose a smooth surface in the barrier region that separates the sample and the tip. We denote the space that contains CHAPTER 1. INTRODUCTION 19

all the points to the tip side of the separation surface T . Taking advantage that (H −Hs)|ψli is eﬀectively zero in the sample subsystem, Eq. 1.14 can be rewritten as Z ∗ 3 M(ψl, φj) = φj (H − Hs)ψl d r T Z 2 Z ∗ h¯ 2 3 ∗ 3 = φj − ∇ + V (r) ψl d r − El φj ψl d r. T 2m T

Using the elastic tunneling condition, El = Ej, Z 2 Z ∗ h¯ 2 3 ∗ 3 M(ψl, φj) = φj − ∇ ψl d r − ψl[Ej − V (r)]φj d r T 2m T 2 Z h¯ 2 ∗ ∗ 2 3 = ψl∇ φj − φj ∇ ψl d r. (1.25) 2m T 2 ∗ ∗ 2 ∗ ∗ As ψl∇ φj − φj ∇ ψl = ∇ · ψl∇φj − φj ∇ψl , Green’s theorem gives 2 Z h¯ ∗ ∗ M(ψl, φj) = ψl∇φj − φj ∇ψl · dS. (1.26) 2m T The selection of the separation surface does not aﬀect the tunneling matrix element. The reader may refer to Ref. [25] for more discussion on the evaluation of tunneling matrix elements.

1.4.2 The Tersoff-Hamann Model The Tersoff-Hamann model of STM is based on Bardeen’s tunneling theory [27, 28] and is valuable in interpretations of STM images and tunneling spectra. According to Eq. 1.23 the tunneling current is dependent on the convolution of the DOS of the two electrodes. However, in STM measurements the structure of the tip is often unknown. A great virtue of the Tersoff-Hamann model is to take the knowledge about the tip out of the equation by assuming a simple s-wave wavefunction localized on the tip. Following this model STM essentially measures the properties of the sample surface since the tip contribution “averages away”. As shown in Fig. 1.10, the STM tip is modeled as a spherically symmetric potential well. The tip has a curvature radius of R centered at position r0 = (0, 0, z0), and is d above the sample surface (z = 0). In the vacuum region the Schrödingerequation is h¯2 − ∇2ψ(r) = −Φψ(r), 2m where the work√ function Φ is assumed to be the same for the sample and the tip for simplicity. By using κ = 2mΦ/h¯ the above equation can be rewritten as ∇2ψ(r) = κ2ψ(r). (1.27) CHAPTER 1. INTRODUCTION 20

Figure 1.10: Schematic of STM geometry in Tersoﬀ-Hamann model. The tip is modeled spherical at the apex, whose radius of curvature is R centered at r0. The tip is distance d above the sample surface.

Now consider a sample wavefunction ψs(r). Let x = (x, y) and q = (kx, ky), the two- dimensional Fourier representation of ψs is Z 2 iq·x ψs(r) = dq f(q, z)e . (1.28)

Plug Eq. 1.29 into Eq. 1.27, we obtain d2f(q, z)/dz2 = (q2 + κ2)f(q, z). The solution for f(q, z) that decays into the vacuum is then √ f(q, z) = a(q)e− q2+κ2 z, where a(q) is the Fourier component of the sample wavefunction at z = 0 (i.e., at the sample surface). The real-space wavefunction can then be expressed as Z √ 2 − q2+κ2 z ψs(r) = d q a(q)e . (1.29)

Tersoff and Hamann assumed the tip wavefunction is spherically symmetric about the 0 center of the curvature of the tip apex, r0. Define r = r − r0 and the spherically symmetric 0 0 0 tip wavefunction φt(r ) (here r = |r |). The Schrödingerequation in the vacuum (Eq. 1.27) in the spherical coordinate for the tip wavefunction is then 1 d2 [rφ (r0)] = κ2φ (r0). (1.30) r0 dr02 t t CHAPTER 1. INTRODUCTION 21

The solution for φt up to a constant is

1 0 φ (r0) = e−κr . t r0

0 In the region of vacuum z < z0 = d + R, the Fourier representation of φt(r ) is √ Z − p2+κ2 z0+ip·x0 0 2 e φt(r ) = d p , (1.31) pp2 + κ2

0 0 0 0 where (x , z ) = r . Using the relation r = r − r0 we have √ 2 2 Z − p +κ (z−z0)+ip·(x−x0) 2 e φt(r) = d p (1.32) pp2 + κ2

With the Fourier expressions of the wavefunctions of the sample and the tip, Eq. 1.29 and Eq. 1.32, the Bardeen matrix element may be evaluated at the separation surface z = 0 following Eq. 1.26:

2 Z ∗ h¯ 2 ∂φt ∗ ∂ψs M(ψs, φt) = − d x ψs − φt 2m z=0 ∂z ∂z Z Z Z p 2 2 ! √ q + κ 2 2 ∝ d2x d2q d2p 1 + a(q)e− q +κ z0+i(q−p)·x+ip·x0 . (1.33) p 2 2 z=0 p + κ

Integration of ei(q−p)·x over x gives a delta function δ(q − p), and therefore Z √ 2 2 2 − q +κ z0+iq·x0 M(ψs, φt) ∝ d q a(q)e . (1.34)

Compared with Eq. 1.32, it can be seen that the tunneling matrix element is proportional to the unperturbed sample wavefunction at the center of the tip curvature,

M(ψs, φt) ∝ ψs(r0). (1.35)

Note that Eq. 1.35 does not imply that the sample wavefunction at the center of the tip curvature is physically relevant to the tunneling matrix element–the tunneling matrix is evaluated entirely in the gap region. However, the analytic forms of the sample and the tip wavefunctions enable ψs(r0) to describe the averaging effect due to the finite tip size [28]. Assuming the tunneling matrix element does not change significantly near the Fermi energy, following Eq. 1.21 one arrives at

X 2 G ∝ |ψs,l(r0)| δ(EF − El), (1.36) l CHAPTER 1. INTRODUCTION 22

where l sums over states whose energies are El. The expression on the right hand side is the local density of states (LDOS) of the sample at the Fermi energy at position r0, or LDOS(EF , r0). Eq. 1.36 is the main conclusion of the Tersoff-Hamann model. If the tip is spherically symmetric, the finite-sized tip can be effectively treated as if it were a point, and the tunneling conductance is proportional to the sample LDOS at the center of the curvature of the tip. The Tersoff-Hamann model thus indicates that STM probes the local electronic structures of the sample (i.e., the local density of states, or LDOS). The result can be generalized for a finite bias and a finite temperature. Using Eq. 1.23 one obtains Z ∞ 2πec I = [f(EF − ecV + ) − f(EF + )] h¯ −∞ X 2 × ρt(EF − ecV + ) |M(El)| δ(EF + − El) d. (1.37) l Note that V here is defined as the sample bias and I is current flowing out of the sample. Supposing that kBT is smaller than the energy resolution of measurements and that the tip DOS is a constant, using Eq. 1.35 one arrives at

Z ecV 2πec X I ∝ ρ |ψ (r )|2δ(E + − E ) d. (1.38) h¯ t s,l 0 F l 0 l Diﬀerentiating Eq. 1.38 with respect to V, the diﬀerential tunneling conductance is dI(V ) X G(V ) ≡ ∝ |ψ (r )|2 δ(E + e V − E ) = LDOS(E + e V, r ). (1.39) dV s,l 0 F c l F c 0 l Eq. 1.39 gives a simple way to interpret STS dI/dV spectra. It suggests that the ampltitude of the tunneling dI/dV signal at the sample bias V is proportional to the sample LDOS at the energy EF + ecV at the tip position. This interpretation will be extensively used to interpret our STS data in the following chapters.

1.5 Atomic Force Microscopy Principles

As discussed in the section above STM probes the electronic structures of samples; however, it is often difficult to obtain chemical structure from only STM/STS measurements (i.e., the specific locations of constituent atoms). For example, STM can image orbitals in organic molecules, whereas identifying individual atoms or chemical bonds is somewhat unreliable. As a result, combined STM and theoretical studies are often needed to understand chemical reactions of organic molecules on surfaces. If molecular structures can be directly imaged, one may gain greater insight into chemical reactions on surfaces. Advances in non-contact atomic force microscopy (nc-AFM) in recent years have allowed direct imaging of covalent bonds in organic molecules [29–31], and I will describe in Chapter 7 our results of directly imaging chemical reactions using nc-AFM. In this section the principles of AFM will be briefly discussed, with emphasis on nc-AFM (or frequency-modulation AFM). CHAPTER 1. INTRODUCTION 23

1.5.1 Operating Modes Generally speaking, AFM can be divided into two categories: static AFM and dynamic AFM [25]. In static AFM, the AFM tip is usually kept in contact with the sample surface. 0 0 A deflection q of a cantilever is then translated into the tip-sample force Fts = kq (k is the spring constant of the cantilever). An AFM operated in the static mode is essentially a stylus profiler. The cantilever should be much softer than the bonds between the bulk atoms in the tip and in the sample in order to avoid damages. Typical values for k are in the range of 0.01–5 N/m [32]. In dynamic AFM, the cantilever oscillates at or near its resonant frequency. The two most common modes of operation of dynamic AFM are amplitude modulation (AM) mode and frequency modulation (FM) mode. In AM-AFM, the cantilever is driven by a fixed amplitude Adrive at a fixed frequency ωd slightly off resonance (see Fig. 1.11). The resonant frequency is p ωo = k/m, where m is the effective mass of the cantilever. If there is a tip-sample force Fts acting on the cantilever, the effective spring constant will be keff = k − ∂Fts/∂z. A change in the force gradient ∂Fts/∂z thus results in a shift in the resonant frequency ∆ω as well as a change in oscillation amplitude ∆A. AM-AFM uses ∆A as the imaging signal. Driving the cantilever off resonance helps define the feedback, say, to maintain a constant ∆A. If the cantilever were driven at resonance in AM-AFM, Fts would, in most cases, decrease the amplitude and make it an inappropriate signal for feedback. In contrast, in FM-AFM

Figure 1.11: Shifts in resonance frequency and steady-state amplitude in dynamic AFM. In the amplitude modulation mode, the cantilever is driven at a frequency ωd slightly oﬀ the unperturbed resonant frequency ω0. Tip-sample interactions shifts the resonant frequency 0 from ω0 to ω0, and reduces the detected amplitude by ∆A.

the cantilever is driven at the resonant frequency (by maintaining a π/2 phase diﬀerence CHAPTER 1. INTRODUCTION 24 between the driving force and the measured oscillation) while the amplitude of oscillation is kept at constant. Forces between the tip and a sample cause a change in resonant frequency f = f0 + ∆f (f0 is the eigenfrequency of the cantilever), and the shift in resonant frequency (∆f) is used as the imaging signal. The FM mode is likely the most common operating mode of AFM in ultrahigh vacuum for its faster response to changes in force. The response time of AM mode to a change in force may be expressed by a time constant τAM ∼ 2Q/f0 (Q is the quality factor of the cantilever). In ultrahigh vacuum the Q-value can reach 105, thereby AM-AFM is slow [32]. In FM mode, the resonant frequency responds to the change within a single oscillation cycle, and the time constant τFM ∼ 1/f0 [33]. Besides, it has been shown that maximizing the Q-value is beneﬁcial in the FM mode because it also increases the cantiliever’s sensitivity to force gradients [33]. The FM mode is thus the preferred operating mode in ultrahigh vacuum.

1.5.2 Amplitude-Modulation Atomic Force Microscopy To better understand the operating principles of dynamic AFM, let’s start with the equation of motion: mz¨ + (mω0/Q)z ˙ + kz = Fdrive cos(ωdt). (1.40)

For an AM-AFM, Fdrive is a constant and ωd is slightly greater than ω0. In a steady state, we may express the tip position as

z = A0 cos(ωdt − θ0) (1.41)

where A0 and θ0 have well-known values

Fdrive/m A0 = (1.42) p 2 2 2 2 (ω0 − ωd) + (ω0ωd/Q) and −1 ω0ωd θ0 = tan 2 2 . (1.43) Q(ω0 − ωd) As discussed in the previous section, when tip-sample forces are taken into account we 0 2 2 obtain an eﬀective spring constant keff = k − ∂Fts/∂z, or mω0 = mω0 − ∂Fts/∂z. The new resonant angular frequency is r 0 1 ∂F ω0 = ω0 1 − 2 . (1.44) mω0 ∂z 0 0 The new oscillation amplitude A0 can be obtained by replacing ω0 with ω0 in Eq. 1.42. The force gradient indeed changes the resonant frequency as well as the oscillation amplitude in AM-AFM. Note that here the tip-sample force is considered to be linear and treated by an eﬀective spring constant. In real applications the force can be non-linear, and quanti- tative analysis of the tip-sample forces requires post-prossessing of both the phase and the amplitude [34]. CHAPTER 1. INTRODUCTION 25

The AM mode was initially intended to be a “non-contact” mode [32]. However, it was latter widely used in a “tapping mode” in ambient systems where the tip “taps” the sample surface and involves short-range repulsive forces. Atomic resolution on silicon has also been obtained by AM-AFM in vacuum [35].

1.5.3 Frequency-Modulation (Non-Contact) Atomic Force Microscopy The FM mode was ﬁrst proposed and demonstrated by Albrecht et al. in 1991 [33]. Because FM-AFM classically probes weak, attractive forces far away from the surface, it is often called non-contact AFM. If the amplitude of oscillation is small compared with the range of the tip-sample force, we may treat kts = −∂F/∂z as a constant. From Eq. 1.44 (which is also valid for the FM 2 mode) and k = mω0 kts one can derive the frequency shift k ∆f ∼ ts f (1.45) 2k 0 However, applications of the FM mode may have various amplitudes of oscillations. In order to gain insight into the inﬂuence of the amplitude on ∆f, we may consider the Hamiltonian

p2 kq02 H = + + V (z), (1.46) 2m 2 ts

0 0 where q is the deﬂection of the cantilever, p = m(dq /dt), and Vts is the potential energy between the tip and the sample. For an unperturbed cantilever, q0(t) may be expressed as

0 q (t) = A cos(2πf0t), (1.47)

and the eigenfrequency f0 is r 1 k f = . (1.48) 0 2π m From the Hamiltonian, we can write down the Newtonian equation of motion

d2q0 m = −kq0 + F (d + A + q0) (1.49) d t02 ts here the cantilever oscillates at a constant amplitude A at the resonant frequency f, and the minimum distance to the sample is d; namely, z(t) = d + A + q0(t) (see Fig. 1.12). The cantilever motion is assumed to be periodic with time 1/f, and therefore it may be expressed in a Fourier series ∞ 0 X q (t) = an cos(n2πf). (1.50) n=0 CHAPTER 1. INTRODUCTION 26

Figure 1.12: Schematic of an oscillating cantilever at its turnaround points. The minimum tip-sample distance is d, and the cantilever oscillates at an amplitude A.

