Electrostatic Sensing and Electrochemistry with
Single Carbon Nanotubes
Proefschrift
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. dr. ir. J. T. Fokkema, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op vrijdag 16 januari 2009 om 12.30 uur door
Iddo HELLER
natuurkundig ingenieur geboren te Rotterdam.
Dit proefschrift is goedgekeurd door de promotoren: Prof. dr. C. Dekker
Prof. dr. S. G. Lemay
Samenstelling van de promotiecommissie:
Rector Magnificus Voorzitter
Prof. dr. C. Dekker Technische Universiteit Delft, promotor
Prof. dr. S. G. Lemay Technische Universiteit Delft, promotor
Prof. dr. J. V. Macpherson University of Warwick, United Kingdom
Prof. dr. D. A. M. Vanmaekelbergh Universiteit Utrecht
Prof. dr. ir. H. S. J. van der Zant Technische Universiteit Delft
Dr. A. Bachtold Institut Català de Nanotecnologia, Spain
Dr. ir. T. H. Oosterkamp Universiteit Leiden
Prof. dr. ir. L. M. K. Vandersypen Technische Universiteit Delft, reservelid
Keywords: Carbon nanotube, graphene, nanowire, nanotechnology, sensor, biosensing, field-effect transistor, electrochemistry, cell
This work is financially supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), and NanoNed.
Published by: Iddo Heller
Cover design by: Ivo van der Ent
Printed by: Gildeprint Drukkerijen B.V.
The production of this thesis is financially supported by Delft University of Technology, Olympus Nederland B.V., and Clean Air Techniek B.V.
An electronic version of this thesis is available at: http://www.library.tudelft.nl/dissertations/
Casimir PhD Series, Delft-Leiden, 2008-07, ISBN: 978-90-8593-047-1 Copyright © 2008 by I. Heller
Preface
This thesis describes the research I did together with a number of people during my time in the molecular biophysics (MB) group at the TU Delft. This work would not have been possible without the invaluable help and support of a large number of people. In this preface I would like to give a flavor of what the time I spent in MB means to me, and take the opportunity to thank the people who made this time possible and worthwhile.
It was March 2003 when I found myself for the first time in the office of a certain Professor Cees Dekker. I was there to ask about the possibility of doing a MSc project in the young group of MB. That day I caught the first glimpse of Cees’s infectious enthusiasm for science and nanotechnology, which would keep me occupied for the coming five years.
Starting a MSc project at that time meant quite an adjustment for me: with Roxane I had just shared the most amazing year traveling around the eastern part of the globe. Our minds were still full of the grandeur and poverty of Burma, of being chased by orangutans in the jungle of Sumatra, and of facing fifty feeding sharks within arms reach in the Coral Sea. But despite all the great things we had seen and done, at the end of that year I was really looking forward to life back in Holland. Time to get back to friends and family, and put my brain back to work again in physics.
MB was greatly welcoming. Cees, you have created a stimulating and harmonious environment, in which ambitious research goes side-by-side with a great social atmosphere. It was Dirk Heering who, in a flurry of words, pictures, and exciting perspectives, convinced me that electrochemistry with carbon nanotubes was the coolest thing to study. Dirk, thanks for convincing me, and for all your help these last years. I am still baffled by the amount of knowledge and ideas that gush from you after being asked one question. Back then I closely worked with two other people: Keith Williams and Jing Kong. Besides initiating me into the art of nanofabrication, Keith taught me to appreciate nanotubes as ‘the best thing since Swiss cheese’. I very much would like to thank Jing, who supervised me during this year, and taught me I should ‘love’ my data. Your drive to get whatever project to work is something I will always remember.
After my MSc project, I got the opportunity to start on a PhD project at MB. The subject was ‘Biological applications of carbon nanotubes’. We first decided to dig deeper into the use of nanotubes for electrochemistry, which unfortunately resulted in a near two year struggle to
find proper insulators. Nevertheless, infected by Jing’s eternal working spirit, and thanks to the great atmosphere in the group, not a moment of these two years was spent in bad spirit. A great help and nice personality in the realm of nanotube electrochemistry was Bernie. It was always nice to work with you and discuss electrochemistry and rate constants. There are many people I would like to thank who made this time worthwhile. I managed to sneak in on some of the fun Wednesday night postdoc dinners, alongside Christine, Uli, Ralf, Brian, Bernie, Freek, Diegoal, five-minutes-of-fury-Derek, Irene, Igor, and Fernano. Christine, MB suffered a loss when you left. Not only because of your inexhaustible efforts in the cleanroom, but also since you were often the motor behind social activities. Together with Igor you were always in for a party, and another, and yet another… Torej, Igor, it was great fun sharing a room with you. Thanks for the many chitchats, fun anecdotes, and ironic comments back and forth. I still do not believe your brother exists though. Of course, a lot of credit goes to the supporting staff of that time, for facilitating the research every day. Thanks Jack, Dick, and Peter. Dick, it seems you will never entirely escape our evaporator, but I hope in between your lab visits you are enjoying your retirement. And Peter, your 1000 $ fine still haunts the biolab!
Within the nanotube project, we decided to change direction. It was great fun and inspiring to brainstorm with Cees about all the exciting things we could do with carbon nanotubes. In fact, the nearly unrestrained optimism and enthusiasm we share about the numerous possibilities of exploiting nanotubes at some point caused me to work on half a dozen projects at a time. Although I never liked to let go of any of these projects, I am glad that toward the end you forced me to focus my research and work toward some solid results. It was especially nice to see a number of the clumsy schematics I drew up two years ago turn into actual data and consequently into actual papers. One of the other people in the lab I owe most to is Serge Lemay. Serge, I am still amazed by the fact that when I came to your office with any piece of data, paper, or lousy sketch of an energy diagram, you managed to assess my problem and formulate a meaningful answer on the spot. I always left having learnt something. I especially appreciate your nice, open attitude, and willingness to help out, no matter how busy you are. Thanks for the many insightful discussions, and all your help, particularly during these last months!
A large part of the research during the second half of my PhD was focused on electrostatic detection with carbon nanotube transistors. During this time, I was lucky to benefit from the knowledge and experience of two great postdocs. Ethan, I really enjoyed working with you, both because of your thorough ways of doing research and your nice personality. And Jaan, I appreciate that we will be working together a bit longer. I would like to thank you for your friendly and honest attitude and your help with a lot of the work in the last years. Although I wish you all the best with the exciting bugs-on-a-chip work that you are doing with Juan, I hope you will still find some time to shoot for single-molecule detection with nanotubes! By now the supporting staff has changed completely, and I would like to say thanks to Jaap,
v
Susanne (no more Schottky barriers for you!), Serge D., Jelle, Jacob, Elsemarieke, Liset, and Emmylou.
During these years, many MSc students came and went, doing a lot of good work for the group. I enjoyed supervising and working together with a number of them. Alexei, thanks for all the hard work you did on trying to get those stubborn stumps of tubes in bilayer membranes. Furthermore, a lot of credit goes to Anne. The large amount of well-documented data you collected found its way into a number of papers! Also many thanks to Wiljan. I hope our conflicting opinions on lab tidiness did not drive you mad. I enjoyed trying to feed those cells nanotubes together. And although we are not there yet, well, there are still many Friday afternoons to go… Finally, thank you Sohail, for allowing me to ‘abuse’ some of your precious graphene samples!
