Graphitic Surface Attachment by Single-Stranded DNA and Metal Nanoparticles
Table of Contents
1.2 History of sp 2 carbon
1.3 Electronic theory of graphene
1.4 Graphene transistors
1.5 DNA - decorated graphitic surfaces and gas sensing
2: Summary of Results
2.1 Single - stranded DNA on graphitic surfaces
2.1.1 TEM of ssDNA on carbon nanotubes
2.1.2 X - ray reflectivity of ssDNA on graphite
2.2 Metal nanoparticles on few - layered graphene flakes
3: Experimental Methods
3.1 TEM of ssDNA on carbon nanotubes
3.1.2 Reactive Ion Etching
3.1.3 Potassium Hydroxide wet etch
3.1.4 Window creation
3.1.5 Nanotube growth
3.1.6 ssDNA application
3.1.7 Transmission Electron Microscopy
3.2 X - ray reflection of ssDNA on graphite
3.2.1 Graphite block preparation
3.2.2 ssDNA appli cation
3.2.3 Sample mounting
3.2.4 X - ray reflectivity experiment
3.3 Metal nanoparticles on few - layer graphene
3.3.2 Mechanical exfoliation
3.3.3 First anneal
3.3.4 Optical identification
3.3.5 Thickness determination
3.3.6 Metal evaporation
3.3.7 Second anneal
3.3.8 Particle height measurement
3.3.9 Particle imaging
4: Methods of Data Analysis
4.1 Interpretation of X - Ray reflectivity data
4.1.1 Extraction of interference data
4.1.2 Interpretation of interference data
4.2 Diameter determination of metal nanoparticles
4.3 Determination of filament width
5: TEM Measurement of ssDNA on Carbon Nanotubes
5.1 Carbon nanotubes in Transmission Electron M icroscope
5.2 Single - stranded DNA distribution across single - walled carbon nanotubes
5.3 Conformation of individual ssDNA strands to carbon nanotubes
5.4 Comparison to simulation
6: X - ray Reflectivity of ssDNA on Graphite
7 : Observation of Metal Nanoparticles on Graphene
7.1.1 Unannealed gold
8: Theories of Nanoparticle Growth and Deformation
8.1 Ostwald Ripening
8.2 Common elements of the modified theories
8.3 Theory of circular nanoparticles
8.4 Theory of irregular nanoparticles
8.4.1 Mathematical description of nanoparticle shape
8.4.2 The line tension energy
8.4.3 The dipole energy
8.4.4 Island shape
8.5 Comparison between circular and deformed particles
9: Conclusions and Future Directions
9.2 Future directions of inquiry
Appendix 1: Experimental Details
A1.1 Chip cleaning
A1.2 Carbon nanotube growth
A1.3 KOH etching
A1.4 AFM image optimization, recovery, and processing
A1.4.1: Image optimization
A1.4.2: Contingencies that can arise during imaging
A1.4.3: Image processing
Appendix 2: Calculation of Dipole Energy
List of Figures
B ernal stacking
– Carbon nanotube’s relation to graphene
– t he approximate band structure of graphene
– r elationship between wrapping vector and brilloin zone cuts
3.1 – lithography overview
3.2 – Silicon Nitride membrane schematic
3.3 – CVD oven schematic
3.4 – gas flow retarder effects
3.5 – Transmission Electron Microscope (TEM) beam path schematic
3.6 – contrast enhancement from slight defocusing
3.7 – X - ray reflectivity system schematic
graphene exfoliation demonstration
optical identification of graphene
3.10 – Atomic Force Microscope (AFM) schematic
AFM height, amplitude, and phase images
Scanning Electron Microscope (SEM) beam path schematic
3.13 – SEM images taken by in - chamber detector and through - lens d etector
4.1 – X - ray reflectivity data
fully normalized and marked up X - ray reflectivity data
ray diagram for interference between reflections from two planes
illustration of process of extraction of particle radii from SEM images
5.1 – th e first TEM image of a carbon nanotube
TEM image of a typical carbon nanotube network
showing relative cleanliness of single and bundled nanotubes
TEM image of a carbon nanotube network with single - stranded DNA applied
TEM image of a carbon nanotube with uneven ssDNA coverage
TEM image of a tube junction
TEM image of a chain of ssDNA on a nanotube
TEM image of ssDNA wrapping around a pair of tubes
TEM images of a ssDNA - decorated tube, from differ ent angles
the free energy landscape of ssDNA on carbon nanotubes
6.1 – X - ray reflectivity measurements of graphite and ssDNA - applied graphite
6.2 – figure 4.2, repeated
7.1 – work function and melting surface tension of selected metals
SEM i mage of gold nanoparticles on 2, 3, and 13 layer graphene
7.3 – SEM imges of gold nanoparticles on 1, 2, and 3 layer graphene
7.4 – SEM image of gold nanoparticles on bulk graphite
7.5 – SEM image of anomalous faceted gold particles on single - layer graphene
7.6 – AFM image of nanoparticles used for height determination