Inserting the expression into Eq. 1.49 gives ∞ X 2 0 an[−(n2πf) m + k] cos(m2πf) = Fts(d + A + q ). (1.51) n=0 Multiplying Eq. 1.51 by cos(l2πf) and integrating over t from 0 to 1/f. Making use of the R 2π orthogonality relations 0 cos(nx) cos(lx)dx = πδnl(1 + δn0) we derive Z 1/f 2 1 0 al −(l2πf) m + k (1 + δl0) = Fts(d + A + q ) cos(l2πft) dt. (1.52) 2f 0 Assuming the perturbation due to tip-sample interactions is weak, q0(t) ∼ A cos(2πft) and ∆f/f0 = f/f0 − 1 1, to the ﬁrst order

Z 1/f0 kA 0 − 2 ∆f ∼ Fts(d + A + q ) cos(2πft) dt (1.53) f0 0 where k is introduced through Eq. 1.48. We can re-write this equation as

2 Z 1/f0 f0 0 ∆f = − 2 Fts(q + d + A)A cos(2πf0t) dt kA 0 f = − 0 hF q0i (1.54) kA2 ts 0 Applying integration by parts on Eq. 1.54, and using kts = −∂Fts/∂q , we can be derive [36] Z A q f0 2 0 2 02 0 ∆f = 2 kts(q + d + A) A − q dq 2k πA −A f = 0 hk i. (1.55) 2k s CHAPTER 1. INTRODUCTION 27

In the small amplitude limit, Eq. 1.55 converges to Eq. 1.45. The semicircle weighting p function A2 − q02 may be considered as a “filter.” By choosing an appropriate amplitude of oscillation A, the range of force to be detected can be tuned selectively. If small amplitudes are used, the weight of short-range forces greatly increases over unwanted long-range forces. This will be helpful to achieve real atomic resolution in AFM. Despite the increased sensitivity to short-range forces, operating conventional cantilevers with small amplitudes suffers from instability (e.g., jump-to-contact issues). To avoid the stability problem while using amplitudes down to the A˚ range, stiff cantilevers (high k) will be needed [32]. An example is the qPlus sensors, which will be discussed in Subsection 2.3. 28

Chapter 2

Instrumentation

2.1 Low-Temperature STM

The STM used for most of the experiments in this dissertation is a home-built, ultra-high vacuum (UHV) low-temperature STM (LT-STM). The base pressure of the UHV chamber is ∼ 1 × 10−10 torr and the base temperature of the STM is ∼ 7 K. The STM was originally designed and constructed by Michael F. Crommie, Wei Chen and Vidya Madhavan. Details about this STM can be found in the Ph.D. theses of Wei Chen [37], Vidya Madhavan [38], Tiberiu Jamneala [39], Michael Grobis [40], and Ryan Yamachika [41]. In this section only an overview of this STM will be presented, and a list modiﬁcations that are not included in previous theses will be given in Subsection 2.1.6. An overview of the STM is shown in Fig. 2.1. The various parts of the STM can be broken down into ﬁve categories:

1. UHV chambers

2. Cryogenics

3. Vibration isolation system

4. STM scanner

5. Electronics and software

Below gives brief descriptions on the categories.

2.1.1 UHV Chambers The chambers and the pumping system allow the STM to operate in a base pressure of ∼ 1× 10−10 torr at at around 7 K. The chambers are made of 304 stainless steel, which can be baked to above 100 for more eﬃcient outgas of the chambers, leading to a better base pressure in the UHV regime. A combination of a 500 l/s turbo pump and a diaphragm-backed pumping CHAPTER 2. INSTRUMENTATION 29

Figure 2.1: Overview of cryogenic UHV STM. station is used to pump the entire system. Two ion pumps, with pumping rates of 500 l/s and 150 l/s, are mounted to the analysis (preparation) chamber and the transfer chamber, respectively. Unlike turbo or diaphragm pumps, the ion pumps do not create mechanical vibrations and therefore are suitable for low-noise STM measurements. In addition, both the analysis and the transfer chambers are equipped with titanium sublimation pumps (TSPs); occasional running of the TSPs helps to keep a lower base pressure in the chambers.

2.1.2 Cryogenics The STM is nominally maintained at ∼ 7 K by liquid helium (LHe). The microscope chamber (a bell jar) locates inside an 80-liter liquid helium dewar, which holds liquid helium for about 12 days. A He exchange gas can surrounds the microscope chamber and separates it from the helium gas vaporized from the LHe dewar. The He gas pressure in the exchange gas can is usually maintained in the range of 3–9 mtorr. The purpose of the He exchange gas is threefold: (1) to minimize the vibration from LHe boiling off, (2) to avoid the pressure range CHAPTER 2. INSTRUMENTATION 30 of ∼ 100 mtorr where high voltage arching occurs (the Paschen effect), and (3) to control the operating temperature of the STM. The exchange gas can is designed to include a series of radiation shields to reduce the effect of the thermal radiation from the transfer chamber, which is at room temperature. The wires in the exchange gas can are stainless steel coaxial cables. Their thermal conductivity is low and therefore is used to connect from connectors at room temperature to electrical feedthroughs on the microscope chamber at low temperature.

2.1.3 Vibration Isolation Vibration isolation is critical to STM measurements, and extensive care has been taken to reduce vibrational coupling to the STM. The UHV chambers are mounted on a dual stage optical table with vibrational isolation legs for each stage. A bellows of low spring constant at the bottom of the transfer chamber also helps decouple the two stages. The microscope chamber is suspended by two bellows that allow for acoustic mismatch between the microscope chamber and the transfer chamber. The entire UHV system locates in a soundproof room, which helps minimize acoustic noise. Typically a 3 mA˚ rms “vibrational” noise can be seen for the tip position; however, it is thought to be of electronic origin. High-quality images can be routinely acquired with a tunneling current of ∼ 1 pA.

2.1.4 STM Scanner The STM scanner utilizes a piezoelectric tripod design, in which the ﬁne displacements of a metallic tip along the X-, Y-, and Z-directions are actuated by three independent piezoelectric ceramics (Fig. 2.2). The metallic tip is shielded and enclosed in the macor scanner body. The tripod scanner is supported by a machined macor piece, which in turn is supported by a body piezo. The entire construction just described is called the bug. Fine (50 µm)gold wires are employed to bring electrical contact to the tip, the tip shield and the piezos. The bug is placed on a walker plate. The walker plate includes four separate electrodes sandwiched between two thin glass plates. The bug can be electrostatically clamped to the walker plate when a high voltage (∼ 500 V) is applied between the bug and the electrodes. This clamping mechanism and the contraction/expansion of the body piezo are combined to drive coarse motion of the bug along the walker plate. Details about how to construct the bug can be found in the appendix to Ryan Yamachika’s Ph.D. thesis [41].

2.1.5 STM Electronics and Software The electronics for the STM consist of home-built and commercial devices. Home-built electronics include the Z-box (the feedback circuit and the ±Z piezo voltages), the XY- box (+X and +Y piezo voltages for scanning), the ﬁeld emission box (tip bias and voltage modulation), the walker box (coarse motion of the bug), and the ground breaking box (to separate the electrical ground in the soundproof room from that outside of the soundproof room). Commercial electronics include a Ithaco 1211 current-to-voltage pre-ampliﬁer, an CHAPTER 2. INSTRUMENTATION 31

Figure 2.2: STM scanner and stage. The STM scanner uses a tripod design. The X piezo is right behind the Y piezo in the schematic from the side view. The construction of the sample receiver is not shown. The scanner sits on a walker body piezo; in conjunction with the electrodes in the walker plate, coarse motion of the scanner can be achieved.

Electronic Development Corporation 522 power supply (tip bias), and two Data precision 8200 power supplies (-X and -Y piezo voltages). For spectroscopy a HP 33120A function generator and a Princeton Applied Research lock-in ampliﬁer are used. A LakeShore 340 temperature controller helps to change the temperature of the STM (mostly used to warm up the STM to ∼ 40 K for removing hydrogen or preparing a system maintenance). Most of the STM electronics are controlled by a home-written C++ software, through the National Instruments PCI-6052E and NI PCI-MIO-16-XE data acquisition (DAQ) cards and a GPIB card on a computer. The software was developed in Microsoft Visual C++ 6.0 and the Microsoft Foundation Class (MFC) was used for the graphical user interface. Nate Jenkins wrote most of this software with help from Mike Grobis. Yuri Zuev, Ryan Yamachika, Xiaowei Zhang and I have debugged and added new features to the software. For the new features I have added, see Subsection 2.1.6.

2.1.6 Modifications Below describes several modifications on LT-STM hardware and software. These modifications were done after the completion of Ryan Yamachika’s Ph.D. thesis in 2009 [41].

1. A cable was added to the STM for gating a sample. Originally the two pentagonal screws on a sample holder were electrically connected through the two BeCu springs on CHAPTER 2. INSTRUMENTATION 32

the sample receiver. Now the two springs are electrically separated (Fig. 2.3). Facing the front side of a sample holder, the pentagonal screw on the left is used as the sample (virtual ground) electrode whereas the screw on the right may be used as a gate electrode. If the gate electrode is not needed, the screw on the right needs to be cut short enough (using a Dremel diamond wheel) that it is not in contact with the BeCu spring for the sample gating.

(a) Before modiﬁcation. (b) After modiﬁcation.

Figure 2.3: Addition of gate electrode to the STM. Photos were taken from the back side of the STM.

2. The original 75 l/s ion pump in the transfer chamber reached the end of its life and was replaced by a Varian Starcell 150 l/s ion pump.

3. A quartz crystal microbalance was added to the preparation chamber (see Section 2.5).

4. A K-type thermocouple was built on a SHV electrical feedthrough and mounted on a linear drive on the preparation chamber. This allows us to directly measure the temperature of a sample (whose voltage is about 1–2 kV during e-beam heating).

5. The “Two-voltage dI/dV ” scanning mode in the LT-STM software (ver. 2011.1 and newer)—which is called the “MULTIdidv SCAN” mode in the C++ source code—now records a constant-current image at the set point. The constant-current image is saved into a separate scan ﬁle, whose name ends with “.constI”.

6. The “SPECIAL SCAN” mode has been implemented to record multiple dI/dV maps and a constant current image at the same time—a real multi-voltage dI/dV mode (ver. 2011.2 and newer). To use this mode, ﬁrst enter in the graphical user interface (GUI) the set point for the tip and the parameters for the desired ﬁrst dI/dV map. After pressing the Start Scan button, switch to the command line window. Follow the instructions from the command line. Enter the total number of dI/dV maps to be acquired (Ntotal, including the one that has been input in the GUI) and the sample biases for the Ntotal − 1 additional dI/dV maps. CHAPTER 2. INSTRUMENTATION 33

7. The LT-STM software has been migrated to a customized computer on which Microsoft Windows XP is installed as the operating system (due to the MFC used in Visual C++ 6.0 we were not able to run the STM software on newer versions of Windows operating systems). The motherboard has three PCI extension slots, which are used for the two National Instrument Data Acquisition cards and the GPIB cards. The computer has a 120 GB solid state drive for the operating system and a 3 TB hard disk drive for data storage. In order to accommodate to the data storage scheme on the computer, the software was modiﬁed to save data in the D drive only (ver. 2014.1, the latest version as of March 19, 2014).

2.2 Room-Temperature STM

An STM that operates at room temperature (RT) has also been used for the work in this dissertation. It is a commercial variable-temperature STM (VT-STM) system from Omicron NanoTechnology GmbH, with SCALA electronics for instrument control/data acquisition. Although it is capable of conducting measurements at cryogenic and elevated temperatures, we only use it at RT. Compared with the LT-STM, the RT-STM is faster in terms of sample preparation and imaging. Therefore it is more suitable for tryout for optimal parameters for growth procedures. Recently the STM circuits were tweaked to introduce an external pre-amplifier, and the default internal and external pre-amplifier were bypassed (due to hardware failure in these default pre-amplifiers). Originally the tip-sample bias was applied on the tip, and in the mean time the tunneling current was detected from the tip; the sample was grounded. The new setup applies the tip-sample bias on the sample side, while the tunneling current is detected on the tip side and converted into a voltage signal by a external pre-amplifier. The SCALA electronics can output tip bias only up to 10 V, which limits the capacity of the RT-STM to perform field emission, a common tip treatment method in STM techniques. Bypassing the default pre-amplifiers and using an external voltage supply thus add field emission to the capability of the instrument. Another customization we have made in this instrument is the sample heating stage. The original design from Omicron used e-beam to heat up a sample. The sample was put to ground while a high voltage is applied on the filament. The heater controller adjusted the emission current by changing the filament current, and its feedback circuit maintained a set temperature according to the reading from a K-type thermocouple fixed to the sample holder plate. However, a large error between the real temperature of the sample and the temperature measured by the thermocouple: the temperature measured by the thermocouple tends to be underestimated. This is because the thermocouple is ∼ 2 cm away from the center of a sample, and the screw used to fix the thermocouple to the sample holder plate may become loose after repeated heating/cooling cycles. As the feedback for e-beam heating solely depends on the temperature reading, the sample can be overheated. To overcome this issue, the thermocouple is now directly spot-welded to a position very close to the CHAPTER 2. INSTRUMENTATION 34 sample-receiving slot. A retractable thermocouple has been built for directly measuring the temperature of a sample surface. Besides, we avoid using the default heater controller. Instead, a high voltage power supply is used to provide high voltage to the sample, and a current power supply controls the current on the filament. Thus we are able to finely adjust the heating power for e-beam heating and to better control the temperature of a sample.

2.3 qPlus Sensors for AFM/STM

The force sensor in nc-AFM plays a crucial role in achieving true atomic resolution. Several properties are desirable for detection of short-range repulsive forces: a small oscillation amplitude A, a high spring constant k, and a high quality factor Q. As has been discussed in Section 1.5.3, (a) a small oscillation amplitude is desired because it will allow characterization of short-range repulsive forces, which is important to achieve true atomic resolution by nc- AFM. (b) A high spring constant k can help avoid stability issues such as the jump-to-contact problem due to tip-sample interactions, and in the mean time reduces noise [32]. The high p k-value also increases the resonant frequency f0 = k/m 2π (m is the effective mass of the cantilever). The cantilever can therefore respond quickly to a change in force gradient within a short characteristic time constant τFM = 1/f0. (c) A high Q-value increases the sensitivity to detection of force gradient, and also reduces the energy dissipation in oscillation of the cantilever [32, 33]. To satisfy all these requirements, a few different types of force sensors have been developed—for example, the qPlus sensor [42, 43] and the KolibriSensor® [44]. We will focus on the qPlus sensor here because the nc-AFM images in Chapter 7 were acquired by a qPlus-equipped Omicron LT-AFM/STM system. A schematic of a qPlus sensor is sketeched in Fig. 2.4. One prong of the quartz tuning fork has a tip attached to it and the other prong is bonded to a mount with epoxy. Metallic electrodes are plated on the prongs, and the tip is electrically connected to the electrode on the same prong. Since the quartz crystal is a piezoelectric material, strain due to the deflection of the cantilever generates a voltage across the quartz crystal. From the current flowing between the two electrodes S+ and S− (or the voltage difference between them) one can extract the amplitude and the phase of cantilever oscillation [42, 43, 45]. The tunneling current between the tip and the sample is read out from the sample side to reduce cross- talk between the tunneling and cantilever deflection signals. The cantilever is driven by the actuator. The phase of the driving force is π/2 ahead of that of the cantilever oscillation in order to keep the cantilever at its resonant frequency. Besides the configuration shown in Fig. 2.4, the tip can also be attached in parallel to the prong, allowing detection of lateral forces [46, 47]. Other types of qPlus sensors may use different ways to electrically contact to the tip in order to reduce the cross-talk between the tunneling current and the piezoelectric signal [45, 48]. CHAPTER 2. INSTRUMENTATION 35

Figure 2.4: Schematic of a qPlus sensor. The tip is glued to a prong of a quartz tuning fork. The other prong is ﬁxed on sensor mount. Two electrodes are connected to the prongs, allowing detection of piezoelectric voltage as well as the tunneling current through the tip. The quartz tuning fork is actuated to oscillate an amplitude of A.

2.4 Knudsen Cells

Knudsen cells are often used in our research projects to sublime organic molecules in UHV. Basic parts of a Knudsen cell includes a crucible, a heating filament and a thermocouple to measure the temperature of the cell. Heat shields and orifice shutters are also often seen in the design of a Knudsen cell. Fig. 2.5 depicts a home-built Knudsen cell. This Knudsen cell design was introduced by Dr. Shaul Aloni to our group; it has been used to deposit a variety of molecules as well as NaCl thin films at operating temperatures 80–600 with corresponding currents 0.7–4.0 A. Although not depicted here, a thermal shield and an optional shutter are also part of the design (for building of the Knudsen cell, see the Ph.D. thesis of Michael Grobis [40]). This Knudsen cell design operates in a relatively wide range in temperature. However, the design was not completely robust. We often experienced short-circuit problems between the filament and the crucible supporting wires; besides, the thermocouple is attached to a supporting wire instead of the crucible itself, potentially giving a large error in the reading of operating temperature. It was also desirable to have more than one crucibles in an evaporator so that we may mix up different molecules on sample surfaces and study their interactions/reactions. All these led us to design and build dual-crucible evaporators that should be easy to assemble, robust and provides reliable temperature readings for the contents in the crucibles. The schematic in Fig. 2.6 shows our design of a dual-crucible evaporator. It was adapted from the design of Dr. Luca Floreano (a senior scientist at the beamline ALOISA in the ELETTRA synchrotron in Trieste, Itatly) and introduced into our lab by postdoc Dr. Dimas G. de Oteyza. For details about how to build an evaporator of CHAPTER 2. INSTRUMENTATION 36 this type, see Appendix A.