And then, of course, there are the MB PhD students. It was great fun riding the doctoral rollercoaster together with you guys. First thanks to the ‘oude garde’. Frank and Daniel, it was sad to see you go, and I hope we keep in touch. The folks next door: Pinky, Thijn, Ralph, and Koen. They are a noisy bunch, but great fun to be around. I especially thank Thijn: you are fair and square but always there to help anyone out. And then there are the locals: Marijn, your unintelligible mumbling behind me made for nice and cozy background music. After a while, it made me feel more at home here! Good luck with your aptly numbered Rad’s and Rec’s. Marcel, you are a cool guy, and very infectious when telling a fun story. Thanks for the many rides to Rotterdam, and I am sure those single molecules will surrender soon. Also good luck to all the ‘new’ PhD students, Stefan, Sjoerd-Jan, Michiel and Rifka. Michiel, there was never a dull (or quiet) moment with you. One day you will proof that the earth is indeed, banana shaped.
Another thing I really like about MB, is the sporty attitude. Possibly this is related to Cees, who is the most competitive professor I have met! I enjoyed the climbing events with several people. Especially, I would like to thank Bernhard, the diving trips were great fun and I hope we stay in touch. Adam, lets try to hit those street courts again some time. Jan, I have never seen anyone as eager for the ball as you, I am sure you will lead MB to the cup one day. Finally, there is the inevitable foosball table. Iwijn, I had lots of fun with you and Jean-Marie. In addition, your “ik haat u” sounds sweeter than any klinker!
It has been great being a part of MB, and seeing the group develop. Cees, I would like to thank you for everything, and whish you lots of success with the group, and of course with the new bionanoscience department.
Finally, I want to thank the home front. Ria, Arthur, Marijke, and Ben, thank you for all your support. After defense day, I hope we will see a lot more of each other! The same holds for all the friends I have neglected over the last years. Thanks for all the fun times we had. In particular, I would like to thank Ivo, for your precious time spent on designing the cover, and my paranimfen, Henk and Narada. The last few years have been a great trip for me, both across the globe, through science, and through different social landscapes. Though I have
tried to divide my attention fairly over these subjects, I feel I have never had enough time to do justice to all. W. Hazlitt (1778-1830) seems to have expressed my feeling very well when he wrote: “I should like to spend the whole of my life travelling, if I could anywhere borrow
another life to spend at home.” Wherever I am, most important to me are the people along the
way, with whom I can enjoy the many great things in life. As L. Sterne (1713-1768) said;
“give me a companion in my journey, be it only to remark to, how our shadows lengthen as the sun goes down.”
Rox, you know that this last quote is pre-eminently for you. You are fantastic. Thanks for always being there by my side, and for all your love and support these last years!
Iddo Heller December 2008
Contents
1. Introduction
... 11
1.1 Nanotechnology: building bridges ... 12
1.2 Carbon nanotubes ... 12
1.2.1 Discovery of fullerenes... 13
1.2.2 From fullerenes to nanotubes ... 13
1.2.3 Carbon nanotube structure... 13
1.2.4 Synthesis ... 14
1.2.5 Properties and applications... 15
1.3 Graphene... 17
1.4 Carbon nanotubes as (bio)sensors... 18
1.4.1 Electrostatic interactions... 19
1.4.2 Electrochemical interactions ... 20
1.5 Overview of this thesis ... 21
1.6 References... 23
2. Individual single-walled carbon nanotubes as nanoelectrodes for
electrochemistry
... 25
2.1 Introduction... 26
2.2 Materials and methods... 26
2.3 Results... 27 2.4 Modeling... 31 2.4.1 Mass transport... 31 2.4.2 Electrode kinetics... 32 2.5 Conclusions... 35 2.6 References... 35
3. Electrochemistry at single-walled carbon nanotubes: the role of band
structure and quantum capacitance
... 37
3.1 Introduction... 38
3.2 Modeling... 40
3.2.1 SWNT electronic density of states (DOS) ... 40
3.2.2 Quantum capacitance... 40
3.3 Results... 43
3.3.1 Electrochemistry at SWNTs... 43
3.3.2 Quantum capacitance and electrode kinetics ... 45
3.3.3 Non-zero charge transfer rate when ρ(εF) = 0... 46
3.3.4 Comparison to Butler-Volmer kinetics ... 47
3.3.5 Charge transfer when εF is near εhf... 50
3.4 Conclusions... 50
3.5 References... 51
4. Carbon nanotube biosensors: the critical role of the reference electrode
.. 53
4.1 Introduction... 54
4.2 Materials and methods... 54
4.3 Results... 56
4.4 Conclusions... 58
4.5 References... 58
5. Identifying the mechanism of biosensing with carbon nanotube transistors
... 61
5.1 Introduction... 62
5.2 Materials and methods... 62
5.3 Results... 63
5.3.1 Biosensing... 64
5.3.2 Sensing mechanisms... 64
5.3.3 Identifying biosensing mechanisms ... 66
5.3.4 Sensing with modified SWNT devices ... 67
5.4 Conclusions... 69
5.5 References... 69
5.6 Supplementary information... 71
6. Sensitivity of carbon nanotube and graphene transistors to local ionic
structure
... 77
6.1 Introduction... 78
6.2 Materials and methods... 78
6.3 Electrolyte gating of SWNT and graphene transistors ... 80
6.4 Electrostatic gating effect ... 80
6.4.1 Electrostatic gating effect as function of ionic strength, pH, and ion type ... 81
6.4.2 Microscopic picture of the electrostatic gating effect... 82
6.4.3 Effect of different cations on electrostatic gating ... 83
ix
6.4.5 Model of the electrostatic gating effect... 85
6.4.6 Comparison of model with electrostatic gating data ... 86
6.5 Changes in p-type and n-type conductance... 88
6.5.1 Effect of ionic strength on p-type and n-type conductance ... 89
6.5.2 Modeling the gate capacitance effect as function of ionic strength ... 90
6.5.3 Effect of pH on p-type and n-type conductance ... 91
6.6 Conclusions and implications... 92
6.7 References... 93
6.8 Supplementary information... 96
7. Charge noise in liquid-gated single-walled carbon nanotube transistors
.. 99
7.1 Introduction... 100
7.2 Materials and methods... 101
7.3 Results... 103
7.4 Conclusions... 106
7.5 References... 107
7.6 Supplementary information... 108
8. Optimizing the signal-to-noise ratio for biosensing with carbon nanotube
transistors
... 111
8.1 Introduction... 112
8.2 Materials and methods... 112
8.3 Results... 113
8.3.1 Gating in two device layouts ... 113
8.3.2 Biosensing signal... 114
8.3.3 The signal-to-noise ratio for real-time sensing ... 116
8.3.4 Gate dependence of the signal-to-noise ratio... 117
8.3.5 Improving the signal-to-noise ratio ... 120
8.4 Conclusions... 122
8.5 References... 122
8.6 Supplementary information... 123
9. Probing macrophage activity with carbon nanotube sensors
... 131
9.1 Introduction... 132
9.2 Materials and methods... 133
9.3 Results... 134
9.3.1 Electrical detection of macrophage activity... 136
9.3.2 Electrochemical detection of macrophage activity... 136
9.4 Conclusions... 139 9.5 Outlook ... 140 9.6 References... 141 9.7 Supplementary information... 142
Summary
... 147
Samenvatting
... 151
Curriculum Vitae
... 157
List of Publications
... 159
Chapter 1
Introduction
This chapter forms an introduction to our experimental studies of carbon nanotube devices in solution. This research is conducted in the field of nanotechnology, an exciting field with a highly interdisciplinary character, which developed over the last decades. Carbon nanotubes and their many potential applications are exemplary for the nature, achievements, and great ambitions of nanotechnology. We describe the developments, dating back to the eighties, which led to the discovery of carbon nanotubes, and continue with a brief overview of their exceptional properties and the wide range of potential applications. Finally, we focus on the early studies of how carbon nanotubes interact electrostatically and electrochemically with a liquid environment, which forms the starting point for the research that is described in this thesis. We end with a concise overview of our studies of electrostatic sensing and electrochemistry with single carbon nanotubes in solution.