Figure 2.5: Schematic of a Knudsen cell.

Figure 2.6: A dual-crucible evaporator CHAPTER 2. INSTRUMENTATION 37

2.5 Quartz Crystal Microbalance

A quartz crystal microbalance (QCM) measures a change in mass by measuring the change in the resonant frequency of a quartz crystal resonator. In our molecule-related projects, a QCM was often used to ﬁnd appropriate temperatures for sublimation of molecules in UHV. The QCM is mounted on a linear motion drive, which in turn is mounted directly on a UHV chamber for sample preparation. This setup allows retraction of the detector of the QCM to avoid crashing with other vacuum parts, such as a sample heating stage. The quartz crystal is adjusted to face the source of molecules (a Knudsen cell in most cases). Usually we wait about 30 min for the QCM to stabilize before sublimation of molecules. The electrical current is then gradually tuned up to raise the temperature of a Knudsen cell. If the molecules are deposited on the quartz crystal resonator, their mass will change the resonant frequency. The QCM controller then converts the change in the frequency to the thickness of the molecular layer. 38

Chapter 3

Experimental Determination of Edge States of Chiral Graphene Nanoribbons

This chapter presents our experimental characterization of chiral graphene nanoribbons obtained from unzipping carbon nanotubes. The content here is adapted from our published paper: C. Tao et al., “Spatially resolving edge states of chiral graphene nanoribbons”, Nat. Phys. 7, 616–620 (2011).

3.1 Introduction

A central question in the field of graphene-related research is how graphene behaves when it is patterned at the nanometer scale with different edge geometries. As described in Subsection 1.2.3 graphene nanoribbons can have different chirality depending on the angle at which they are cut. A GNR can, therefore, serve as a model system to study the effects of edge geometries on the properties of graphene. Most GNRs explored experimentally up to now have been characterized via electrical conductivity, leaving the critical relationship between electronic structure and local atomic geometry unclear (especially at edges) [49–51]. This chapter presents a sub-nm-resolved scanning tunnelling microscopy and spectroscopy study of GNRs that allows us to examine how GNR electronic structure depends on the chirality of atomically well-defined GNR edges. The GNRs used here were chemically synthesized via carbon nanotube unzipping methods that allow flexible variation of GNR width, length, chirality, and substrate [52, 53]. Our STS measurements reveal the presence of 1D GNR edge states [4–6, 8, 54, 55] whose spatial characteristics match theoretical expectations for GNR’s of similar width and chirality. We observe width-dependent splitting in the GNR edge-state energy bands, providing evidence of their magnetic nature. These results show that it is possible to create chiral GNRs with atomically clean edges, thus opening the door to new applications exploiting the unique magnetoelectronic properties of chiral GNR edge CHAPTER 3. EDGE STATES OF CHIRAL GRAPHENE NANORIBBONS 39 states [7, 11].

3.2 STM and STS Characterization of Chiral Graphene Nanoribbons

The chirality of a GNR is characterized by a chiral vector (n, m) or, equivalently, by chiral angle θ, as schematically shown in Fig. 3.1A. (n, m) expresses the GNR edge orientation in graphene lattice coordinates while θ is the angle between the zigzag direction and the actual edge orientation (also see Subsection 1.2.3). GNRs having different widths and chiralities were deposited onto a clean Au(111) surface and measured using STM. Fig. 3.1B shows a room temperature image of a single monolayer GNR (GNR height is determined from linescans such as that shown in Fig. 3.1B inset; some multilayer GNRs were observed, but we focus here on monolayer GNRs). The GNR of Fig. 3.1B has a width of 23.1 nm, a length greater than 600 nm, and exhibits straight, atomically smooth edges (the highest quality GNR edges, such as those shown in Figs. 3.1 and 3.3, were observed in GNRs synthesized as in ref. [52]). Such GNRs are seen to have a “bright stripe” running along each edge. This stripe marks a region of curvature near the terminal edge of the GNR which has a maximum extension of ∼ 3 A˚ above the mid-plane terrace of the GNR, and a width of ∼ 30 A˚ (see line scan in Fig. 3.1B inset). Such edge-curvature was observed for all high quality GNRs examined in this study (more than 150, including GNRs deposited onto a Ru(0001) surface). This is reminiscent of curved edge structures observed previously near graphite step-edges [56]. We rule out that these GNRs are collapsed nanotubes from the measured ratio for GNR width to nanotube height for partially unzipped CNTs (observed to be π; for a collapsed nanotube one would expect a π/2 ratio. See Fig. 3.2). Low temperature STM images (Figs. 3.1C, 3.3A) reveal finer structure in both the interior GNR terrace and the edge region. Fig. 3.3A, for example, shows the atomically-resolved edge region of a monolayer GNR and clearly exhibits how the periodic graphene sheet of the GNR terminates cleanly and with atomic order at the gold surface. Such high-resolution images allow us to experimentally determine the chirality of GNRs, and to create structural models of observed edge regions. In Fig. 3.3A, for example, we see rows of protrusions (with a spacing of ∼ 2.5 A)˚ near the edge of a GNR having a width of 19.5 ± 0.4 nm. These protrusions have the spacing expected for adjacent graphene hexagons, and thus the orientation of the observed rows determines the zigzag direction. By comparing this row orientation with the GNR outer edge orientation we are able to extract the GNR chirality (details in Supplementary Information for Ref. [21]). The GNR displayed in Fig. 3.3A has an (8, 1) chirality (equivalent to θ = 5.8◦), and the resulting structural model for this GNR is shown in Fig. 3.3B. We find the distribution of GNR chiralities to be essentially random. This is consistent with our structural data which indicates that the CNT unzipping direction is very close to the axial direction of the precursor CNTs (see Fig. 3.2 and the caption to it), as well as the fact that the precursor CNTs have a broad chirality distribution [57]. CHAPTER 3. EDGE STATES OF CHIRAL GRAPHENE NANORIBBONS 40

Figure 3.1: Topography of GNRs from unzipping CNTs on Au(111). (A) A schematic drawing of an (8, 1) GNR. The chiral vector (n, m) connecting crystallographically equivalent sites along the edge deﬁnes the GNR edge orientation (black arrow). The blue and red arrows are the projections of the (8, 1) vector onto the basis vectors of the graphene lattice. Zigzag and armchair edges have corresponding chiral angle of θ = 0◦ and θ = 30◦, respectively, while the (8, 1) edge has an chiral angle of θ = 5.8◦. (B) Constant-current STM image of a monolayer GNR on Au(111) at room temperature (Vs = 1.5 V, I = 100 pA). Inset shows the indicated line proﬁle. (C) Higher resolution STM image of a GNR at T = 7 K (Vs = 0.2 V, I = 30 pA, grey-scale height map).

We explored the local electronic structure of GNR edges using STS, in which dI/dV measurement reﬂects the energy-resolved local density of states of a GNR. Figs. 3.3C and 3.3D show dI/dV spectra obtained at diﬀerent positions (as marked) near the edge of the (8, 1) GNR pictured in Fig. 3.3A. dI/dV spectra measured within 24 A˚ of the GNR edge typically show a broad gap-like feature having an energy width of ∼ 130 meV. This is very similar to behaviour observed in the middle of large-scale graphene sheets, and is attributed CHAPTER 3. EDGE STATES OF CHIRAL GRAPHENE NANORIBBONS 41

Figure 3.2: STM characterization of partially unzipped carbon nanotube. (A) STM image of the GNR-CNT transition region of a partially unzipped CNT (Vs = −1.5 V, I = 100 pA). (B) Line profiles of the GNR part and the CNT part of the partially unzipped CNT in (A). The corresponding positions of the line profiles are marked by blue lines in (A). The ratio of the GNR width w to the CNT height h is 3.2 ± 0.1. The ratio is close to π, indicating that the CNT was unzipped along the axial direction. to the onset of phonon-assisted inelastic electron tunnelling [58] for |E| ≥ 65 meV. This feature disappears further into the interior of the GNR, as expected due to increased tunnelling to the Au substrate [59]. Very close to the GNR edge, however, we observe additional features in the spectra. The most dominant of these features are two peaks that rise up within the elastic tunnelling region (i.e. at energies below the phonon-assisted inelastic onset) and which straddle zero bias. For the GNR shown in Fig. 3.3A (which has a width of 19.5 ± 0.4 nm) the two peaks are separated in energy by a splitting of ∆ = 23.8 ± 3.2 meV. Similar energy-split edge-state peaks have been observed in all clean chiral GNRs that we investigated spectroscopically at low temperature. For example, the inset to Fig. 3.3C shows a higher resolution spectrum exhibiting energy-split edge-state peaks for a (5, 2) GNR having a width of 15.6 nm and an energy splitting of ∆ = 27.6 ± 1.0 meV. The two edge-state peaks are often asymmetric in intensity (depending on specific location within the GNR edge region), and their mid-point is often slightly offset from Vs = 0 (within a range of ±20 meV). As seen in the spectra of Fig. 3.3C, the amplitude of the peaks grows as one moves closer to the terminal edge of the GNR, before falling abruptly to zero as the carbon/gold terminus is crossed into the gold surface. The spatial dependence of the edge-state peak amplitude as one moves perpendicular from the GNR edge is plotted in Fig. 3.4A and shows exponential behavior. The edge-state spectra also vary as one moves parallel to the GNR CHAPTER 3. EDGE STATES OF CHIRAL GRAPHENE NANORIBBONS 42

Figure 3.3: Edge states of GNRs. (A) Atomically-resolved topography of the terminal edge of an (8, 1) GNR with measured width of 19.5±0.4 nm (Vs = 0.3 V, I = 60 pA, T = 7 K). b, Structural model of the (8, 1) GNR edge shown in (A). (C) dI/dV spectra of the GNR edge shown in a, measured at different points (black dots, as shown) along a line perpendicular to the GNR edge at T = 7 K. Inset shows higher-resolution dI/dV spectrum for edge of a (5, 2) GNR with width of 15.6 ± 0.1 nm (initial tunnelling parameters Vs = 0.15 V, I = 50 pA; modulation voltage Vrms = 2 mV). The dashed lines are a guide to the eye. (D) dI/dV spectra measured at points (red dots, as shown) along a line parallel to the GNR edge shown in a at T = 7 K (initial tunnelling parameters for c and d are Vs = 0.3 V, I = 50 pA; modulation voltage Vrms = 5 mV). CHAPTER 3. EDGE STATES OF CHIRAL GRAPHENE NANORIBBONS 43 edge, as shown in Fig. 3.3D. The parallel dependence of the edge-state peak amplitude is plotted in Fig. 3.4B, and is seen to oscillate with an approximate 20 A˚ period (i.e., there are two dips in the edge-state amplitude), corresponding closely to the 21 A˚ periodicity of an (8, 1) edge. We have also characterized monolayer GNRs having different chiralities and widths (the lengths of the GNRs used in these measurements are greater than 500 nm). In Fig. 3.4C, we plot the width dependence of the measured energy gap of GNR edge states for a broad range of chirality (3.7◦ < θ < 16.1◦). The measured edge-state energy splitting shows a clear inverse correlation with GNR width. Our gap values tend to be smaller than those observed previously for lithographically patterned GNRs (probably due to uncertainty in the edge structure of lithographically obtained GNRs) [50, 60]. The high quality of the atomically well-defined edge structures observed here allows us to quantitatively compare our experimental data to theoretical calculations of the electronic structure of chiral GNRs. We find that the spectroscopic features we observe correspond closely to the spatial and energy-dependence predicted for 1D magnetic edge states coupled across the width of a chiral GNR. This behaviour is quite different from the properties observed previously for graphite step edges, armchair nanoribbons, and comparatively less ordered graphene platelet edges where no magnetism-induced energy splitting has been seen [19, 61–63].

3.3 Hubbard Model Theory of Chiral GNRs

In order to compare our experimental data with theoretical predictions for GNRs, we used a Hubbard model Hamiltonian solved self-consistently within the mean-ﬁeld approximation [5] for an (8, 1) GNR having the same width as the actual (8, 1) GNR shown in Fig. 3.3A. The Hubbard model Hamiltonian:

X † X H = −t [ciσcjσ + h.c.] + U ni↑ni↓ (3.1) hiji,σ i consists of a one-orbital nearest-neighbor tight-binding Hamiltonian (first term) with an on- site Coulomb repulsion term (the latter term leads to magnetic ordering). In this expression † ciσ and ciσ are operators that create and annihilate an electron with spin σ at the nearest neighbor sites i and j respectively, t = 2.7 eV is a hopping integral [64, 65], is the spin- resolved electron density at site i, and U is an on-site Coulomb repulsion. This GNR model is defined only by the π-bonding network. The terminal σ-bonds at the GNR edges are considered to be passivated and do not alter the π-system (this should, in general, correctly model a range of different possible edge-adsorbate bonding configurations [7, 66], including the likely oxygen-related functional group termination seen in our measurements [52]). The out-of-plane curvature seen experimentally near GNR edges (i.e., the nonzero contact angle resulting from edge-surface interactions) is not included in this model since the measured radii of curvature are sufficiently large (> 20 A)˚ that they are not expected to significantly CHAPTER 3. EDGE STATES OF CHIRAL GRAPHENE NANORIBBONS 44

Figure 3.4: Position and width-dependent edge-state properties. (A) Solid blue dots show experimental edge-state peak amplitude at points along a line perpendicular to the carbon/gold edge terminus (same positions as shown in Fig. 3.3C). The energy positions of the peaks over the range −30mV < Vs < 30mV were found to be 6.7 ± 1.6 mV and −17.2 ± 2.2 mV. The positional dependence of the average peak amplitude of these two peaks is plotted. Dashed red line shows calculated local density of states (LDOS) at locations spaced perpendicular to the edge terminus for an (8, 1) GNR (see text) at the energy of the DOS peak nearest the band-edge. Theoretical LDOS values include a single global constant offset to model the added contribution from Au surface LDOS, and a single global constant multi- plicative factor to model the unknown total area of the STM tunnel junction. (B) Solid blue dots show experimental average edge-state peak amplitude (determined as in a) at locations spaced along a line parallel to the carbon/gold edge terminus (same positions as shown in Fig. 3.3D). Dashed red line shows theoretical edge-state LDOS for an (8, 1) GNR at points parallel to the edge terminus (calculated as in a). The edge-state LDOS amplitude oscillates parallel to the edge with a 21 A˚ period. (C) Width dependence of the edge-state energy gap of chiral GNRs. From left to right, the chiralities of experimentally measured GNRs are (13, 1), (3, 1), (4, 1), (5, 2), and (8, 1) respectively, corresponding to a range of chiral angle 3.7◦ < θ < 16.1◦. The pink shaded area shows the predicted range of edge-state band gaps as a function of width evaluated for chiral angles in the range 0◦ < θ < 15◦ (U = 0.5t, t = 2.7 eV) [11]. affect GNR electronic structure [67] (we tested this conjecture by including the observed curvature in some calculations, and found that it has no significant effect—either via σ-π coupling or via pseudofield effects—on the calculated GNR electronic structure). The effect CHAPTER 3. EDGE STATES OF CHIRAL GRAPHENE NANORIBBONS 45 of the gold substrate here is taken only as a charge reservoir that can slightly shift the location of EF within the GNR band structure and reduce the magnitude of the effective U parameter via electrostatic screening (the experimental charge-induced energy shifts seen here are within the range of charge-induced energy shifts observed previously for CNTs on Au [68]).

Figure 3.5: Theoretical band structure and density of states (DOS) of a 20-nm-wide (8, 1) GNR. (A) Dashed blue line shows the calculated GNR electronic structure in the absence of electron-electron interactions (U = 0). Solid red line shows the calculated GNR electronic structure for U = 0.5t (t = 2.7 eV). Finite U > 0 splits degenerate edge states at E = 0 into spin-polarized bands opening a band gap (arrows). (B) Dashed blue line shows the (8, 1) GNR DOS for the U = 0 case in a. The peak at E = 0 is due to the degeneracy of edge states in the absence of electron-electron interactions. Solid red line shows the (8, 1) GNR DOS for U = 0.5t. The opening of the band gap (arrows) reﬂects the predicted energy splitting due to the onset of magnetism in spin-polarized edge states for U > 0, and compares favorably with the experimental data for the (8, 1) GNR of Fig. 3.3.