1.1 Nanotechnology: building bridges
Our physical world is built up of individual atoms and molecules. The young field of nanotechnology is concerned with the observation, study, and manipulation of our world at the level of single atoms and molecules. This exciting line of research has only started to take off over the last few decades. From the late 20th century on, progression in the fields of
physics and engineering allowed scientists to, for the first time, directly access individual atoms and molecules. The developed techniques grant us eyes and ears in this largely uncharted nanoscopic world. But access is not just limited to observation as passive bystanders; we are in fact able to actively manipulate the single atoms and molecules with a set of tools to shape the nanoworld in a controlled way.
At the level of single atoms and molecules, the borders between the disciplines of physics, chemistry, and biology fade. Therefore, nanotechnology imaginably has a very interdisciplinary character, building bridges between these disciplines, and most importantly, between our macroscopic world and the nanoscopic world. A promising example of this is the relation of nanotechnology with biology. Nanotechnology allows us to for the first time directly look at, sniff, touch, and jiggle the individual proteins and enzymes that make up a single living cell. With the anticipation of many discoveries in biology and medicine using nanotechnology, and vice versa using elements from biology for applications in nanotechnology, some say that the coming century will be the century of a new discipline labeled bionanotechnology. One of the elements that can play a role in interfacing nanotechnology with biology is the carbon nanotube.
1.2 Carbon nanotubes
The carbon nanotube is an exquisite example of a molecule of which the discovery, fundamental study, exploration, and exploitation has been made possible by the developments in nanotechnology.1 Carbon nanotubes are part of a special family of carbon molecules called
fullerenes.
Figure 1.1 Two types of carbon molecules. (a) Buckminster fullerene or buckyball. (b) Single-walled carbon
1.2 Carbon nanotubes 13
1.2.1 Discovery of fullerenes
The first member of the fullerene family, the Buckminster fullerene or buckyball, was discovered in 1985during experiments intended to simulate the chemistry in interstellar space and in the atmosphere of giant stars.2 A buckyball is a tiny carbon sphere, 0.6 nanometer in diameter, which has the same ‘perfect’ geometry of a soccer ball (see Figure 1.1a) It was completely unexpected that besides graphite and diamond, carbon could exist as a stable sphere, made up of as little as 60 carbon atoms. This discovery inspired a great number of researchers that envisioned novel chemical reactions, applications in batteries and electronics, room-temperature superconductivity, and exciting properties of metal atoms encaged in these little carbon domes. Signifying the impact of fullerenes on the scientific world, in 1996 the Nobel Prize in chemistry was awarded to Curl, Kroto, and Smalley for the discovery of these fullerenes.
1.2.2 From fullerenes to nanotubes
With the great excitement surrounding fullerenes, a large effort was put into the fabrication of these molecules. While studying results of the fabrication process, several other fullerenes were discovered, slightly different in structure from the buckyball. In 1991, the Japanese scientist Sumio Iijima discovered carbon nanotubes, elongated fullerenes that consist of concentric nanometer scale cylinders, which were up to several micrometers long.3 These fullerenes were aptly named multi-walled carbon nanotubes. Two years later, single-walled carbon nanotubes were discovered experimentally (see Figure 1.1b).4,5 A major breakthrough that allowed wide-scale exploration of carbon nanotubes was the work of Richard Smalley and coworkers in 1996, who found ways to produce bundles of single-walled carbon nanotubes at high yields.6 With these fullerenes that are easily a thousand times longer than they are wide, a new class of materials had become available with tremendous potential in electronic, chemical and structural applications. Interestingly, these late 20th century scientists were not the first to produce carbon nanotubes. The first evidence of human produced carbon nanotubes dates back to seventeenth century Damascus sabers; the steel blades of these swords, which originate from ancient India, contain carbon nanotubes and have extraordinary mechanical properties.7 Man-made nanotubes however are likely to date back even further. Since fullerenes and nanotubes are simply a special form of carbon soot that can be formed in fuel-rich flames,8,9 the first humanoid that produced these special carbon molecules is likely to be homo erectus, the species that is thought to first control fire, a million years ago.
1.2.3 Carbon nanotube structure
The structure of a single-walled carbon nanotube is that of a rolled up sheet of graphene (a single sheet of graphite), which is seamlessly wrapped into a cylinder, as illustrated in Figure 1.2.1 The nanotube atomic structure is fully defined along its length by the angle that the
graphene lattice makes with the nanotube axis, and the nanotube diameter. Most nanotubes are chiral. This means that lines of connected hexagons spiral around the nanotube, as in Figure 1.2b. The ends of the cylinder can be either capped or open. The electronic properties, which are of particular interested for this thesis, are fully determined by the chiral angle and the diameter of the nanotube. Depending on the chirality, about one third of carbon nanotubes is metallic, and two thirds are semiconducting. The special properties related to the small dimensions and excellent conductivity make nanotubes particularly interesting as elements in electronics.
Figure 1.2 Constructing a carbon nanotube from a graphene sheet. (a) A carbon nanotube can be formed by
wrapping the graphene sheet, cut out along the dashed lines, into a cylinder. The arrow indicates the wrapping direction, which, when the head of the arrow is connected to its tail forms a nanotube with the atomic structure as depicted in (b). The row of dark hexagons in (a) are at an angle φ with the axis of the nanotube. This is illustrated in (b) by the winding of the hexagons along the tube direction. The nanotube structure is commonly defined by the indices (n,m), which denote the wrapping vector (arrow in (a)) in units of the graphene lattice vectors. The (n,m) indices determine the electronic properties: When n – m = 3i, with i an integer number, the nanotube is metallic, otherwise it is semiconducting. The (11,7) nanotube depicted here is a semiconductor. (Adopted from ref 1)
1.2.4 Synthesis
Early synthesis of carbon nanotubes relied on the bulk production methods that were developed for fullerenes. By means of electrical arc discharge or laser ablation, a graphite target is converted into carbon soot, which consists of fullerenes alongside other forms of less
1.2 Carbon nanotubes 15
well-defined carbon structures. A great step forward in practical exploration of the single-walled form of carbon nanotubes was the work of Jing Kong in the group of Hongjie Dai, who found a route to synthesize single-walled carbon nanotubes on silicon wafers by chemical vapor deposition (CVD) at lithographically defined locations.10 Now the special
electronic properties of carbon nanotubes could be integrated with silicon technology and nanofabrication techniques. In this thesis, we use this CVD technique to fabricate carbon nanotube devices. Although further control of carbon nanotube structural properties is required to allow integration of carbon nanotubes with mass-produced electronics, progress is being made. Nowadays, single-walled carbon nanotubes can be grown in predefined directions with lengths up to centimeters.11 Note that these molecules have a length which is
ten million times longer than their diameter! A crucial issue that is still to be overcome is to produce nanotubes of uniform chirality and diameter, which guarantees monodispersity in electronic properties. Already, carbon nanotubes can be produced with relatively uniform diameters, and metallic carbon nanotubes can be selectively eliminated, leaving only semiconducting nanotubes.12 Furthermore, cunning bulk purification techniques have been
devised to select for specific types of carbon nanotubes.13-15 Finally, an intriguing idea is the
carbon nanotube cloning method that was envisioned by Richard Smalley, and of which Tour and coworkers reported an initial experimental demonstration.16 In this method a carbon nanotube of specific chirality is elongated, cut, and the individual pieces elongated again to ‘amplify’ a nanotube of specific chirality and diameter.
1.2.5 Properties and applications
What are the properties that make carbon nanotubes so interesting? As Richard Smalley said, “These nanotubes are so beautiful, that they must be useful for something.” 1 In fact it is
not just one property that makes carbon nanotubes so extraordinary, but the combination of exceptional properties all combined in one molecule. These properties range from structural to chemical, and from electrical to optical. A short, non-exhaustive summary of carbon nanotube properties and possible applications follows below.
Structurally, nanotubes are probably the strongest and stiffest material on earth: they have record-high tensile strength in combination with an extremely high elastic modulus.17-19 This means that, in theory, they can be made into the strongest fibers possible, stronger than steel or spider silk. Carbon nanotubes are very interesting for fabrication of composite materials because of these exceptional mechanical properties in combination with their low density.20 Furthermore, their high aspect ratio combined with exceptional mechanical strength makes carbon nanotubes for instance interesting for adhesive applications. Qu et al. recently demonstrated that vertically aligned carbon nanotube arrays have an adhesive strength almost 10 times stronger than that of gecko feet.21 The one-dimensional structure and strong
mechanical properties have also been explored at the single nanotube level. When mounted on the tip of a scanning probe, a carbon nanotube forms the ultimate high aspect ratio tip for
scanning probe microscopy.22 Finally, interesting mechanical applications have been realized
related to multi-walled carbon nanotubes. The outer concentric cylinders of multi-walled carbon nanotubes can be made into very low friction bearings that slide or rotate around the inner cylindrical nanotube axis.23,24
Chemically, a carbon nanotube is very inert, and therefore highly stable. This is related to the stability of the sp2-bonded carbon network. Nevertheless, when subjected to extreme
conditions, defect sites can be made in the carbon structure.25 After creating defects, the
well-known carbon chemistry can be used to covalently functionalize the defect sites. Structurally the end caps are the weakest points in the lattice, which means that defects will first occur at these locations. Thus, the ends can be opened and the cylinders shortened, leaving dangling carbon bonds accessible for functionalization. This was for instance exploited by Williams and coworkers, who showed that nucleic acid sequences can be attached to the ends of carbon nanotubes, allowing for the specific hybridization to complementary DNA strands in order to self-assemble molecular electronics.26 Alternatively, Chen et al. have demonstrated that
non-covalent interaction with the inherently hydrophobic carbon nanotube sidewall can be exploited to attach functionalities.27 This has the advantage that the electronic properties are
minimally perturbed. An interesting research direction which explores the possibility to attach molecules to carbon nanotubes is to use carbon nanotubes as mediators for drug delivery and imaging agents in living cells and tissues.28,29
The optical properties of carbon nanotubes go side-by-side with their interesting electronic properties, which will be discussed next. Semiconducting carbon nanotubes have been demonstrated as nanoscale light-emitting devices.30 Also, in larger networks, carbon
nanotubes can be exploited to fabricate flexible transparent optoelectronic devices.31 An
interesting application of this is the use of carbon nanotubes in photovoltaic cells.32
Furthermore, the fluorescence properties of individual carbon nanotubes suspended in solution are influenced by interaction with molecules in their environment. Daniel Heller in the Strano group has demonstrated that carbon nanotubes can be used as non-bleaching optical sensors in strongly absorbing media such as cells in tissue and blood.33
Finally we turn to the electronic properties, which are most important in the context of this dissertation. The sp2-bonded carbon lattice forms a large conjugated system of π-electrons through which electronic conduction can occur. Carbon nanotubes are among the smallest metallic wires that have been made to date. In addition, the charge carrier mobility in carbon nanotubes is extremely high. As explained earlier, depending on the chirality of the carbon nanotube the electronic properties can also be semiconducting. The size of the band gap of a semiconducting nanotube depends inversely on its diameter.1 Typically we synthesize nanotubes with a diameter near 2 nm, which have a band gap near 0.5 eV. It was shown by Sander Tans and coworkers that a carbon nanotube can be employed as a molecular field-effect transistor that can be operated at room temperature.34 In fact, three years later in the
1.3 Graphene 17
possible to construct a room-temperature single-electron transistor.35 The small size and high
strength of carbon nanotubes can be exploited to make flexible, transparent electronic devices. Finally, because the electronic transport properties of a molecular field effect transistor are easily affected by the presence of other molecules, these devices are also very interesting for constructing sensors. In this thesis we explore the electronic properties in combination with the high-aspect ratio and small diameter to make highly sensitive nanoscale sensors operated in liquid.
1.3 Graphene
Recently single-layer graphene, another member of the sp2-bonded carbon family, has
become available experimentally. In 2005 Novoselov and coworkers succeeded in isolating single-layer graphene flakes.36 Previously, these purely two-dimensional flakes were often
thought not to exist due to presumed thermodynamic instability when a free-standing monatomic layer is removed from its ‘parent’ three-dimensional crystal. Novoselov and coworkers used the deceivingly simple technique of rubbing a graphite crystal against a solid surface, which is essentially the working principle of a pencil, to produce a collection of single and multi-layer flakes. The key to identifying a single-layer graphene flake was the realization that on an oxidized silicon wafer, even a monatomic carbon layer can change the interference color of reflected light enough to be observed in an optical microscope.36
Similar to the discovery of carbon nanotubes, the availability of graphene, previously just a theoretical toy model, spurred great excitement amongst scientists. A large number of studies have since explored this new two-dimensional material, demonstrating several fundamental physical phenomena unique to the two-dimensional nature of graphene.37
Among these is for instance an anomalous quantum Hall effect, which is measurable up to room temperature.38
In contrast with the metallic or semiconducting electronic structure of carbon nanotubes, graphene is a zero band-gap semiconductor.37 As a result, it cannot be fully depleted of charge
carriers at room temperature, and it maintains a finite conductivity. Nevertheless, the conductivity of graphene can be modulated using a gate electrode that changes the number of charge carriers through a field effect.39 Novoselov and coworkers demonstrated in 2007 that
also the adsorption of gas molecules on graphene can change the device conductance, thus creating the first graphene-based gas sensor.40 Even more interesting, in the same publication
Novoselov and coworkers exploited the Hall effect to obtain the ultimate sensitivity in gas sensing: by applying a large magnetic field, they were able to observe step-wise changes in the Hall resistance, which they attributed to the adsorption and desorption of individual gas molecules.40
It is clear from Figure 1.3, which shows the number of scientific publications generated per year for fullerenes, carbon nanotubes, and graphene, that these carbon allotropes provide
fertile grounds for fundamental and application-driven research. Although we are currently still waiting for major applications that widely impact the general public, a promising future lies ahead for this low-dimensional carbon family.