We first calculated the GNR electronic structure for U = 0, which effectively omits the electron-electron interactions responsible for the onset of magnetic correlations. This results in the theoretical band structure and density of states (DOS) shown in Figs. 3.5A, B (blue dashed lines). The finite width of the GNR leads to a family of sub-bands in the band structure, with no actual band gap (Fig. 3.5A). A flat band at E = 0 due to localized edge states spans the entire 1D Brillouin zone for the (8, 1) GNR, leading to a strong van Hove singularity (i.e., a peak) in the DOS at E = 0 (Fig. 3.5). The DOS in this case does not resemble what is seen experimentally. We next calculated the (8, 1) GNR electronic structure for U > 0. Here the electron-electron interactions lift the degeneracy of the edge states by CHAPTER 3. EDGE STATES OF CHIRAL GRAPHENE NANORIBBONS 46 causing ferromagnetic correlations to develop along the GNR edges and antiferromagnetic correlations to develop across the GNR. This leads to a spin-polarization of the edge states that splits the single low-energy peak seen in the U = 0 DOS into a series of van Hove singularities, thus opening up a gap at E = 0. Such behavior is seen in the band structure and DOS of Figs. 3.5A, B (solid red lines). We identify the lowest-energy pair of van Hove singularities with the pair of peaks observed experimentally near zero bias for GNR edges. We focus our experiment/theory comparison to the low-energy regime (|E| ≤ 65 meV) because higher energy experimental features are complicated by the onset of phonon-assisted inelastic tunnelling [69] (the low-energy edge-state peaks, by contrast, do not have the characteristics of inelastic modes).

3.4 Discussion

We find that our experimental spectroscopic edge-state data for the (8, 1) GNR is in agreement with model Hamiltonian calculations for U = 0.5t. The theoretical band gap of 29 meV is very close to the experimentally observed value of 23.8 ± 3.2 meV (the value of U used here is lower than a value obtained previously from a first-principles calculation [64, 65], presumably due to screening from the gold substrate). Our experimentally observed energy-split spectroscopic peaks thus provide evidence for the formation of spin-polarized edge states in pristine GNRs (such splitting does not arise for the non-magnetic U = 0 case described above). We are further able to compare the spatial dependence of the calculated edge states with the experimentally measured STS results. The dashed line in Fig. 3.4A shows the theoretical local density of states (LDOS) calculated at the energy of the low- energy edge-state peaks as one moves perpendicular away from the GNR edge and into the (8, 1) GNR interior. The predicted exponential decay length of ∼ 12 A˚ is in reasonable agreement with the experimental data. Variation seen in the calculated LDOS of the edge state in the direction parallel to the GNR edge also compares favorably with our experimental observations (Fig. 3.4B). The oscillation in edge-state amplitude is seen to arise from “kinks” in the zigzag edge structure due to the chiral nature of the (8, 1) GNR edge (see edge structure of Fig. 3.3B, each of the two dips in spectroscopic amplitude occurs at the location of a kink). We are similarly able to compare the GNR width dependence of our experimentally measured edge-state gaps to theoretical calculations. Since the measured GNRs having different widths also have different chiralities (over the range 3.7±0.3◦ < θ < 16.1±2.2◦), we have calculated the theoretical edge-state gap vs. width behaviour over a range of chiralities (0◦ < θ < 15◦). The pink shaded region in Fig. 3.4C shows the results of this calculation for spin-polarized GNR edge states, and is seen to compare favorably with our experimentally observed width-dependent edge-state gap. This provides strong evidence that the edge- state gap we observe experimentally is not a local effect, as might occur, say, in response to some unknown molecules bound to the GNR edge, but rather depends on the full GNR electronic structure, including interaction between the edges (as expected for spin-polarized CHAPTER 3. EDGE STATES OF CHIRAL GRAPHENE NANORIBBONS 47 edge states).

3.5 Summary

In summary, we provide strong experimental evidence for the existence of one-dimensional interacting edge states in chiral GNRs with atomically well-deﬁned edges. These states are found highly localized near the GNR edges, and their intensity decays exponentially into the interior of the GNRs. Furthermore, the energy gap between the edge states are found to be inversely proportional to the GNR width, indicating that the edge states are interacting across the width. This behavior, according to theoretical calculations, implies that the edge states are spin-polarized. Therefore, it should be possible to create new tunable magnetoelectronic nanostructures by producing chiral GNRs with precisely deﬁned crystallographic orientation and edges, thus creating opportunity for a wide range of new electronic and spintronic applications. 48

Chapter 4

Modifying Graphene Nanoribbon Edge Terminations

This chapter describes our work on experimental modiﬁcation and thermodynamic study of the edges of chiral graphene nanoribbons. This chapter is based on our published paper: X. Zhang et al., “Experimentally engineering the edge termination of graphene nanoribbons”, ACS Nano 7, 198–202 (2013).

4.1 Introduction

In Chapter 1 we have seen the edges of graphene oriented along the high-symmetry zigzag direction or along any low-symmetry (chiral) direction give rise to unique localized edge states [18–20, 61, 62, 70] that are predicted to result in magnetic ordering [4, 8, 71]. Such edge-dependent behavior is expected to be even more pronounced in graphene nanoribbons, where edges make up an appreciable fraction of the total nanostructure volume, thus creating new nanotechnology opportunities regarding novel electronic and magnetic nanodevices [8, 71]. Chapter 3 described our experimental observation of edge states in chiral nanoribbons, but it remains challenging to control and correlate nanoribbon edge electronic structure with specific chemically defined terminal edge groups. This chapter describes a scanning tunneling microscopy study of GNRs that are treated by hydrogen plasma etching. We find that hydrogen plasma etches away the original edge groups and develops segments with different chiralities along the edge. We have closely examined three different types of representative GNR edge segments: zigzag segments, (2, 1) chiral edge segments, and armchair segments. Comparison between our experimental data and first-principles theoretical simulation of energetically most favorable structures shows good agreement. For example, we find that the edge carbon atoms of our etched GNRs are terminated by only one hydrogen atom, and that both zigzag and chiral edges show the presence of edge states. The edges of hydrogen-plasma-etched GNRs are seen to be generally free of structural reconstructions and curvature [21, 22], with the outermost carbon CHAPTER 4. MODIFYING GRAPHENE NANORIBBON EDGE TERMINATIONS 49 edge atoms being in the sp2 hybridization state. Hydrogen plasma etching thus enables the engineering of GNR edges from an unknown terminal group (with associated edge curvature [21, 22]) to a flat edge morphology with known atomic termination and terminal bonding symmetry.

4.2 Hydrogen Plasma-Etched GNRs

The investigated GNRs were obtained by hydrogen plasma treatment [72] of chemically unzipped carbon nanotubes [52] deposited onto a Au(111) substrate and then plasma etched. Prior to hydrogen plasma treatment, these GNRs typically exhibit curved edges [21, 22, 56], that hinder access via STM to the very outermost edge atoms. The chemical nature of the pre-etched outermost atoms is therefore unknown, but based on the GNR chemical treatment they are likely terminated with some form of oxygen-containing functional groups [21]. Fig. 4.1A shows a typical room temperature STM image of a GNR that has been deposited onto Au(111) before being etched by hydrogen plasma. The line proﬁle indicates typical edge curvature, where the curved part of the edge has a width of 5 nm and a height of 0.3 nm above the center terrace region of the GNR.

Figure 4.1: Eﬀect of hydrogen plasma treatment on GNRs deposited on a Au(111) substrate. (A) Room temperature constant-current STM topograph (VS = 1.5 V, It = 100 pA) of a GNR before hydrogen plasma etching. (B) Room temperature STM image of a GNR after hydrogen plasma treatment (VS = 1.97 V, It = 50 pA). Insets show the indicated line proﬁles.

The effect of hydrogen plasma treatment on these GNRs is two-fold. First, the hydrogen plasma etches away the original edge groups, and substitutes them with hydrogen (the simplest possible monovalent edge termination). Second, the edges become significantly rougher and develop short segments (several nanometers long) that display different chiralities within the same GNR (Figs. 4.1B, 4.2A–E) (the entire GNR thus does not achieve global CHAPTER 4. MODIFYING GRAPHENE NANORIBBON EDGE TERMINATIONS 50 thermodynamic equilibrium that would result in an overall preferred edge orientation). The combination of these two factors changes the interaction between the edges and the substrate, resulting in a flat, uncurved morphology with the outermost edge atoms being more exposed. Fig. 4.1B shows that the bright strips due to edge curvature are no longer visible in etched GNRs. Instead, the etched GNRs are flat, with a height similar to the height of the interior terrace of unetched GNRs, indicating that the etching process starts from the edges and moves towards the center.

Figure 4.2: Atomically-resolved STM topographs of GNR edges: experiment vs. first- principles simulations. (A–B) Larger scale room temperature STM topographs of two segments of a GNR (VS = 0.97 V, It = 50 pA). (C–E) Zoomed-in atomically-resolved images of edge segments circled in figs. 4.2A and B having different chiralities: a zigzag edge (VS = 0.97 V, It = 50 pA), a (2, 1) chiral edge (VS = 0.97 V, It = 50 pA), and an armchair edge (VS = 0.97 V, It = 50 pA), respectively. (F–H) STM images simulated from first principles using the Tersoff-Hamann approximation for the STM tunneling current, the same bias voltage as in the experiments, and the thermodynamically most stable hydrogen edge configuration. These simulations suggest that the plasma treatment results in simple edge termination with one hydrogen atom saturating each dangling bond. The atomic structures of the underlying lattices of carbon atoms are shown as black lines.

Higher resolution topographic images (Figs. 4.2A–E) on different parts of an etched GNR CHAPTER 4. MODIFYING GRAPHENE NANORIBBON EDGE TERMINATIONS 51 show the honeycomb structure of the interior graphene. By superimposing a hexagonal lattice structure, we are able to identify the chirality of each segment of the GNR edge. Figs. 4.2C–E show close-up images of three different types of representative GNR edge segments: a zigzag segment, a chiral edge segment orientated along the (2, 1) vector of the graphene lattice, and an armchair segment, respectively. The 2-nm-long zigzag edge segment (Fig. 4.2C) appears as a sequence of bright spots visible along the edge, which then decays into the interior graphene. This segment exhibits a small depression near the middle of the outer row of edge atoms, while the second row of edge atoms next to the depression appear to be brighter than adjacent second row atoms. The (2, 1) chiral edge segment (Fig. 4.2D) shows a periodic modulation in STM intensity along its length. Comparison with a superimposed lattice structure shows that the periodic bright spots are localized along zigzag-like fragments. A break in the periodic pattern is observed in the middle of the chiral edge, possibly due to the presence of a vacancy defect. The armchair edge (Fig. 4.2E), in contrast, shows no edge enhancement in the STM intensity. Instead, the armchair edge exhibits a pronounced standing-wave feature with periodicity of ∼ 0.4 nm at the −0.97 V bias voltage used in our measurements. Because the experiments were carried out at room temperature (see Methods section) thermal effects limit our ability to perform highly resolved STM spectroscopy. Nevertheless, our STM images contain a significant amount of information regarding GNR edge electronic structure. In order to understand this information we must first determine the bonding arrangement of hydrogen atoms at the GNR edges. Once we know this bonding arrangement we can then calculate the GNR electronic local density of states and compare it to the STM data to self-consistently confirm the structural model and electronic behavior. Our strategy for performing this procedure is to first calculate the energetic stability of different edge structures, and then to use the thermodynamically favorable structures to guide our first- principles electronic property calculations which are then compared to experiment.

4.3 Theoretical Calculations of Etched-Edge Free Energies and Corresponding STM Images

We determined the thermodynamically most favorable structures by calculating the edge formation energy of different hydrogen-bonded GNR edge structures in contact with a reservoir of hydrogen. Edge carbon atoms were allowed to terminate with either one (sp2 hybridization) or two (sp3 hybridization) hydrogen atoms, and we restricted our consideration only to structural terminations having the same periodicity as the unterminated bare edge, since such symmetry is observed experimentally. Different hydrogenated edge structures differ in their local chemical composition, and thus their formation energies per edge unit length depend on the chemical potential of hydrogen, µH , according to [73]

1 N N G(µ ) = E − C E − H E − N µ , (4.1) H 2a GNR 2 graphene 2 H2 H H CHAPTER 4. MODIFYING GRAPHENE NANORIBBON EDGE TERMINATIONS 52

Figure 4.3: Thermodynamic stability of hydrogenated graphene edges calculated from ﬁrst principles. Edge formation energy per unit length (G) as a function of chemical potential of hydrogen (µH ) calculated from ﬁrst principles for various hydrogen termination patterns for (A) a zigzag, (B) an armchair, and (C) a (2, 1) chiral edge of a GNR. The structures for stable edge terminations are sketched below. The sp2 carbon atom bonding networks are highlighted in color (matched to the energy plot) while sp3 carbon atoms and terminating bonds are shown in black. The shaded areas denote the range of chemical potentials µH for which graphane is more stable than graphene.

where a is the edge periodicity, NC and NH are the number of carbon and hydrogen atoms per unit cell, and EGNR and Egraphene are the total energies of the model GNR and ideal graphene per unit cell, respectively. The chemical potential, µH , here defined using the total energy of an H2 molecule as a reference, is a free parameter which depends on particular experimental conditions. For this reason, we analyzed a broad range of chemical potentials, as shown in Fig. 4.3. Structures having the lowest formation energies, G(µH ), at a given µH are highlighted with thick lines and the corresponding structures are shown below with the π bonding network emphasized. We note that more stable structures with long-range periodicity can in principle be realized [74], but they are not observed here since global thermodynamic equilibrium is not achieved under the present experimental conditions. For the zigzag edge (Fig. 4.3A), two hydrogen configurations are possible—either a “sim- 2 3 ple” sp -bonded hydrogen zigzag edge for µH < 0.33 eV or an sp -bonded edge with two hydrogen atoms per carbon edge atom for µH > 0.33 eV (the latter results in a Klein edge π bonding network topology [75]). The shaded region in Figure 3 shows the condition for graphene to transform into graphane [76, 77], with a full basal hydrogenation of stoichiom- etry CH (µH > 0.2 eV). Since this is not observed experimentally, meaning µH < 0.2 eV, we are able to exclude the Klein edge scenario. We thus conclude that the zigzag GNR is terminated with one hydrogen atom per carbon edge atom. The armchair edge (which has two carbon edge atoms per unit cell) can, in principle, CHAPTER 4. MODIFYING GRAPHENE NANORIBBON EDGE TERMINATIONS 53 support three possible hydrogen terminations. As shown in Fig. 4.3B, however, only two of them have regions of stability—either both carbon edge atoms terminated with one hydrogen atom (µH < 0.19 eV) or both carbon edge atoms terminated with two hydrogen atoms (µH > 0.19 eV). These two configurations are equivalent from the point of view of the π electron system topology, and both have an identical electronic structure that is consistent with the experimental observation. However, the condition of observing graphene instead of graphane requires µH < 0.2 eV, thus indicating that the armchair edge is most likely terminated with one hydrogen atom per carbon atom. The situation is somewhat more complicated for the case of the (2, 1) chiral edge, which has three inequivalent edge atoms per unit cell and thus can realize, in principle, eight distinct possible hydrogen terminations. Only three of these, however, have regions of stability (Fig. 4.3C): the case where all edge atoms are terminated with one hydrogen atom (µH < 0.19 eV), the case where two adjacent edge atoms are terminated with two hydrogen atoms and the third edge atom is bonded only to one hydrogen (0.19eV < µH < 0.33 eV), and the case where all three edge atoms are each terminated with two hydrogen atoms (µH > 0.33 eV). The first two structures realize the same π electron network topology. However, because the upper limit of µH realized under the present experimental condition is −0.2 eV, we conclude that the (2, 1) chiral edge termination should involve only one hydrogen atom per edge carbon atom. This chiral edge termination is equivalent to the previously used models of Refs. [21] and [11]. To further confirm that the calculated thermodynamically favorable edge terminations correspond to what we observe experimentally, we performed first-principles simulations (see Methods section) of the STM images for these structures (Figs. 4.2F–H) and compared them to our experimental data. The structural models have utilized the energetically most stable termination (i.e., one hydrogen atom per edge carbon atom), and did not involve any covalent bonding reconstructions other than six-membered rings. We did not include the Au(111) substrate in our calculations since Au does not have a significant effect on the overall electronic structure of graphene [78]. The resulting simulated STM images nicely match the experimental data. This can be seen first for the zigzag segment in Fig. 4.2F, which shows a sequence of bright spots along the edge. A single carbon atom was removed from the center of the zigzag edge in the simulation, and this is seen to explain the depression in the middle of the outer row of atoms and the slight enhancement in the second row of carbon atoms. The simulation of the (2, 1) chiral edge (Fig. 4.2G) shows very pronounced edge states in agreement with the experimental data. It also features the observed intensity modulation along the length of this edge, which results from edge states localized along the zigzag-like fragments. An extra pair of edge carbon atoms was added to the middle of this edge segment which effectively elongates one of the zigzag-like fragments and shortens the neighboring one, thus explaining a break in the periodic pattern observed in the middle of the experimental edge segment. The simulated armchair segment (Fig. 4.2H) does not show intensity enhancement along the edge, as seen experimentally for this structure. This is consistent with the fact that this edge orientation does not give rise to localized states (this is further confirmed by average CHAPTER 4. MODIFYING GRAPHENE NANORIBBON EDGE TERMINATIONS 54