Figure 1.3 Number of publications per year from 1985 to 2007 on the subject of fullerenes, carbon nanotubes, and
graphene. Data obtained from ISI Web of Knowledge.
1.4 Carbon nanotubes as (bio)sensors
In this dissertation, we describe experimental research that studies the interaction of carbon nanotubes with a liquid environment. We study these interactions in the broader context of biological applications. A carbon nanotube has a diameter of about one nanometer, which is directly comparable to the size of single biomolecules like proteins. At the same time, the micrometer length of a carbon nanotube facilitates connection to macroscopic electrodes that make the nanotube electronically accessible to the outside world. This combination of length scales allows devices based on carbon nanotubes to interface our macroscopic world with the world of single biomolecules. Because the biologically relevant environment of biomolecules is an aqueous solution, we operate our devices in liquid. The interaction of carbon nanotubes with an aqueous environment can be of both electrostatic and electrochemical nature (see Figure 1.4). In this thesis we study these types of interactions electronically, with the aim to learn how carbon nanotubes can be used as the active elements in nanoscale biosensors. Finally, we explore the micrometer length of carbon nanotubes, which is comparable to the size of single cells, to study the possibility of single-cell probing with carbon nanotube devices.
1.4 Carbon nanotubes as (bio)sensors 19
Figure 1.4 Electronic detection of electrostatic and electrochemical interactions with a carbon nanotube in
solution. (a) A carbon nanotube employed as a field-effect transistor, where a bias voltage, Vsd, is applied over
source and drain contacts to the carbon nanotube, which drives a current, Isd, through the nanotube. The Isd current
can be modulated by applying a liquid-gate potential, Vlg through a reference electrode inserted in solution. In
addition, the presence of biomolecules (as illustrated by the positively charged spheres) can change the Isd current,
which is the working principle of the electrostatic sensor. (b) A carbon nanotube employed as a working electrode for electrochemistry. A potential difference, Vlg, applied between the carbon nanotube and the liquid can drive
electrochemical reduction/oxidation reactions that cause charge transfer between the solution and the carbon nanotube. This electrochemical charge transfer is mediated by redox molecules in solution (depicted by the sphere that changes between a reduced and an oxidized state while it accepts/donates an electron from/to the nanotube), which is the working principle of an electrochemical sensor.
1.4.1 Electrostatic interactions
First we turn to the electrostatic interaction of carbon nanotubes with their environment. The electronic transport properties of a carbon nanotube that is employed in a field-effect-transistor layout can be modulated by applying an external electric field. The first experimental demonstration of this molecular field-effect used a solid-state back gate to change the device conductance.34 Modulation of the conductance is however not limited to this solid-state back gate. It was shown by Jing Kong and coworkers that adsorption of gas molecules can also modulate the device conductance.41 This was the first demonstration of a sensor based on a carbon nanotube field-effect transistor, which spurred a large interest in molecular nanosensors.
In 2002, Rosenblatt et al demonstrated that a carbon nanotube field-effect transistor can also be operated in an aqueous solution.42 In this liquid-gated configuration, a potential
difference is applied over the interface of the carbon nanotube and the liquid, as depicted in Figure 1.4a. This potential difference attracts ions to the interface between the nanotube and solution, where they form an electrical double layer. The intimate contact between the carbon nanotube and the electrolyte ions causes the gating efficiency to approach the theoretical upper limit, providing a very strong coupling of the nanotube with its electrostatic environment. As a result, the liquid gate can be used to tune the Fermi level (the chemical potential) of the carbon nanotube to either the valence band or the conductance band on
opposite sides of the band gap. This ambipolar conductance behavior does not commonly occur in field-effect transistors, and is related to the exceptional properties of the carbon nanotube. Similar to gating of carbon nanotubes by electrolyte ions, it was demonstrated in 2003 both by Chen et al and Besteman et al that the adsorption of biomolecules induces large changes in device conductance.43,44 Since these first demonstrations of a liquid-gated
carbon-nanotube transistor as a biosensor, many studies followed showing that carbon carbon-nanotubes are versatile and sensitive nanoscale electrostatic sensors. An alternative route to electrostatic detection using carbon nanotubes was pioneered by Männik and coworkers.45 By creating
point defects in metallic carbon nanotubes, a local barrier for electronic transport is introduced. This point defect can be functionalized, where the attachment, and consequent changes at this attachment site, can induce changes in the barrier and thus the device conductance.
Nanoscale electrostatic sensors based on other materials than carbon nanotubes have also been demonstrated. A prominent example is the development of sensors based on silicon nanowires, which was largely pioneered by the group of Charles Lieber.46 The carbon
nanotube however is arguably the ultimate biosensor in the class of nanoscale sensors. It has the smallest diameter, and with all of its atoms located at the surface, it allows for the strongest interaction with its environment. Because its diameter is of the same order as the size of individual molecules and the electrostatic screening length in solution, electrostatic interactions can be studied on a scale that is not accessible to larger electrostatic sensors.
An important scientific drive to study carbon nanotube sensors is the ultimate goal of single-molecule detection. To date this goal has not been attained, even though carbon nanotubes are claimed to have the highest possible sensitivity. An important reason is that the physical mechanism by which carbon nanotubes interact with their electrostatic environment has been under debate. Until this issue is resolved, full exploitation of a carbon nanotube as an electrostatic probe on the nanometer scale will be hampered.
In this thesis, we study the mechanisms of biosensing with electrostatic carbon nanotube sensors in solution. We elucidate these mechanisms and demonstrate ways to identify which mechanisms are dominant. In addition, we study ionic effects on the nanoscale using carbon nanotube transistors. Since the noise properties of electronic devices are crucial for their operation, we study the noise mechanisms and the factors that affect the signal-to-noise ratio for biosensing with carbon nanotube transistors. Also, we show initial experiments of liquid-gating of graphene transistors, and how these can be used as electrostatic sensors in solution.
1.4.2 Electrochemical interactions
In a liquid-gated field-effect transistor, molecules in solution change the device conductance purely through electrostatic interaction with the transistor. In electrochemical sensors however, the sensing principle is based on the actual transfer of charge across the
1.5 Overview of this thesis 21
electrode-liquid interface as depicted in Figure 1.4b. The potential difference across this interface can drive electrochemical reactions in which electrons from redox molecules or redox enzymes in solution are transferred to the electrode or vice versa. Since the late seventies, electrochemists have developed a wide range of ever smaller electrodes for electrochemistry. These electrodes were called microelectrodes or ultramicroelectrodes. Decreasing the electrode size down to the nanoscale allows the study of phenomena related to the finite size of ions and electrostatic screening at the nanoscale. Thus far, several techniques have been developed to fabricate nanoscale electrodes for electrochemistry. A disadvantage of most of these techniques is that the exact geometry and dimensions of the electroactive surface are poorly defined, which forms a limitation on the analysis of electrochemical data.
Because a carbon nanotube has an atomically well-defined structure, it is an excellent candidate to study electrochemistry in the nanoregime. Electrochemical studies have so far been conducted on large ensembles of carbon nanotubes, exploiting their high surface area. In 1999, Campbell and coworkers demonstrated that an individual multi-walled carbon nanotube can be used as an electrode for electrochemistry.47 Thus far however, the nanometer
dimension of an individual single-walled carbon nanotube has not yet been explored. Furthermore, the study of electron transfer at a carbon nanotube with its distinct electronic structure can teach us about the influence of the electrode density of states on electrochemical reactions. Finally, experiments with individual carbon nanotubes may shed light on the controversy that exists about the electrochemical reactivity of different types of carbon electrodes.
A number of interesting biological applications of carbon nanotubes can be envisioned. Because of the small size of a nanotube and the possibility to interface it with biomolecules, it can act as a nanoscale wire that relays the electrons from a single redox enzyme, thus allowing single-redox-molecule studies at very low background-current levels and with minimal steric hindrance. Also, the combination of a small diameter with the micrometer length may in principle allow for electrochemical probing of cellular environments with high resolution and little perturbation.
In this thesis, we demonstrate the use of an individual single-walled carbon nanotube as a nanoelectrode for electrochemistry. Furthermore we explore the influence of the density of states of carbon nanotubes on the rate of electrochemical reactions. Finally, we report on our exploratory studies of using carbon nanotubes as combined electrostatic and electrochemical probes to study cellular environments.
1.5 Overview of this thesis
This thesis describes electrostatic sensing and electrochemistry with single carbon nanotubes in solution. The first part of this thesis describes an experimental and theoretical study of carbon nanotubes as electrodes for electrochemistry. The second part of this thesis
presents a thorough experimental study of electrostatic sensing with carbon nanotube transistors in solution. We consider the mechanisms of sensor response to different stimuli: In three separate studies we elucidate the origins of the sensor response related to the reference electrode, to biomolecule adsorption, and to changes in electrolyte properties. Then we consider the signal-to-noise ratio for biosensing. We study the noise mechanism and demonstrate ways to optimize sensing. In the last part of this thesis we describe our exploratory studies of carbon nanotubes as probes to study single cells.
The outline of this thesis is as follows.
Chapter 2 demonstrates that individual carbon nanotubes, both metallic and semiconducting, can be used as nanoelectrodes for electrochemistry. Due to the small diameter of nanotubes, the relative influx of electrochemically active molecules is so high that the kinetics of charge transfer become rate limiting.
Chapter 3 provides a theoretical description of electrochemical charge transfer at nanotube electrodes. We find that, although the distinct electronic structure of nanotubes does play a role in the charge transfer process, metallic and semiconducting nanotubes cannot readily be distinguished. Even when a semiconducting nanotube is switched ‘off’, charge transfer can still take place at high rates.
Chapter 4 introduces biosensing with carbon nanotube transistors. We show that the sensor response can be affected by an artifact related to the reference electrode. By eliminating this artifact we can study the effect of biomolecule adsorption near nanotube sensors unambiguously.
Chapter 5 describes a method to identify the different mechanisms that can lead to a sensor response. We find that the origin of sensor response to biomolecule adsorption is a combination of a change in surface potential, and alterations to the tunnel barrier at the nanotube-metal contact. Contact effects make sensing unreliable, but they can be suppressed by covering up the contact regions.
Chapter 6 shows that carbon nanotube and graphene transistors are sensitive to changes in the ionic strength, the pH, and even the type of ions of the electrolyte. Changes in these electrolyte properties lead to a sensor response by changing the surface charge and the spatial distribution of ions, and thus the surface potential.
Chapter 7 studies the mechanism responsible for low-frequency noise in liquid-gated carbon nanotube transistors. We show that the noise is consistent with the fluctuation of nearby charges that gate the nanotube through a field-effect. The power of the noise is inversely proportional to the length of the nanotube.
Chapter 8 presents a study of the signal-to-noise ratio for biosensing with nanotube transistors. We find that, surprisingly, the signal-to-noise ratio is highest in the sub-threshold regime. The decrease of the signal-to-noise ratio in ‘on’ state is due to additional noise
1.6 References 23
sources and depends on device architecture. In specific cases the back gate can enhance the signal-to-noise ratio.
Chapter 9 reports our exploratory studies of carbon nanotube sensors as probes to study living cells. Although our results are suggestive that we can successfully detect cellular activity, the transistor stability and electrochemical sensitivity need to be improved. We show that the electrochemical sensitivity can be improved by coating nanotubes with catalytic nanoparticles.
1.6 References
1 Dekker, C. Physics Today 1999, 52, (5), 22-28. 2 Kroto, H. W. et al. Nature 1985, 318, 162. 3 Iijima, S. Nature 1991, 354, 56.
4 Iijima, S. et al. Nature 1993, 363, 603. 5 Bethune, D. S. et al. Nature 1993, 363, 605. 6 Thess, A. et al. Science 1996, 273, 483. 7 Reibold, M. et al. Nature 2006, 444, 286.
8 Gerhardt, Ph. et al. Chem. Phys. Lett. 1987, 137, 306. 9 Duan, H. M. et al. J. Phys. Chem. 1994, 98, 12815. 10 Kong, J. et al. Nature, 1998, 395, 878.
11 Zheng, L. X. et al. Nature Materials 2004, 3, 673. 12 Collins, P. G. et al. Science 2001, 292, 706. 13 Zhang, G. et al. Science 2006, 314, 974. 14 Hou, P.-X. et al. Carbon 2008, 46, 2003-2025. 15 Zheng, M. et al. Science 2003, 302, 1545.
16 Smalley, R. E. et al. J. Am. Chem. Soc. 2006, 128 (49), 15824-15829. 17 Treacy, M. M. J. et al. Nature 1996, 381, 678-680.
18 Wong, E. W. et al. Science 1997, 277, 1971.
19 Peng, B. et al. Nature Nanotechnology 2008, 3, 626.
20 Thostenson, E. T. et al. Composites Science and Technology 2001, 61, 1899-1912. 21 Qu, L. et al. Science 2008, 322, 238.
22 Dai, H. et al Nature 1996, 384, 147. 23 Cumings, J. et al Science 2000, 289, 602. 24 Fennimore, A. M. Nature 2003, 424, 404. 25 Chen, J. et al Science 1998, 282, 95.
26 Williams, K. A. et al. Nature 2002, 420, 761.
27 Chen, R. J. et al. J. Am. Chem. Soc. 2001, 123, 3838. 28 Kam, N. W. S. et al. Proc. Nat. Ac. Sci. 2005, 102, 11600. 29 Bianco, A. et al. ChemComm 2005, 5, 571.
30 Misewich, J. A. et al. Science 2003, 300, 783. 31 Zhang, M. et al. Science 2005, 309, 1215. 32 Chen, C. et al. Small 2008, 4, 1313-1318. 33 Heller, D. A. et al. Science 2006, 311, 508. 34 Tans, S. J. et al. Nature 1998, 393, 49-52.
35 Postma, H. W. C. et al. Science 2001, 293, 76-79.
36 Novoselov, K. S. et al. Proc. Nat. Ac. Sci. 2005, 102, 10451. 37 Geim, A. K. et al Nature Materials 2007, 6, 183.
38 Novoselov, K. S. et al. Science 2007, 315, 1379. 39 Novoselov, K. S. et al. Nature 2005, 438, 197. 40 Schedin, F. et al. Nature Materials 2007, 6, 652. 41 Kong, J. et al. Science 2000, 287, 622-625. 42 Rosenblatt, S. et al. Nano Lett. 2002, 2, 869.