Figure 4.4: Comparison of line profiles derived from experiment and simulation for GNR zigzag and armchair edges. (A, B) Experimental images (VS = −0.97 V, It = 50 pA) of (A) GNR zigzag and (B) GNR armchair edges, with blue regions showing areas where linescans were averaged. (C) GNR zigzag and (D) GNR armchair edge LDOS simulations with red areas indicating where linescans were averaged. Average linescan profiles for the experiment (blue lines) and the simulations (red lines) are shown for (E) GNR zigzag and (F) GNR armchair edges. linescans shown in Fig. 4.4). The armchair edge simulation also features a standing-wave pattern, in agreement with previously reported predictions [79, 80] and the experimental data of Fig. 4.2E. Other possible edge terminations were also simulated for these different edge orientations (see Supplementary Information for Ref. [23]), but they did not reproduce the experimental results nearly as well as those shown. This in-depth experiment/theory comparison provides confirmation that the experimentally observed edge terminations match the theoretically derived most stable hydrogen configurations. CHAPTER 4. MODIFYING GRAPHENE NANORIBBON EDGE TERMINATIONS 55

4.4 Summary

We have investigated hydrogen plasma treated GNRs on a Au(111) substrate. We ﬁnd that hydrogen plasma etches away unknown edge terminal groups and promotes formation of short segments having diﬀerent chiralities along the edge. From more than 20 GNRs examined in this study, we observed no apparent preferred orientation of the edge segments. The chirality of edge segments likely has some dependence on the initial chirality of the whole GNR, local environments, and the out-of-equilibrium nature of the hydrogen plasma, thus thermodynamics is expected to play only a minor role in determining the overall statis- tics of edge orientations. We have primarily studied three types of GNR edge segments: zigzag segments, (2, 1) chiral edge segments, and armchair segments. Our combination of local probe microscopy and ab initio simulation enables us to determine both the terminal hydrogen-bonding structure and the edge electronic structure for edge-engineered graphene nanoribbons. This work has important implications for graphene research and technology as it introduces a new method for controlling the chemical termination and direction of GNR edges required for manipulating their electronic properties. 56

Chapter 5

Bottom-Up Synthesis and Bandgap Tuning of Graphene Nanoribbons

This chapter presents our experimental results for modifying the width of armchair graphene nanoribbons using a bottom-up synthesis method. The content here is based on our published paper: Y.-C. Chen et al., “Tuning the band gap of graphene nanoribbons synthesized from molecular precursors”, ACS Nano 7, 6123–6128 (2013).

5.1 Introduction

While numerous top-down approaches have been used to produce GNRs, these methods provide only limited control over the precise dimension and symmetry of the resulting GNRs [50, 52, 53, 82–85]. For example, although graphene nanoribbons formed from unzipping carbon nanotubes have smooth edges as shown in Chapter 3, the random ensemble nature of the nanotube precursors yields GNRs of various widths and chiralities. To use GNRs as electronic components it is highly desirable to produce GNRs of a uniform geometry, so that precise control over their electronic properties can be achieved. This requirement motivates us to pursue molecule-based, bottom-up synthesis of GNRs. By rational design of the molecular building blocks, one may be able to obtain GNRs of a defined dimension and symmetry. A breakthrough in this bottom-up strategy was achieved by Cai et al. [63]. In their work, 10,100-dibromo-9,90-bianthracene (DBBA) was used as the building block to synthesize atomically precise N = 7 armchair GNRs (7-AGNRs). The scheme to synthesize 7-AGNRs is illustrated in Fig. 5.1. DBBA was first sublimed to a Au(111) surface maintained at 200 . Homolytic cleavage of the C–Br bonds in DBBA is induced by the heat and assisted by the metal surface, resulting in an sp2 carbon-centered diradical intermediate [86]. The intermediate then diffuses on the surface and recombines with other diradicals in a step-growth polymerization to form linear chains of poly-DBBA. Annealing poly-DBBA to 400 induces a cyclization/dehydrogenation sequence, and thus turns poly-DBBA into a fully conjugated CHAPTER 5. BOTTOM-UP SYNTHESIS AND BANDGAP TUNING 57

200 °C 400 °C

DBBA n

poly-DBBA 7-AGNR Figure 5.1: Synthesis of 7-AGNR.

7-AGNR. Scanning tunnelign microscopy (STM) and spectroscopy (STS) performed on 7- AGNRs have revealed an intrinsic bandgap greater than 2.3 eV [87, 88]. A shift in conduction bandedge has also been observed for 7-AGNRs that undergo uncontrollable fusion to form wider ribbons [89]. Controlling the GNR structure by the appropriate selection of molecular precursors, however, remains a challenging task as evidenced by the fact that for three years (from 2010 to 2013) no GNRs featuring widths greater than N = 7 were synthesized in a controllable fashion using this technique. Following the work by Cai et al., we set out to design and develop a variety of molecular building blocks for bottom-up GNR synthesis. This strategy was designed to allow us to fabricate GNRs with various edge structures, doping levels or widths. In particular, we ﬁrst chose to develop bottom-up AGNRs with widths diﬀerent from N = 7. This is because AGNRs have emerged as a promising candidate for introducing device-relevant energy gaps— predicted to be inversely proportional to GNR width—into graphene [6, 7, 79, 90]. If an AGNR with width greater than N = 7 is synthesized, narrower device-relevant energy gaps will be expected.

5.2 Synthesis of 13-AGNRs

We now discuss our synthesis and characterization of new, atomically precise N = 13 AGNRs. These 13-AGNRs were fabricated using a radical step-growth polymerization of a newly developed small-molecule building block on Au(111) in UHV. We performed local electronic characterization of these new, wider GNRs using STM and STS. The 13-AGNRs feature atomically smooth hydrogen terminated armchair edges and 13 carbon dimer lines across their width. STS reveals the energy gap of these new GNRs to be 1.4 ± 0.1 eV, 1.2 eV smaller than the energy gap determined for narrower 7-AGNRs. We have also observed localized states at the ends of 13-AGNRs which extend up to 30 A˚ into the ribbons. These “end-states” are associated with the zigzag structure of the 13-AGNR short edge (i.e., the edge that terminates 13-AGNRs at their ends). CHAPTER 5. BOTTOM-UP SYNTHESIS AND BANDGAP TUNING 58

Figure 5.2: Synthesis of 1.

200 °C 400 °C

n 1 poly-1 13-AGNR Figure 5.3: Synthesis of 13-AGNRs from the molecular building block 1.

In order to precisely control and expand the width of bottom-up fabricated AGNRs we developed a small-molecule building block (1) derived from DBBA (see 1 in Fig. 5.3). 2,20-di((1,10-biphenyl)-2-yl)-10,100-dibromo-9,90-bianthracenethe (1) was obtained through a Suzuki cross coupling reaction of 2,20-dibromo-9,90-bianthracene [91] (2) with (1,10-biphenyl)- 2-boronic acid followed by a selective bromination of the bianthracene core (see Fig. 5.2). The 13-AGNR building block 1 was subsequently sublimed under UHV onto a Au(111) surface maintained at 200 . At this stage the building blocks combine into poly-1 (Fig. 5.3). Annealing these AGNR precursors at 400 induced a stepwise cyclization/dehydrogenation sequence that yields fully conjugated 13-AGNRs (Fig. 5.3). A home-built low-temperature (T = 7 K) STM was used to characterize the polymer precursors poly-1 (by cooling the sample from T = 200 to 7 K) as well as the fully cyclized 13-AGNRs (by cooling the sample from T = 400 to 7 K). STM spectroscopy was performed by measuring the diﬀerential conductance (dI/dV ) of the STM tunnel junction. Fig. 5.4A shows an STM image of a representative sample of linear polymer chains formed from building block 1 after being deposited onto the Au(111) surface at 200 and subsequently cooled for imaging. The close-up image of the polymer chain in Fig. 5.4B clearly exhibits a corrugated pattern along the backbone of the polymer chain. The maxima in this image alternate between the two opposite edges of the polymer chain. The apparent height of the polymer chains is 3.5 ± 0.3 A˚ and the period of the corrugation is 9.5 ± 0.1 A.˚ CHAPTER 5. BOTTOM-UP SYNTHESIS AND BANDGAP TUNING 59

Figure 5.4: Images of poly-1 and 13-AGNRs. (A) STM image of the polymer (poly-1) formed after the deposition of 1 onto a Au(111) surface held at 200 (Vs = 0.50 V, It = 3 pA). (B) High-resolution STM image of the polymer poly-1. The polymers are non-planar with an apparent height of 3.5 A(˚ Vs = 0.30 V, It = 33 pA). (C) STM image of 13-AGNRs formed after annealing poly-1 at 400 (Vs = 0.50 V, It = 12 pA). (D) Close-up STM image of a 13-AGNR (Vs = 0.70 V, It = 7.02 nA; a higher tunneling current was used here to obtain higher spatial resolution). A structural model of a 13-AGNR has been overlaid onto the STM image. Poly-1 tends to align with the Au(111) herringbone reconstruction, while 13-AGNRs do not exhibit a preferred orientation.

The bright contrast along the center of the chain is consistent with protrusions expected to arise from the poly-anthracene subunits [63], while contrast arising from the biphenyl groups lining the edges of the polymer is more diffuse. The significant deviation from planarity in the polymer is attributed to steric hindrance between hydrogen atoms in the peri-positions along the poly-anthracene backbone, and has also been observed for polymer chains grown from DBBA [63]. Fig. 5.4C shows an STM image of the surface after annealing samples of poly-1 at 400 for 5 min to complete the cyclization/dehydrogenation sequence. The di-(biphenyl)- bianthracene subunits have fused into a fully conjugated linear nanoribbon (Fig. 5.4C) fea- CHAPTER 5. BOTTOM-UP SYNTHESIS AND BANDGAP TUNING 60 turing a width of 19 ± 2 A˚ and an apparent height 2.1 ± 0.1 A˚ (significantly lower than the height of the polymer chains prior to cyclization/dehydrogenation). The close-up topographic image in Fig. 5.4D confirms the atomically precise molecular structure of the resulting 13-AGNRs. These nanoribbons feature atomically smooth hydrogen terminated armchair edges along the entire length of the ribbon, and are composed of 13 dimer lines of carbon atoms at the widest point.

5.3 STM dI/dV Measurement of 13-AGNRs

The local electronic structure of 13-AGNRs was characterized by performing STS measurements on 15 different nanoribbons of varying lengths (from 3 nm up to 11 nm). A characteristic dI/dV spectrum of a 13-AGNR is shown in Fig. 5.5A (blue line). The tunneling conductance (dI/dV ) reflects the energy-dependent local density of states (LDOS) at the position beneath the STM tip. A spectrum recorded directly on the bare Au(111) substrate with the same STM tip serves as a background reference (green line). In the empty states (V > 0) the 13-AGNR dI/dV is featureless (other than simply reflecting the Au(111) and tip DOS) until a prominent shoulder rises that is centered at 1.19 eV above the Fermi energy (EF ). The magnitude of this shoulder varies from position to position on the GNR (and can also vary with different STM tips), and this feature often presents as a prominent peak rather than a shoulder (see Fig. 5.6 for example), but its energy remains constant near the average value of 1.21 ± 0.06 V for all GNRs measured. We identify this feature as the 13-AGNR conduction bandedge. Other empty state peaks in the 13-AGNR spectra are often observed at higher voltages (such as at ∼ 1.6 V), with their amplitudes also dependent on location within the GNR and the condition of the STM tip (see Fig. 5.7). In the filled state part of the 13-AGNR dI/dV spectrum (V < 0) a broad resonance centered at ∼ −0.2 V is the first prominent feature. This resonance also varies in magnitude for different positions on the GNR and with different tips, but the 0.2 V resonance is present on all 15 GNRs that we examined. Upon closer inspection we observe that this resonance is composed of two energy-split resonances with the average energy splitting being 0.11 ± 0.04 eV (found via Lorentzian peak fitting). The filled-state resonance closest to EF is always found centered near the average value −0.15 ± 0.04 V, and we identify this feature as the 13-AGNR valence bandedge. Other GNR resonances in the filled states (with amplitudes depending on position and STM tip) are often seen at even lower energies (such as at ∼ −0.6 V). In summary, an average over all of our 13-AGNR spectra yields a conduction bandedge at 1.21±0.06 V and a valence bandedge at 0.15±0.04 V, thus leading to an average bandgap for 13-AGNRs on Au(111) of ∆ = 1.4 ± 0.1 eV. Narrower 7-AGNRs, by comparison, have an energy gap of ∆ ∼ 2.6 eV using similar measurement criteria [87, 88] (we have also measured an energy gap of ∆ = 2.5 ± 0.1 eV for 7-AGNRs using the same instrument and characterization techniques that we used here for 13-AGNRs—see Fig. 5.6). To gain insight into the spatial distribution of the electronic structure of 13-AGNRs we CHAPTER 5. BOTTOM-UP SYNTHESIS AND BANDGAP TUNING 61

Figure 5.5: STM dI/dV spectroscopic measurement of 13-AGNR energy gap. (A) dI/dV spectra recorded on a 13-AGNR (blue line) and on bare Au(111) (green line). The 13-AGNR spectrum is oﬀset vertically by 1 a.u. for clarity (open-feedback parameters: Vs = 1.00 V, It = 35 pA; modulation voltage Vrms = 10 mV). Crosses in inset topographic image indicate the positions where spectra were recorded (inset Vs = 1.00 V, It = 35 pA). (B–D) dI/dV maps of 13-AGNR taken at (B) valence bandedge (Vs = −0.12 V, It = 35 pA), (C) in the gap (Vs = 0.59 V, It = 35 pA), and (D) at the conduction bandedge (Vs = 1.19 V, It = 35 pA). Dashed lines indicate the outer edges of the 13-AGNR. Bandedge states have higher intensity near the edges of the GNR, while the GNR appears relatively featureless for energies within the gap. CHAPTER 5. BOTTOM-UP SYNTHESIS AND BANDGAP TUNING 62

Figure 5.6: Normalized STM dI/dV spectra for a 13-AGNR versus a 7-AGNR. The 13- AGNR spectrum (blue line) exhibits an energy gap of 1.4 eV, whereas the 7-AGNR spectrum (green line) shows a gap of 2.5 eV (open-feedback parameters: Vs = 1.00 V, It = 35 pA, and modulation voltage Vrms = 10 mV for 13-AGNR. Vs = 1.20 V, It = 15 pA, and Vrms = 5 mV for 7-AGNR). performed constant-bias dI/dV mapping (Figs. 5.5B–D) of 13-AGNRs at diﬀerent sample biases. Figs. 5.5B and D show dI/dV maps at sample biases corresponding to the valence and conduction bandedges, respectively. The bright intensity along the two longitudinal edges of the ribbon indicates a higher LDOS with respect to the gold surface at these energies (at some biases the surrounding gold surface shows oscillatory contrast due to quantum interference of the Au(111) surface state [92]). In contrast, dI/dV maps recorded at sample biases that fall within the bandgap exhibit no strong intensity on the ribbon. Fig. 5.5C, for example, shows the 13-AGNR dI/dV map at a bias of 0.59 V and the ribbon edges are dark. dI/dV mapping at biases corresponding to resonances either lower than the valence bandedge or higher than the conduction bandedge also reveal increased intensity near the GNR edges, but these maps additionally show stronger longitudinal nodal patterns than bandedge dI/dV maps (see Fig. 5.7).