43 Chen, R. J. et al. Proc. Nat. Ac. Sci. 2003, 100, 4984-4989. 44 Besteman, K. et al. Nano Lett. 2003, 3, 727.
45 Männik, J. et al. Phys. Rev. Lett. 2006, 97, 016601. 46 Cui, Y. et al. Science 2001, 293, 1289.
Chapter 2
Individual single-walled carbon nanotubes as
nanoelectrodes for electrochemistry
We demonstrate the use of individual single-walled carbon nanotubes (SWNTs) as nanoelectrodes for electrochemistry. SWNTs were contacted by nanolithography and cyclic voltammetry was performed in aqueous solutions. Interestingly, metallic and semiconducting SWNTs yielded similar steady-state voltammetric curves. We clarify this behavior through a model that considers the electronic structure of the SWNTs. Interfacial electron transfer to the SWNTs is observed to be very fast, but can nonetheless be resolved due to the nanometer critical dimension of SWNTs. These studies demonstrate the potential of using a SWNT as a model carbon nanoelectrode for electrochemistry.*
* This chapter has been published as I. Heller, J. Kong, H. A. Heering, K. Williams, S. G. Lemay, and C. Dekker,
2.1 Introduction
Electrodes with nanometer dimensions provide exciting new tools for electrochemical studies. The small dimensions lead to a high current density at the electrode surface, allowing the study of fast heterogeneous electron transfer kinetics, molecular interactions, and mass transport in the nanometer regime. In addition, exploiting the small dimensions of nanoelectrodes may allow innovative biological applications by means of probing local cellular environments and ultimately measuring the activity of a single redox-enzyme coupled to a nanoelectrode. Several techniques have been developed for the fabrication of nanoscale electrodes for electrochemistry.1-5 However, no nanoelectrode fabrication technique has yet been developed where the electrode geometry is known at the nanometer level, which poses a limitation to the interpretation of electrochemical data.6
Here we explore the use of individual single-walled carbon nanotubes (SWNTs) as electrodes for electrochemistry. The unique structural and electronic properties7,8 of a SWNT
render it an ideal candidate to function as a model carbon nanoelectrode for electrochemistry. SWNTs have a very well defined cylindrical geometry and are readily synthesized9 with a
diameter in the nanometer range. Moreover, advances on the functionalization of SWNTs8,10,11 open the route towards electrochemical single-biomolecule studies using
individual SWNT electrodes.12
Large ensembles of carbon nanotubes have been used as electrode material for electrochemical experiments, which allowed exploring their high chemical stability and good conductive properties.8 Although electrochemistry with an individual 150 nm diameter
multi-walled carbon nanotube (MWNT) has been reported,13 the unique structural properties of an
individual SWNT as an electrode with a nanometer critical dimension have to our knowledge not been explored thus far.
We report the first study of electrochemistry using individual SWNT electrodes. We observe a steady-state electrochemical current that is proportional to the exposed length of the SWNT. Interestingly, both metallic and semiconducting SWNTs yield similar behavior. We demonstrate that this can be understood from a model that incorporates the electronic structure of the electrode into the estimation of heterogeneous electron transfer kinetics. The experimental curves can be described by classic Butler-Volmer kinetics, and show that the SWNT sidewall allows for high electron transfer rates.
2.2 Materials and methods
Figure 2.1a shows the device schematic consisting of a SWNT on a substrate contacted by leads that are covered by an insulating layer. SWNTs are grown through chemical vapor deposition9 on a substrate consisting of a degenerately doped silicon wafer with a 500 nm
2.3 Results 27
thermally grown oxide layer. The sample is coated with a 20 nm electron-beam evaporated SiOx layer.14 After consequent resist patterning by electron-beam lithography, the SiOx layer
is briefly etched in a highly diluted buffered HF solution to expose the SWNTs. We contact the SWNTs by 40 nm thick titanium leads. A 500 nm poly(methyl methacrylate) (PMMA) layer is coated on the entire surface, which serves as an insulating layer to prevent electrochemical reactions taking place at the leads. In addition, the titanium has a natural oxide that further suppresses any leakage current. Micrometer-sized rectangular pits are patterned in the PMMA to partially expose the contacted SWNTs. The pits are created at a distance of at least several hundreds of nanometers away from the leads. Figure 2.1b shows an AFM amplitude image in which an exposed section of SWNT is visible crossing the bottom of the pit in the PMMA insulation. The titanium leads are not visible under the PMMA. Whether each individual SWNT is semiconducting or metallic is determined through electrical transport measurements in air using the silicon wafer as a back gate prior to electrochemical measurements.15
The devices were exposed to aqueous solutions containing reduced ferrocenylmethyl-trimethylammonium (FcTMA+), with counterion hexafluorophosphate (PF
6-).5 FcTMA+ was
chosen for its uncomplicated electrochemistry and its good chemical stability in an aerobic aqueous environment. No supporting electrolyte was used. To minimize evaporation the solution was contained by a poly(dimethylsiloxane) (PDMS) cell pressed against the sample and sealed using a commercial Ag/AgCl 3M NaCl reference electrode (model MF-2078, BAS). Sampled-current voltammetry was performed in a low-current measurement setup as depicted in Fig. 2.1c using the SWNT as the working electrode. An electrometer (Keithley 6430) was used to cycle the potential applied to the SWNT between 0.2 and 0.6 V with respect to the grounded Ag/AgCl reference electrode. Typically, the current is sampled over 0.2 seconds after a delay of 0.1 seconds per 10 mV step.
2.3 Results
We observed a steady-state electrochemical current through the SWNT devices. In Fig. 2.1d, we show the cyclic voltammograms acquired from two metallic SWNT devices of different exposed length, and a control device on the same wafer. At high potential, an anodic current was observed that corresponds to the oxidation of FcTMA+. The magnitude of the
steady-state electrochemical current is of the order of several picoamperes and scales with the length of the exposed section of SWNT. The black curve in Fig. 2.1d is a measurement for a control pit that lacks a SWNT on the same sample. This control pit was created near titanium leads similar to the SWNT devices and displayed no electrochemical wave due to the absence of a SWNT. These measurements show that the electrochemical current can be attributed to the oxidation of FcTMA+ at the SWNT sidewall, and the titanium leads are sufficiently
Figure 2.1: (a) Device schematic. SWNTs are grown on Si wafers with 500 nm thermal SiO2, and contacted by Ti
leads. A layer of SiOx and PMMA is used as insulating layer, in which windows are opened to selectively expose
the SWNT. (b) AFM-amplitude image of an exposed section of a SWNT crossing the bottom of the pit through the PMMA and SiOx layers. (c) Low current measurement setup. The SWNT is exposed to a solution containing a
redox-active species. To avoid evaporation during measurements, the solution is contained by a PDMS cell. A potential is applied to the SWNT versus a standard Ag/AgCl 3M NaCl electrode. (d) Sampled current voltammograms measured from two metallic SWNT devices (1 µm and 2 µm exposed) and a control device exposed to an aqueous 1.2 mM FcTMA+ solution. The control device consists of a pit located near the leads but
without a SWNT. Three full forward and backward scans are plotted for each device. The good overlap shows that the voltammograms are well reproducible.