5.4 Localized End-States

We observe a mid-gap state localized near the short zigzag segment that marks the end of all non-reconstructed 13-AGNRs (which is the great majority of all observed nanoribbons). CHAPTER 5. BOTTOM-UP SYNTHESIS AND BANDGAP TUNING 63

Figure 5.7: Empty-state resonances in STM dI/dV measurement of 13-AGNR. (A) dI/dV spectra recorded on a 13-AGNR (blue line) and on bare Au(111) (green line). The 13-AGNR spectrum is oﬀset vertically by 1.5 a.u. for clarity (open-feedback parameters: Vs = 2.20 V, It = 105 pA; modulation voltage Vrms = 10 mV). Crosses in inset topographic image indicate positions where spectra were obtained (inset Vs = 2.20 V, It = 105 pA). (B-D) dI/dV maps of 13-AGNR taken at (B) the 1.20 V resonance (conduction band edge) (Vs = 1.20 V, It = 105 pA), (C) the 1.60 V resonance (electron-like GNR excited state) (Vs = 1.60 V, It = 105 pA), and (D) the 1.90 V resonance (electron-like GNR excited state) (Vs = 1.90 V, It = 105 pA). CHAPTER 5. BOTTOM-UP SYNTHESIS AND BANDGAP TUNING 64

As seen in Fig. 5.8A, the dI/dV spectrum recorded on the same 13-AGNR as shown in Fig. 5.5 at a distance of 15 A˚ from such a zigzag end clearly reveals the presence of an “end- state” at 0.20 ± 0.02 eV. The energies of the previously observed conduction and valence bandedges remain unchanged. The end-state feature is absent in “bulk” 13-AGNR spectra (i.e., recorded at positions remote from the GNR terminus) as depicted in Fig. 5.5A. We explored the spatial distribution of the end-state by performing dI/dV mapping at a sample bias of 0.19 V on this nanoribbon. Fig. 5.8C indicates that the end-state is localized in close proximity to the short zigzag end of the 13-AGNR, extending only 30 A˚ along the GNR’s longitudinal axis. Close-up STM images (Figs. 5.8D and E, using a diﬀerent 13-AGNR) reveal the precise position of all carbon atoms comprising the edges at the end of a 13- AGNR (in Fig. 5.8E a structural model of the 13-AGNR end region has been overlaid onto the STM image of Fig. 5.8D).

5.5 Discussion

The 13-AGNRs developed herein belong to the same sub-family of N-AGNRs (N = 3p + 1, with p = 1, 2, 3, ...) as 7-AGNRs, but have a bandgap (1.4 eV) that is ∼ 1.2 eV smaller than the one determined for 7-AGNRs [87, 88, 93]. This energy gap vs. width trend is qualitatively consistent with theoretical models [6, 7, 90], but the measured energy gaps are consistently narrower than those predicted by first-principles density functional theory (DFT) (2.4 eV for a 13-AGNR and 3.8 eV for a 7-AGNR, respectively) [90]. This discrepancy likely arises from image charge screening due to the gold substrate, as has been shown for the N = 7 case [87, 94, 95]. Another inconsistency with theory is the fact that the experimental LDOS of the 13-AGNR conduction and valence bandedge states are strongly localized along the edges of the ribbon (Figs. 5.5B, D). This is in clear contrast to the spatially extended nature of the bandedge states predicted for isolated AGNRs [6, 96]. Similar spatial localization of bandedge states has also been observed for 7-AGNRs on Au(111) [87, 88]. We will discuss this inconsistency in greater detail in Chapter 6, where this discrepancy is explained by out- of-plane potential difference between GNR edges and interiors. The existence of stronger longitudinal nodal variation in the LDOS intensity (Fig. 5.7) along the 13-AGNR edges for resonances above (below) the conduction (valence) bandedge suggests that these resonances are higher excited electron-like (hole-like) states of the GNRs, thus further supporting identification of the conduction (valence) bandedge state. The experimentally observed 13-AGNR end-state (Figs. 5.8A, C) likely arises from the zigzag segment comprised of sp2-hybridized carbon atoms localized at the ends of each 13-AGNR (Figs. 5.8D, E). Related behavior has been observed at the ends of 7-AGNRs [88]. The mechanism by which the linear growth of GNRs is truncated remains a crucial question. Comparison between Figs. 5.8D and E indicates that, aside from the substitution of the terminal bromine atom by hydrogen, no further reconstruction of the edge atoms can be observed for 13-AGNRs. Since these non-reconstructed ends have no apparent bright spots associated with bromine atoms or apparent depressions induced by radical-surface CHAPTER 5. BOTTOM-UP SYNTHESIS AND BANDGAP TUNING 65

Figure 5.8: Localized end-state of a 13-AGNR. (A) STM dI/dV spectra taken near the end of the same 13-AGNR shown in Fig. 5.5 (blue line) and on bare Au(111) (green line) (open-feedback parameters: Vs = 1.00 V, It = 35 pA; modulation voltage Vrms = 10 mV). The GNR spectrum is oﬀset vertically by 1 a.u. for clarity. The spectra were recorded at the positions indicated by color-coded crosses in (B). The 13-AGNR spectrum exhibits an end-state resonance at +0.19 eV (shaded red). (B) STM topographic image of a 13- AGNR showing a non-reconstructed hydrogen terminated end (Vs = 1.00 V, It = 35 pA). (C) dI/dV map at +0.19 V of the 13-AGNR in (B) shows that the end-state resonance is localized near the short edge of the GNR and extends only 30 A˚ along the GNR axis (open-feedback parameters: Vs = 1.00 V, It = 35 pA; modulation voltage Vrms = 10 mV). (D) Close-up STM image of the end of a diﬀerent 13-AGNR (Vs = −0.05 V, It = 2.01 nA). (E) A structural model of the non-reconstructed end of a 13-AGNR overlaid onto the STM image shown in (D). interactions, 13-AGNRs are likely terminated by single hydrogen atoms (i.e., one per carbon atom) [88, 97]. This is further supported by the observation of 13-AGNR localized end- states (Figs. 5.8A, C) which are associated with sp2hybridized CH bonds. This leads us to deduce that two possible mechanisms for the truncation of 13-AGNR growth are (i) hydrogen abstraction during the chain-growth polymerization of the small molecule precursor 1 at 200 and (ii) quenching of the aryl radical at the end of the chain during the 400 cyclization/dehydrogenation process. We are currently unable to distinguish between these two mechanisms. CHAPTER 5. BOTTOM-UP SYNTHESIS AND BANDGAP TUNING 66

5.6 Summary

We have demonstrated the atomically precise synthesis of 13-AGNRs on Au(111) via covalent self-assembly from small-molecule building blocks. We ﬁnd that the energy gap of 13-AGNRs is 1.4 ± 0.1 eV, 1.2 eV narrower than the analogously deﬁned bandgap of a 7- AGNR. Spatially localized 13-AGNR end-states are observed at 0.20 eV above the Fermi level in the region near zigzag ends. Our work demonstrates precise and controlled tunability of bandgaps in bottom-up fabricated semiconducting AGNRs through width variation. The realization of AGNRs with widths other than N = 7 brings up the opportunity to develop more complex nanostructures, such as semiconducting GNR heterojunctions, that are of interest in electronic/optoelectronic applications (see Chapter 6). 67

Chapter 6

Molecular Bandgap Engineering of Bottom-Up Synthesized Graphene Nanoribbon Heterojunctions

This chapter describes our work exploring bandgap engineering of graphene nanoribbon heterojunctions synthesized from two diﬀerent molecular precursors. The content here is based on a manuscript currently prepared with the same title as this chapter. The coauthors are Yen-Chia Chen, Ting Cao, Chen Chen, Zahra Pedramrazi, Danny Haberer, Dimas G. de Oteyza, Felix R. Fischer, Steven G. Louie and Michael F. Crommie.

6.1 Introduction

Bandgap engineering has played a vital role in technology for more than half a century by enabling numerous semiconductor heterostructures that exhibit novel behavior such as resonant tunneling [98, 99] and enhanced solar conversion efficiency [100, 101]. As conventional devices reduce even further in size, however, they are expected to suffer degraded performance due to short-channel effects and rough interfaces [2, 102]. To overcome these obstacles, graphene-based molecular electronics has emerged as a possible candidate for controlling electronic transport down to single-molecule scales [2, 50, 51, 103, 104]. In Chapter 5 we have discussed bottom-up synthesis of GNRs from molecular precursors. Using bottom- up strategies, GNR-based electronic components with single-atom thickness and sub-2 nm width have been demonstrated [63, 81, 87, 88, 93, 105–108]. It has been predicted that bandgap engineering through selective placement of molecular building blocks having different widths may be achieved in GNRs, but the experimental realization remains challenging [109–111]. Here in this chapter we demonstrate bottom-up synthesis of width-modulated armchair GNR heterostructures, obtained by combining two different molecular building blocks. We study the resultant heterojunctions at sub-nanometre length scales via STM and STS, and identify spatially modulated electronic structure that demonstrates molecular- CHAPTER 6. GRAPHENE NANORIBBON HETEROJUNCTIONS 68 scale bandgap engineering. First-principles calculations support our experimental findings and provide further insight into the microscopic electronic structure of bandgap-engineered GNR heterojunctions.

6.2 Width-Modulated Graphene Nanoribbon Heterojunctions

Our width-modulated GNR heterojunctions were fabricated by combining the molecular building blocks 10,10’-dibromo-9,9’-bianthracene (1) and 2,2’-di((1,1’-biphenyl)-2-yl)-10,10’- dibromo-9,9’-bianthracenethe (2). As sketched in Fig. 6.1A, molecules 1 and 2 are precursors to N = 7 and N = 13 armchair GNRs, respectively, where N is the number of carbon dimer lines across the GNR width [63, 81]. The molecules were initially sublimed onto a Au(111) surface held at room temperature in UHV. The surface was then heated to 470 K for 10 minutes to induce homolytic cleavage [86] of the labile C–Br bonds in the molecular building blocks 1 and 2, thus resulting in diradical intermediates. Since 1 and 2 share the same bianthracene backbones, their diradical intermediates are compatible with each other and are able to colligate into linear polymers. Upon further heating to 670 K for 10 minutes the polymers converted into 7-13 GNR heterojunctions through additional cyclization/dehydrogenation reactions (Fig. 6.1) [63, 81]. The samples were then cooled down to 7 K for STM and STS measurements. Fig. 6.1B shows an STM topographic image of a sample thus prepared, which includes 7-13 GNR heterojunctions whose shapes resemble the sketch in Fig. 6.1A. The narrower segments in these heterojunctions measure 1.3± 0.1 nm in width in the STM image and are composed of monomers of 1 (N = 7). The wider segments measure 1.9 ± 0.2 nm in width and consist of monomers of 2 (N = 13). Since the building blocks mixed and colligated randomly with each other, various N = 7 and N = 13 segment lengths were observed (see the inset to Fig.6.1B, a larger-scale STM image of 7-13 GNR heterojunctions on Au(111)). To investigate the local electronic structure of these 7-13 GNR heterojunctions, tunneling conductance dI/dV spectra were recorded for the STM tip placed at diﬀerent positions above the GNR heterojunctions (dI/dV magnitude reﬂects the energy-dependent local density of states at the STM tip position. See Subsection 1.4.2). As a background reference, a dI/dV spectrum taken on bare Au(111) is shown in green in Fig. 6.2. A characteristic spectrum (red curve) recorded on the marked N = 13 segment of a single heterojunction (image shown in Fig. 6.2 inset) exhibits prominent peaks at Vs = 1.45 ± 0.02 V (labeled state 3) and Vs = −0.12 ± 0.02 V (Vs refers to the sample voltage). In contrast, the marked N = 7 segment (blue curve) shows a pronounced shoulder at Vs = 1.86 ± 0.02 V (labeled state 4) and a peak at Vs = −0.90 ± 0.02 V. The energy locations of these states are similar to the valence and conduction bandedges seen previously for “pure” 7-GNRs and 13-GNRs [81, 87]. Additional states are observed in dI/dV spectra measured at locations near the interface between the N = 7 and N = 13 segments of a heterojunction (black cross in Fig.6.2 inset). CHAPTER 6. GRAPHENE NANORIBBON HETEROJUNCTIONS 69

Figure 6.1: Bottom-up synthesis of 7-13 GNR heterojunctions. (A) Sketch of the synthesis of 7-13 GNR heterojunctions from molecular building blocks 1 and 2. The building blocks 1 and 2 are co-deposited onto a pristine Au(111) surface held at room temperature. Step- wise heating induces cleavage of the labile C–Br bonds and colligation (at 470 K) and then cyclization/dehydrogenation (at 670 K), resulting in 7-13 GNR heterojunctions. (B) High- resolution STM topograph of a 7-13 GNR heterojunction (Vs = 60 mV, It = 200 pA). Inset: larger-scale STM image of multiple GNR heterojunctions, showing a variety of segment lengths (Vs = 0.50 V, It = 2 pA).

The black curve in Fig. 6.2 shows a spectrum obtained at this interface location, which is seen to exhibit two additional closely-spaced peaks labeled state 1 and state 2. Lorentzian peak fitting yields peak positions for states 1 and 2 as Vs = 1.13 ± 0.02 V and Vs = 1.25 ± 0.02 V, respectively. All of these spectroscopic features were consistently observed on all ten GNR heterojunctions whose nanoribbon segments and interfaces were inspected via dI/dV tunneling spectroscopy using different STM tips (all heterojunctions inspected via dI/dV also had N = 7 and N = 13 segments composed of at least two monomers each (i.e., segment lengths ≥ 1.6 nm)). The spatial distribution of GNR heterojunction states 1–4 were explored using dI/dV mapping (Figs.6.3A–D). Fig. 6.3A shows the dI/dV map obtained for the highest-energy state (state 4) at Vs = 1.86 V for the same heterojunction shown in the inset to Fig. 6.2. The dI/dV map of state 4 exhibits significant LDOS at the edges of the narrower N = 7 segment, and some LDOS at the edges of the wider N = 13 segment. Fig. 6.3B shows the dI/dV map obtained at the energy of state 3 (Vs = 1.45 V). This lower-energy state shows significant LDOS near the edges of the wider N = 13 heterojunction segment, but no LDOS in the narrower N = 7 segment. Fig. 6.3C shows the dI/dV map of state 2 at Vs = 1.25 V. This lower-energy state exhibits significant LDOS at the corners of the interface between the N = 7 and N = 13 segments, as well as some LDOS at the outer edges of the wider CHAPTER 6. GRAPHENE NANORIBBON HETEROJUNCTIONS 70

Figure 6.2: STM dI/dV spectroscopy of 7-13 GNR heterojunction electronic structure. Blue curve shows dI/dV spectrum acquired on narrower, N = 7 segment of 7-13 GNR heterojunction at location of blue cross in inset topography. Red curve shows spectrum acquired on wider, N = 13 segment at location of red cross in inset. Black curve shows spectrum acquired at interface region between N = 7 and N = 13 segments (at black cross in inset). Green curve shows calibration spectrum acquired with tip held over bare Au(111) area (all spectra shown here were acquired with the same STM tip). The black, red and blue curves are vertically oﬀset by 1, 4 and 6 a.u., respectively, for viewing clarity (open-feedback parameters: Vs = 1.00 V, It = 35 pA; modulation voltage Vrms = 10 mV). Resonant peaks showing the locations of four heterojunction states in the unoccupied states are labeled 1–4. Inset shows STM topograph of the 7-13 GNR heterojunction measured spectroscopically in this series of dI/dV spectra (Vs = 0.10 V, It = 95 pA).

N = 13 segment. Fig. 6.3D shows the dI/dV map of state 1, the lowest-energy peak for the unoccupied states, at Vs = 1.15 V. This state shows LDOS localized to the corners of the interface between the N = 7 and N = 13 regions, but very little LDOS anywhere else. The electronic structure thus exhibited by the 7-13 GNR heterojunction shows some features that can be intuitively understood for a nanostructure engineered in this particular way. For example, the fact that the highest-energy state (#4) shows signiﬁcant LDOS in the narrower segment while the adjacent lower-energy state (#3) shows signiﬁcant LDOS in the wider segment is consistent with simple quantum-well behavior. Other features, however, are harder to explain. The interface states 1 and 2, for example, are not intuitive, as well as CHAPTER 6. GRAPHENE NANORIBBON HETEROJUNCTIONS 71

Figure 6.3: Comparison of experimental dI/dV maps and theoretically simulated LDOS for 7-13 GNR heterojunctions. (A–D) Experimental dI/dV spatial maps recorded at energies of spectroscopic peaks 4–1 for the 7-13 GNR heterojunction shown in Fig. 6.2 inset (It = 35 pA; modulation voltage Vrms = 10 mV). The dashed lines are drawn at the mid-height topographical positions at the edges of the 7-13 GNR heterojunction. (E–H) DFT-simulated dI/dV maps of states 4–1 calculated at a height of 4 A˚ above a 7-13 GNR heterojunction. The dashed lines here are drawn at positions located a distance equal to one carbon dimer- dimer spacing outside of the 7-13 GNR heterojunction border carbon atoms. the fact that the GNR heterojunction exhibits high LDOS intensity at its edges but not in its interior.

6.3 First-Principles Calculations for 7-13 GNR Heterojunctions

In order to answer these questions and to better understand the properties of the 7-13 GNR heterojunction, we used ﬁrst-principles density functional theory within the local density approximation (LDA) to calculate its electronic structure. The simulation was based on the isolated 7-13 junction structure shown in the inset to Fig. 6.4A. The resulting density of states is plotted in Fig. 6.4A (localized end-states [4, 96] were manually removed since we probed regions far away from the ends of the GNR heterostructures). The lowest unoccupied states are numbered 1–4 in ascending order of energy analogous to the resonant states observed experimentally (Fig. 6.2). Out-of-plane height-integrated LDOS plots (Figs. 6.4B–E) provide CHAPTER 6. GRAPHENE NANORIBBON HETEROJUNCTIONS 72

Figure 6.4: Theoretical simulation of electronic structure of 7-13 GNR heterojunction. (A) Simulated density of states of the isolated 7-13 GNR heterojunction structure shown in the inset. Four unoccupied resonant states are labeled 1–4 in the figure (states here are labeled analogous to the peaks observed experimentally (Fig. 6.2)). (B–E) Height-integrated LDOS maps of theoretical states 4–1 for 7-13 GNR heterojunction. The plots are normalized with respect to their maximum intensities (270, 348, 500 and 416 a.u. in B–E, respectively). (F) Simulated electron potential energy difference between edge and inner atoms as a function of height above the carbon plane of the 7-13 GNR heterojunction. The red (green) curve shows the potential energy difference between atomic positions A1 and A2 (B1 and B2) marked in the inset. The inset structural drawing depicts the boxed region in the inset to (A). The lower inset sketch represents the height dependence of the potential at one atomic location and the resulting decay of the wavefunction vertically into the vacuum. The horizontal black dashed line indicates the vacuum energy level. (G–I) Simulated LDOS of 7-13 GNR heterojunction state 3 at heights of (G) 2 A,˚ (H) 3 A,˚ and (I) 4 A˚ above the plane of the GNR heterojunction. The LDOS plots are normalized with respect to their maximum intensities (180, 9.05 and 0.84 a.u. in G–I, respectively). CHAPTER 6. GRAPHENE NANORIBBON HETEROJUNCTIONS 73 detailed information regarding the spatial distribution of these simulated states. The lower- energy states 1, 2, and 3 are localized mainly on the wider N = 13 segment and can be understood as confined states in a potential well, with the adjacent and narrower N = 7 segments acting as energy barriers. The higher-energy state 4 extends over the entire heterojunction including both the wide N = 13 and narrow N = 7 segments. All four states show significant intensity in the interior of the heterojunction and there are no localized edge-states (as expected for armchair-edged GNR structures [4]). This appears to be in contradiction, however, with the experimental dI/dV maps shown in Figs. 6.3A–D where only the edges exhibit higher LDOS than the background. We are able to resolve this apparent contradiction by examining the height dependence of the simulated heterojunction LDOS. This is shown by the simulated dI/dV maps depicted in Figs. 6.4G–I, which exhibit the height dependence of the LDOS for one particular state (#3) at different distances above the GNR heterojunction. At a height of 2 A˚ from the carbon plane (Fig. 6.4G) the LDOS appears rather uniformly distributed across the N = 13 segment, resembling the height-integrated LDOS shown in Fig. 6.4C. However, as one moves higher above the carbon plane the heterojunction edges begin to exhibit more intense LDOS than the interior (Figs. 6.4H and I), to the point where the edges completely dominate the LDOS at a height of 4 A˚ above the carbon plane (Fig. 6.4I). Simulated dI/dV maps at even higher distances appear similar. This type of behavior was seen for all four of the simulated states of the heterojunction. Since our STM tip is estimated to be approximately 5 A˚ above the GNR heterojunctions when we perform dI/dV mapping (estimated via the resistance at the open-feedback set points), the experimental dI/dV maps should be directly compared with the simulated LDOS calculated in a plane above the heterojunction (see Subsection 1.4.2). Indeed, the simulated LDOS of heterojunction states 1–4 at a height of 4 A˚ above the carbon plane (Figs. 6.3E–H) match the corresponding experimental dI/dV maps very well (Figs. 6.3A–D). The strong dependence of the LDOS distribution with height can be explained by the difference in potential felt by electrons at different positions above a GNR heterojunction, as illustrated in Fig. 6.4F. The red curve in Fig. 6.4F shows the DFT simulated potential difference between positions A1 and A2 in the N = 7 segment (marked in the inset structural drawing) as a function of height; A1 marks a carbon atom at the very edge of the segment whereas A2 marks a carbon atom just one dimer row into the interior. The potential at the edge is seen to be lower than the potential in the interior for heights greater than 1.6 A˚ above the GNR heterojunction. This implies a smaller out-of-plane potential barrier in the vacuum for electrons closer to the edge. The wavefunction at the edge therefore decays vertically into the vacuum more slowly than the wavefunction in the interior, resulting in higher LDOS at the edges as shown in Fig. 6.4I (see Fig. 6.4F inset sketch). The same argument also applies to the N = 13 segment (green curve in Fig. 6.4F). The stronger spectroscopic dI/dV signal observed near the edges of armchair GNRs is thus attributed to spatial variation in the electronic potential, even though the states themselves are not completely localized to the edges. CHAPTER 6. GRAPHENE NANORIBBON HETEROJUNCTIONS 74

6.4 Summary

These results imply that 7-13 GNR heterojunctions are very similar to type I semiconductor junctions since the lowest unoccupied (highest occupied) state in the N = 13 segment is lower (higher) than that in the N = 7 segment. The N = 7 segment might therefore serve as an energy barrier for charge carriers trapped in the N = 13 segment. This provides a possible means for constructing graphene quantum dots down to sub-10 nm scale with single-atom thickness. A potential beneﬁt of constructing graphene quantum dot-based devices from GNR heterojunctions is that electrical contacts to the quantum dots are readily available via the outer GNR segments. Bottom-up GNR-based synthesis methods thus have potential for creating useful gap-modulated semiconductor junctions with feature sizes smaller than what is possible using conventional top-down lithography. 75

Chapter 7

Imaging Single-Molecule Chemical Reactions

This chapter presents our ideas on using enediyne Bergman cyclizations for GNR synthesis, as well as our experimental results in imaging single-molecule enediyne chemical reactions using non-contact atomic force microscopy. The content here is based on our published paper: D. G. de Oteyza et al., “Direct imaging of covalent bond structure in single-molecule chemical reactions”, Science 340, 1434–1437 (2013).

7.1 Introduction

For electronic applications it is often required to have GNRs placed on insulators. The previous chapters have presented results from studies of GNRs on metallic surfaces. However, the Ullmann-like reactions studied in Chapters 5 and 6 cannot be performed directly on insulating surfaces, and therefore an alternative kind of chemical reaction is needed to grow GNRs directly on insulating surfaces. A candidate reaction involves Bergman cyclization of enediynes. As shown in Fig. 7.1, the structure of an enediyne unit consists of a carbon-carbon double bond (namely, ene) and two triple bonds (namely, di-yne). C1–C6 cyclization may be triggered by heat or ultraviolet light in a solution, resulting in a diradical intermediate (this reaction is reversible) [113, 114]. The isomerization here is not supposed to rely on

Figure 7.1: Bergman cyclization of enediyne. any metal catalyst, and thereby it has the potential to grow long polymer chains directly on insulating surfaces [115, 116]. We therefore have proposed to synthesize GNRs by way CHAPTER 7. IMAGING SINGLE-MOLECULE CHEMICAL REACTIONS 76 of Bergman cyclizations. Fig. 7.2 shows one possible scheme proposed to synthesize GNRs from enediyne monomers. Enediyne monomers are deposited on a sample surface, and then heated to induce C1–C6 Bergman cyclizations. The resultant diradical intermediates may diﬀuse along the surface, colligating with one another to form polymer chains. Upon being further heated, the polymer chains may undergo cyclization/dehydrogenation sequences, and eventually turn into GNRs.

Figure 7.2: Proposed synthesis of GNR from isomerizing enediyne monomers.

To help rational design of functional enediynes as building blocks for GNRs/conductive polymers, we started by imaging single enediynes in surface-supported chemical reactions. The ability to understanding the microscopic rearrangements of matter that occur during chemical reactions is of great importance for catalytic mechanisms and might lead to dramatic optimization of industrially relevant processes [117, 118]. Traditional chemical structure characterization methods, however, are typically limited to ensemble techniques where different molecular structures, if present, are convolved in each measurement [119]. This limitation complicates the determination of final chemical products, and often renders such identification impossible for products present only in small amounts. Single-molecule characterization techniques, such as STM [120, 121], potentially provide a means for sur- passing these limitations. Structural identification using STM, however, is limited by the microscopic contrast arising from the electronic local density of states, which is not always easily related to chemical structure. Another important sub-nanometer-resolved technique is transmission electron microscopy. Here, however, the high-energy electron beam is often too destructive for organic molecule imaging. Recent advances in tuning-fork-based non- contact atomic force microscopy (nc-AFM) provide a method capable of non-destructive sub-nanometer spatial resolution [29–31, 122, 123]. Single-molecule images obtained with this technique are reminiscent of wire-frame chemical structures and even allow differences in chemical bond-order to be identified [31].

7.2 Imaging Enediyne Reactions on Ag(100)

In this section we show that, by using nc-AFM, it is possible to resolve intramolecular structural changes and bond rearrangements associated with complex surface-supported enediyne cyclization cascades, thereby revealing the microscopic processes involved in chemical reaction pathways. CHAPTER 7. IMAGING SINGLE-MOLECULE CHEMICAL REACTIONS 77

Intramolecular structural characterization was performed on the products of a thermally- induced enediyne cyclization of 1,2-bis((2-ethynylphenyl)ethynyl)benzene (1). Enediynes exhibit a variety of radical cyclization processes known to compete with traditional Bergman cyclizations [113, 114], thus often rendering numerous products with complex structures that are diﬃcult to characterize using ensemble techniques [124]. In order to directly image these products with sub-nanometer spatial resolution, we thermally activated the cyclization reaction on an atomically clean metallic surface under UHV. We probed both the reactant and ﬁnal products at the single molecule level using STM and nc-AFM. Our images revealed that the thermally induced complex bond-rearrangement of 1 results in a variety of unexpected products, from which we have obtained a detailed mechanistic picture of the cyclization processes. These mechanisms are corroborated by ab initio density functional theory (DFT) calculations, revealing the power of nc-AFM to provide new insight into chemical reactions and catalysis.

Figure 7.3: Synthetic route toward 1,2-bis((2-ethynylphenyl)ethynyl)benzene (1).

We synthesized 1,2-bis((2-ethynylphenyl)ethynyl)benzene (1) through iterative Sono- gashira cross-coupling reactions (Fig. 7.3). We deposited 1 from a Knudsen cell onto a Ag(100) surface held at room temperature under UHV. Molecule-decorated samples were transferred to a cryogenic imaging stage (T ≤ 7 K) before and after undergoing a thermal annealing step. Cryogenic imaging was performed both in a home-built T = 7 K scanning tunneling microscope and in a qPlus-equipped [32, 43], commercial Omicron LT-STM/AFM at T = 5 K. nc-AFM images were recorded by measuring the frequency shift of the qPlus resonator while scanning over the sample surface in constant height mode. For nc-AFM CHAPTER 7. IMAGING SINGLE-MOLECULE CHEMICAL REACTIONS 78 measurements the apex of the tip was ﬁrst functionalized with a single CO molecule [29]. To assess the reaction pathway energetics we performed ab initio DFT calculations within the local density approximation [125] using the Grid-based Projector Augmented Wavefunction method code GPAW [126, 127].

Figure 7.4: (A) Constant-current STM image of 1 as deposited on Ag(100) (I = 25 pA, V = 0.1 V, T = 7 K). A model of the molecular structure is overlaid on a close-up STM image. (B) STM image of products 2 and 3 on the surface shown in (A) after annealing at T = 145 for 1 minute (I = 45 pA, V = 0.1 V, T = 7 K).

Fig. 7.4A shows a representative STM image of 1 on Ag(100) before undergoing thermal annealing. The adsorbed molecules each exhibited three maxima in their LDOS at positions suggestive of the phenyl rings in 1 (Fig. 7.4A). Annealing the molecule-decorated Ag surface up to 80 left the structure of the molecules unchanged. Annealing the sample at T ≥ 90 , however, induced a chemical transformation of 1 into distinctively different molecular products (some molecular desorption was observed). Fig. 7.4B shows an STM image of the surface after annealing at 145 for 1 min. Two of the reaction products can be seen in this image, labeled as 2 and 3. The structure of the products is unambiguously distinguishable from one another and from the starting material 1, as shown in the close-up STM images of the most common products 2, 3, and 4 in Figs. 7.5B–D. The observed product ratios are 2 : 3 : 4 = (51 ± 7)% : (28 ± 5)% : (7 ± 3)% with the remaining products comprised of other minority monomers as well as fused oligomers (see Fig. 7.6). Detailed sub-nanometer-resolved structure and bond conformations of the molecular reactant 1 and products (2 to 4) were obtained by performing nc-AFM measurements of the molecule-decorated sample both before and after annealing at T ≥ 90 . Fig. 7.5E shows an nc-AFM image of 1 prior to annealing. In contrast to the STM image (Fig. 7.5A) of 1, which reflects the diffuse electronic LDOS of the molecule, the AFM image reveals the highly spatially resolved internal bond structure. A dark halo observed along the periphery of the molecule is associated with long-range electrostatic and van der Waals interactions [29, 128]. The detailed intramolecular contrast arises from short-ranged Pauli repulsion, which is maximized in the regions of highest electron density [128]. These regions include CHAPTER 7. IMAGING SINGLE-MOLECULE CHEMICAL REACTIONS 79

Figure 7.5: Comparison of STM images, nc-AFM images, and structures for molecular reactant and products. (A) STM image of 1 on Ag(100) prior to annealing. (B–D) STM images of individual products 2–4 on Ag(100) after annealing at T > 90 (I = 10 pA, V = −0.2 V, T = 5 K). (E) nc-AFM image of the same molecule (reactant 1) depicted in (A). (F–H) nc-AFM images of the same molecules (products 2–4) depicted in (B–D). nc-AFM images were obtained at sample bias V = −0.2 V (qPlus sensor resonance frequency = 29.73 kHz, nominal spring constant = 1800 N/m, Q-value = 90000, oscillation amplitude = 60 pm). (I–L) Schematic representation of the molecular structure of reactant 1 and products 2–4. All images were acquired with a CO modiﬁed tip.

the atomic positions and the covalent bonds. Even subtle differences in the electron density attributed to specific bond orders can be distinguished [31], as evidenced by the enhanced contrast at the positions of the triple bonds within 1. This effect is to be distinguished from the enhanced contrast observed along the periphery of the molecule, where spurious effects, e.g. because of a smaller van der Waals background, enhanced electron density at the boundaries of the delocalized π-electron system, and molecular deviations from planarity, generally influence the contrast [31, 128]. CHAPTER 7. IMAGING SINGLE-MOLECULE CHEMICAL REACTIONS 80

Figure 7.6: STM (A–B) and nc-AFM images (C–D) of the products 9 and 10. A schematic representation of the proposed molecular structure of 10 is depicted in (F). Imaging parameters were (I = 5 pA, V = 0.066 V), (I = 10 pA, V = −0.2 V), (V = −0.25 V, amplitude = 60 pm) and (V = −0.2 V, amplitude = 70 pm) for A, B, C and D, respectively. For the nc-AFM measurements, the sensor parameters were the following: qPlus sensor resonance frequency = 29.73 kHz, nominal spring constant = 1800 N/m, Q-value = 90000.