Figure 2.2: Sampled-current voltammograms (three averaged forward scans) of the oxidation of 1.2 mM FcTMA+
at (a) three metallic and (b) three semiconducting SWNT devices. The blue curves are devices from one wafer and the red and green curves are the devices on another wafer. The data was collected in absence of supporting electrolyte. The exposed lengths of SWNT for the metallic devices were, from top to bottom 1 µm, 2 µm, and 0.6 µm, and for the semiconducting devices 0.75 µm, 1.75 µm, and 0.8 µm. (c) The electrochemical current at 0.6 V vs. Ag/AgCl exhibits a linear dependence on the exposed length of SWNT within one wafer. The closed circles indicate devices where the SWNT crosses the entire bottom of the pit and open circles indicate devices where the pit was created over the end of a SWNT and thus the SWNT does not span the entire bottom of the pit, resulting in more effective mass transport and a consequently higher current density.
2.3 Results 29
The voltammetric curves obtained from the SWNT devices deviate from the classic nernstian curve-shape controlled by thermodynamics and mass transport. Within the scanned potential window we do not observe a diffusion-limited plateau and the voltammetric waves appear stretched. We attribute this to the heterogeneous electrode kinetics that control the rate of the electrode reaction. Due to the small critical dimension of the SWNT, mass transport is highly effective, and the rate of mass transport may become comparable to or larger than the rate of electron transfer. In this case there will be a deviation from thermodynamic equilibrium between oxidized and reduced species at the electrode surface and the voltammetric curve will depart from the nernstian limit.
In total we fabricated four wafers with multiple devices per wafer. The devices on one wafer are processed simultaneously. We measured 43 devices of which 11 devices gave no or poor waves, which may be attributed to the breakdown or contamination of devices. The remaining 32 devices yielded a range of voltammetric behavior similar to the curves displayed in Fig. 2.2a and b. Although the deviation from nernstian voltammetry varies between the curves, the shape is relatively consistent for simultaneously processed devices, suggesting that the observed variations are related to sample preparation. We tentatively attribute this to contamination of the SWNT surface, which can effectively slow down the rate of electron transfer, changing the classic nernstian appearance of the steady-state current-potential characteristics.
We used both metallic and semiconducting SWNT devices for electrochemistry, as shown in Fig. 2.2a and b respectively. Interestingly, no significant difference in electrochemical properties was found. In Fig. 2.2c we plot the electrochemical current at 0.6 V against the exposed length of SWNT for all devices of the wafer for which the voltammograms displayed the smallest departure from nernstian voltammetry, i.e. the devices that are considered to be the least or not contaminated. A linear fit through the origin is shown yielding I(0.6V) = 22 ± 1 pA/µm. Devices on other, presumably more contaminated wafers display a smaller current per µm of exposed SWNT. The reduced current combined with the departure from the nernstian voltammetric curve-shape is consistent with a kinetic limitation on the reaction rate.
The enhanced mass transport rate at a nanoelectrode allows the kinetics of electrode reactions to be accessed through voltammetry. Using the classic Butler-Volmer model of electrode kinetics, the oxidative current iBV for a one-step, one-electron process can be written as16 0 ' 0 ' ( ) / 1 (1 )( ) / 0
1
mt BV F U U RT F U U RTi
i
e
− −K
−e
− −α −=
+
+
. (2.1)Here imt is the mass-transport limited current, F is the Faraday constant, R is the molar gas constant, T is absolute temperature, U is the applied potential, U0’ is the formal potential of the
redox-couple, α is the transfer coefficient, and K0 is the dimensionless heterogeneous rate constant,16 K
0 = FACk0/imt, where A is the electrode surface area, C the bulk concentration of the reduced species, and k0 the standard heterogeneous rate constant. Fig. 2.3 shows a fit of Eq. (2.1) to the experimental data using k0, α, and i
mt as fitting parameters. U0’, A, and C are fixed, where U0’ = 0.42 V, C = 1.2 mM, and A was calculated as πrL, where the radius r of the SWNT was determined from AFM. Eq. (2.1) appears to provide an excellent description of the experimental curve shape. The fit of Fig. 2.3 yields k0 = 7.62 ± 0.03 cm/s, α = 0.670 ± 0.002 and imt = 48.4 ± 0.1 pA.
Figure 2.3: Fit of the classic Butler-Volmer kinetics of Eq. (2.1) to the experimental voltammogram of a 2 µm
long metallic SWNT with a 1.8 nm diameter, using U0’ = 0.42 mV and C = 1.2 mM.
We fitted Eq. (2.1) for all devices of Fig. 2.2c yielding an average α = 0.65 ± 0.07 and
k0 = 4 ± 2 cm/s. We performed a linear regression of the fitted mass-transport-limited currents
versus the exposed lengths, yielding imt = 24 ± 2 pA/µm. The high k0 value, comparable to common metallic electrodes, indicates that the SWNT sidewall allows very fast electron transfer. Indeed, the values are in very good agreement with values measured by Watkins and co-workers, who found α = 0.6 ± 0.2 and k0 = 5 ± 3 cm/s for the oxidation of FcTMA+ at
platinum nanoelectrodes.6 Further research is needed to determine to what extent this high
electron transfer rate is intrinsic to the sidewall of the SWNT or should be attributed to surface defects along the SWNT sidewall.
Two further remarks can be made with respect to the curve fitting of Fig. 2.3. First, no contamination of the SWNT surface was taken into account. As a result of a potential extra tunneling barrier and reduced electro-active area on the SWNT, the result for the heterogeneous rate constant may be underestimated. Secondly the data were acquired in the absence of supporting electrolyte. Although caution should be taken to interpret voltammetric curves acquired in absence of supporting electrolyte, preliminary measurements in the
2.4 Modeling 31
presence of a supporting electrolyte (0.1 M KCl) show the same current-potential curve shape, indicating that the electrical double-layer has little effect on voltammetry at the SWNT electrode. Indeed, due to the high aspect ratio, the depletion layer around the SWNT is about two orders of magnitude larger than the electrical double-layer, which is expected to minimize the influence of the electrical double-layer on molecular transport.
Figure 2.4: Numerical simulation of the diffusion-limited current and voltammetric behavior. (a) A SWNT
crossing the bottom of the pit in the PMMA. (b) Cross-section of the three-dimensional steady-state concentration profile perpendicular to the SWNT axis with contour-lines calculated by a finite-element method. Inset: three-dimensional view of the calculated concentration profile cross-sectioned both perpendicular to the SWNT and through the SWNT axis. Blue and red indicate the reactant concentrations at the SWNT surface and the bulk respectively, the arrow indicates the position of the SWNT. (c) Calculated steady-state diffusion-limited current for a 1 nm radius SWNT as a function of the exposed length for different pit widths W. H = 0.5 µm. (d) Calculated electrochemical current as a function of overpotential (U – U0’) for a SWNT electrode of 1 nm radius in a pit with
dimensions L = 1 µm, W = 1.5 µm, and H = 0.5 µm, using k0 = 4 cm/s and α = 0.65 (solid blue line). The dashed
line indicates the nernstian limit, K0 → ∞.
2.4 Modeling
2.4.1 Mass transport
We estimated the steady-state diffusion-limited current using a finite element package (Femlab3.0a, COMSOL AB) to solve the three-dimensional diffusion equation for a SWNT device with the geometry as defined in Fig. 2.4a. The resulting steady-state concentration profile in Fig. 2.4b shows a gradual transition from cylindrical diffusion near the SWNT to spherical diffusion towards the bulk. Due to the spherical diffusion field the SWNT device behaves like a common microelectrode, giving a steady-state current despite its cylindrical electrode shape.