Figs. 7.5F–H show sub-nanometer-resolved nc-AFM images of reaction products 2 to 4 that were observed after annealing the sample at T > 90 . The structure of these products remained unaltered even after further annealing to temperatures within the probed range from 90 to 150 (150 was the maximum annealing temperature explored in this study). The nc-AFM images reveal structural patterns of annulated six-, ﬁve-, and four- membered rings. The inferred molecular structures are represented in Figs. 7.5J–L. Internal bond lengths measured by nc-AFM have previously been shown to correlate with Pauling bond order, but with deviations occurring near a molecule’s periphery, as described above. As a result, we could extract clear bonding geometries for the products (Figs. 7.5J–L), but not their detailed bond order. The subtle radial streaking extending from the peripheral carbon atoms suggests that the valences of the carbon atoms are terminated by hydrogen [128]. This is in agreement with molecular mass conservation for all proposed product structures, and CHAPTER 7. IMAGING SINGLE-MOLECULE CHEMICAL REACTIONS 81 indicates that the chemical reactions leading to products 2 to 4 are exclusively isomerization processes.1 Our ability to directly visualize the bond geometry of the reaction products (Figs. 7.5F– H) provides insight into the detailed thermal reaction mechanisms that convert 1 into the products. We will herein focus our discussion to the reaction pathways leading from 1 to the two most abundant products, 2 and 3. The reactivity of oligo-1,2-diethynylbenzene 1 can be rationalized by treating the 1,2-diethynylbenzene subunits as independent but overlapping enediyne systems that are either substituted by two phenyl rings for the central enediyne, or by one phenyl ring and one hydrogen atom in the terminal segments. This treatment suggests three potential cyclizations along the reaction pathway (resulting in 6-membered, 5-membered, or 4-membered rings) [129], in addition to other possible isomerization processes such as [1,2]-radical shifts or bond rotations that have been observed in related systems [130]. Combinations of these processes leading to the products in a minimal number of steps were explored and analyzed using DFT calculations.

7.3 Thermodynamics of Reaction Routes

To understand the observed dynamical reactions, we ﬁrst calculated the total energy of a single adsorbed molecule of the reactant 1 on a Ag(100) surface. Activation barriers and the energy of metastable intermediates were next calculated (including molecule-surface interactions) for a variety of isomeric structures along the reaction pathway leading toward the products 2 and 3. Our observations that the structure of reactants on Ag(100) remains unchanged for T < 90 and that no reaction intermediates can be detected among the products indicates that the initial enediyne cyclization is associated with a notable activation barrier that represents the rate-determining step in the reaction. In agreement with experiments, DFT calculations predict an initial high barrier for the ﬁrst cyclization reactions, followed by a series of lower barriers associated with subsequent bond rotations and hydrogen shifts. Fig. 7.7A shows the reaction pathway determined for the transformation of 1 into product 2. The rate-determining activation barrier is associated with a C1–C6 Bergman cyclization of a terminal enediyne coupled with a C1–C5 cyclization of the internal enediyne segment to give the intermediate diradical Int1 in an overall exothermic process (60.8 kcal·mol−1). Rotation of the third enediyne subunit around a double bond, followed by the C1–C5 cyclization of the fulvene radical with the remaining triple bond leads to Int2. The rotation around the exocyclic double bond is hindered by the Ag surface and requires the breaking of the bond between the unsaturated valence on the sp2 carbon atom and the Ag. Yet, the activation barrier associated with this process does not exceed the energy of the starting material used as a reference. The formation of three new carbon-carbon bonds and the extended aromatic

1Fig. 7.5G suggests a 4-membered ring between two 6-membered rings, but does not resolve it perfectly. DFT calculations indicate that other structural isomers, such as an 8-membered ring next to a 6-membered ring, are energetically very unfavorable compared to the structure of 3. CHAPTER 7. IMAGING SINGLE-MOLECULE CHEMICAL REACTIONS 82

Figure 7.7: Proposed pathways for the cyclization of reactant 1 into (A) product 2 and (B) product 3 on Ag(100). Energies for 1, 2, and 3 (filled circles), intermediates Int1Int3, tInt1, and tInt2 (filled circles), and reaction barriers (open circles) as calculated using ab initio DFT theory (14). 3D-models show the non-planar structure of intermediates. (‡) rate-determining transition state; red line, reference energy of 1 on Ag(100). CHAPTER 7. IMAGING SINGLE-MOLECULE CHEMICAL REACTIONS 83 conjugation stabilize Int2 by 123.9 kcal·mol−1 relative to 1. Lastly, a sequence of radical [1,2]- and [1,3]-hydrogen shifts followed by a C1–C6 cyclization leads from Int2 directly to the dibenzofulvalene 2. Our calculations indicate that the substantial activation barriers generally associated with radical hydrogen shifts in the gas phase (5060 kcal·mol−1) [131, 132] are lowered through the stabilizing effect of the Ag atoms on the surface, and thus, do not represent a rate limiting process (Fig. 7.7A). The reaction sequence toward 3 is illustrated in Fig. 7.7B. The rate-determining first step involves two C1–C5 cyclizations of the sterically less hindered terminal enediynes to yield benzofulvene diradicals. The radicals localized on the exocyclic double bonds subsequently recombine in a formal C1–C4 cyclization to yield the four-membered ring in the transient intermediate tInt1. This process involves the formation of three new carbon-carbon bonds, yet it lacks the aromatic stabilization associated with the formation of the naphthyl fragment in Int2 and is consequently less exothermic (60.7 kcal mol1). A sequence of bond rotations transforms tInt1 via Int3 into tInt2. Alignment of the unsaturated carbon valences in diradical tInt1 with underlying Ag atoms maximizes the interaction with the substrate and induces a highly non-planar arrangement, thereby making subsequent rotations essentially barrierless. [1,2]-hydrogen shifts and a formal C1–C6 cyclization yield the biphenylene 3. Both reaction pathways toward 2 and 3 involve C1–C5 enediyne cyclizations. These are generally energetically less favorable compared to the preferred C1–C6 Bergman cyclizations [129], but factors such as the steric congestion induced by substituents on the alkynes [114, 129], the presence of metal catalysts [133], or single-electron reductions of enediynes [134, 135] have been shown to sway the balance toward C1–C5 cyclizations yielding benzofulvene diradicals. All three of these factors apply to the present case of the thermally induced cyclization of 1 on Ag(100) (e.g., bulky phenyl substituent on C1 and C6, a metallic substrate, and a charge transfer of 0.5 electrons from the substrate to 1 (14)) thus facilitating the C1–C5 cyclizations. The precise order of the low-energy processes (such as the Int3/tInt2 rotation and the tInt2/3 [1,2]-hydrogen shifts) following the rate limiting initial cyclizations cannot be strictly determined experimentally. However, the sequence does not change the overall reaction kinetics and thermodynamics discussed above.

7.4 Summary

Our bond-resolved single-molecule imaging allows us to extract an exhaustive picture and unparalleled insight into the chemistry involved in complex enediyne cyclization cascades on Ag(100) surfaces. Even if trace-amount products in chemical reactions can be resolved, which is often inaccessible by analysis methods based on ensemble properties of chemicals. From this work one also learns that distinctly diﬀerent reaction pathways can occur on surfaces from those in solutions. This detailed mechanistic understanding based on nc-AFM thus guides the rational design of precursors for surface-supported synthesis of molecular architectures (such as GNRs). 84

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Appendix A

Dual-Crucible Evaporator

This appendix provides details about building a Knudsen dual-crucible evaporator. Fig- ure A.3 depicts the design of the evaporator. We chose boron nitride as the material for the crucibles because of its relatively high thermal conductivity. In contrast, Macor® is selected to make the thermal shields for its low thermal conductivity. Although more power is required for a crucible in this design to reach the same temperature as that in another Knudsen cell design used by our group (see Fig. 2.5), this design is easier to assemble and less likely to have short-circuit issues.

A.1 Parts List

Below lists the required parts to build the dual-crucible evaporator:

1. 8-pin electrical feedthrough, nickel rods, 5 kV, 15 Amp (vaqtec srl, PN: 1-PW-0597. When obtaining a quote specify to have all the pins are on the a circle (i.e., no central pin). By default vaqtec quotes the model with a central pin). Quantity: 1.

2. Inline barrel connectors. Be-Cu, 0.120 ID, 0.56 long (Kurt J. Lesker, PN: FTAIBC120). Quantity: 8.

3. Boron nitride crucibles (Kurt J. Lesker, PN: EVC7BN). Quantity: 2

4. Copper bare wire, 0.094 OD (Kurt J. Lesker, PN: FTAWCU094). Quantity: 2 ft.

5. Tungsten wire, 0.016 OD (California Wire Company). Quantity: 1 ft.

6. 0.010 nickel chromium wire for K-type thermocouples (Chromega®, Omega Engineer- ing Inc., PN: SPCH-010-50). Quantity: 2 ft.

7. 0.010 nickel aluminum wire for K-type thermocouples (Alomega®, Omega Engineer- ing Inc., PN: SPAL-010-50). Quantity: 2 ft. APPENDIX A. DUAL-CRUCIBLE EVAPORATOR 95

8. Aluminum oxide spacer, Fig. A.1 (made in the Physics Machine Shop). Quantity: 1.

9. Macor® thermal shields, Fig. A.2. The thermal shield has a bucket shape, with a through hole drilled at the bottom (made in the Physics Machine Shop). Quantity: 2.

10. Optional: thin molybdenum foil (thickness < 0.005). Quantity: 0.5× 0.5.

Figure A.1: Dimensions for an aluminum oxide spacer.

Figure A.2: Dimensions for a Macor® thermal shield. APPENDIX A. DUAL-CRUCIBLE EVAPORATOR 96

A.2 Construction Procedure

1. Cut the nickel rods of the 8-pin electrical feedthrough at every other position down to ∼ 1.5 inches.

2. Connect four copper rods to the uncut nickel rods of the electrical feedthrough with inline barrel connectors. The length of the copper rods are determined by the setup of the evaporator (For example, when setting up the evaporator in front of a gate valve, choose the length that the crucibles can be as close to the gate as possible).

3. Pass the aluminum oxide spacer through the copper rods and place it on top of the inline barrel connectors installed in Step 2

4. Put on barrel connectors at the end of the coppor rods.

5. Wind a 0.016 tungsten wire a few turns around the BN crucible. Put the wire through the bottom hole of the thermal shield (see Fig. A.4).

6. Connect the tungsten wire to two adjacent copper rods (see Fig. A.3) with the inline barrel connectors installed in step 4.

7. Twist and spot-weld the nickel-chromium and the nickel-aluminum wires together to form a K-type thermocouple. Optional: the junction may be in turn spot-welded onto a piece of molybdenum foil whose size is slightly larger than the interior of the crucible.

8. Insert the thermocouple into the crucible (may need to bend the Mo foil).

9. Wind each thermocouple wire around the aluminum oxide spacer as shown in Fig. A.3, and spot-weld it on a rod that was cut previously in Step 1.

10. Repeat Steps 5 through 9 to build another cell.

To test the dual-crucible evaporator, mount it on a loadlock and pump the loadlock down to at least 5 × 10−5 mbar. Run currents through the ﬁlaments and observe the operating temperatures with the K-type thermocouples. It may be useful to record the cross-talk between the crucibles. This test also helps to degas the evaporator. APPENDIX A. DUAL-CRUCIBLE EVAPORATOR 97

Figure A.3: A dual-crucible evaporator.

Figure A.4: Cell assembly. 98

Appendix B

Growth of Boron Nitride Thin Films on Cu(111)

This appendix describes how to grow boron nitride thin film on Cu(111) in UHV. Borazine (B3N3H6) is used as the precursor for BN in our recipe (the Felix Fischer group in UC Berkeley Chemistry Department synthesized borazine for us). Borazine can easily react with water to form boric acid (often showing up as white-colored flakes), and therefore it is critical to prepare it in a glove box to avoid moisture. KF and CF vacuum parts are used to ensure good sealing of borazine from the air. Borazine is leaked into a UHV chamber through a leak valve while a Cu(111) crystal in the chamber is heated and held at ∼ 850 . Borazine thus decomposes on the copper surface and forms a BN film. This process is self-terminating at one monolayer as the metallic surface is required to catalyze the decomposition of borazine. After growth, STM is used to confirm the existence of the BN thin film.

B.1 System Setup and Growth Procedure

At room temperature borazine is a liquid and has a relatively high vapor pressure ∼ 350 mbar. Due to this high vapor pressure it is important to reduce the volume of the setup for borazine source so that less of the material will be wasted (KF NW16 and CF DN16 flanges are preferred). Fig. B.1 shows our setup for the borazine source. Sealed-off glass is used to contain borazine, and a valve is employed to close the container when necessary (e.g., when transferring borazine between a glove box and a vacuum chamber). This borazine source setup is then connected through a tee to a pumping station (with an inline vacuum valve in between) and a leak valve on a UHV chamber. The pumping station will be used to purge the lines; for safety its exhaust must be connected to the chemical exhaust in the laboratory. Below describes the procedure to prepare the source setup and grow BN thin film on Cu(111): 1. Prepare the borazine source container. Connect the container to the pumping station and pump the setup down to < 10−4 mbar. Cover the glass with a layer of aluminum APPENDIX B. GROWTH OF BORON NITRIDE THIN FILMS 99

Figure B.1: Borazine source container.

foil and heat up the entire setup with a heat gun (this helps to remove water in the lines). 2. Close the valve of the source container. Detach it from the setup. 3. Transfer borazine into the container in a glove box. Make sure the container is sealed off before taking it outside of the glove box. 4. Connect the source container back to the vacuum system and keep the valve to the source container closed. Pump the setup down to < 10−4 mbar. 5. Use a heat gun to quickly bake the lines. 6. Freeze borazine with liquid nitrogen (held either in a Styrofoam container or in a small liquid nitrogen dewar). 7. Open slowly any closed inline valve. Pump the lines down to < 10−4 mbar. 8. Remove liquid nitrogen. The solid borazine will start to warm up and melt. When seeing bubbles, close the valve to the pumping station. 9. Repeat Steps 6 through 8 two more times. Borazine should be ready to be leaked into the UHV chamber for BN growth. To make sure the Cu(111) surface is reasonably clean for BN growth, one can heat the crystal to ∼ 850 during the annealing stage in standard surface cleaning cycles, and scan surface afterwards with STM. For growth of a BN thin film, 10. Maintain the Cu(111) crystal at 850 . 11. Leak borazine into the UHV chamber to pressure 2×10−6 mbar. Maintain the pressure for 10 min and then close the leak valve. 12. Stop heating the crystal. This completes the growth of the BN film. APPENDIX B. GROWTH OF BORON NITRIDE THIN FILMS 100

B.2 STM Imaging

One can use STM to confirm successful growth of the BN film on Cu(111). It has been observed that the BN film can appear transparent at certain sample biases under STM. Therefore, it is important to image the BN film with an appropriate sample bias, such as Vs = +4 V when the apparent height is ∼ 1.5 A˚ according to Joshi et al [136]. Fig. B.2 shows an STM topographic image of a BN film grown on Cu(111), in which the Moirépattern can be clearly seen.

Figure B.2: Room-temperture STM image of Moir´e pattern of BN monolayer ﬁlm on Cu(111). Vs = 4.01 V, It = 0.12 nA.