7.7 – plot of nanoparticle height vs diameter
histograms of gold particle radius ,
by graphene thickness, curvefit to gaussians
gold particle radius distribution center vers us layer count, fit to a power law
7.10 – SEM image of unannealed gold
7.11 – SEM image of silver nanoparticles on various graphene layers; AFM inset
7.12 – histograms of silver particle radii, showing lack of layer count dependence
7.13 – SEM image of lar ger silver particles
7.14 – radius histograms of regions showing unconstrained silver particle growth
7.15 – SEM image of titanium nanoparticles on 4 layer graphene
7.16 – SEM image of titanium nanoclusters on 7 layer graphene
7.17 – SEM image of titanium nanoparticles on 2 layer graphene, with dark halos
7.18 – plot of titanium particle radius distribution center versus layer count
7.19 – SEM image of palladium nanoparticles
7.20 – SEM image of nanoparticles from 0.12 nm ytterbium on 1 layer of graphene
7. 21 – SEM image of nanoparticles from 0.12 nm ytterbium on 3 layer graphene
7.22 – SEM images of networks from 0.5 nm ytterbium, on 2 and 4 layer graphene
7.23 – width histogram for ytterbium filaments
7.24 – SEM data showing ytterbium filament thickness
8. 1 – the chemical potential of a circular nanoparticle, as a function of radius
8.2 – illustration of m = 2 and m = 3 Fourier modes
9.1 – ytterbium filaments and dense networks
The carbon forms Graphene and Carbon Nanotubes have occupied a large fraction of the attention of the condensed matter community since their discoveries. They possess exceptional tensile strength [26,99] and electronic mobility  , among other exceptional properties. These all have great promise for technological applications, and the high scattering length has permitted a stonishing pure science results such as the observation of the Quantum Hall Effect at room temperature  .
Electronic - readout chemical sensing is one of the technological applications for which single - walled carbon nanotubes and graphene are well suited, for a variety of reasons that will be explored in section 1 .5. The Johnson group has developed a variety of gas and fluid sensors based on these materials, with the sensitizing agents being single - stranded DNA (ssDNA) [42,47,48,60,89] , RNA, antibodies to specific antigens  , or human olfactory proteins  . The mechanisms for the sensing based on ssDNA and RNA is unknown and presumably complex. One of the focuses of this work is to investigate the form of systems closely analo gous to such sensors.
Graphene film thickness determines its properties in ways that do not simply follow from scaling of intensive properties. One such property, which forms the second focus of this work, is the formation of metal nanoparticles on the sur face. We show this dependence and give a theory accounting for it.
1.2 History of sp 2 carbon
Graphene, the conceptual component material of graphite and parent material of carbon nanotubes, is a two - dimensional crystal with a hexagonal latti ce and a two ca rbon atom basis; all bonds are sp 2 . Graphene was long used by theorists as a model system for derivations of properties of these structures and as a subject in its own right  , even when its existence on is own was believed to be physically impossible. This belief in the impossibility of graphene was d ue to the seminal 1937 paper by Lev Landau  , the first part of which gave the theory of second or der phase transitions, and the second part of which declared the impossibility of free - standing two dimensional structures in three dimensional space. This paper was correct; the following deduction that graphene cannot exist was flawed. Even setting aside the issue that the paper clearly doesn’t exclude the case of a thin film on a backing, which is how graphene is usually arranged in the laboratory, there is a more core issue. While graphene is most simply described as two dimensional, it remains graphene even if slightly deformed. The fluctuations required by Landau’s theory do not destroy graphene, nor force it to immediately roll up into a spiral graphite structure or fold into graphite, nor even eliminate its essentially two dimensional character. Whil e folding and rolling are ultimately the stable states, wrinkles provide sufficient metastability that graphene can exist in uncondensed states for extended timescales.
Graphite is composed of a stack of graphene sheets. When graphene stacks, there are two relevant stackings: Bernal stacking, as in graphite; and turbostratic, which is to say,
misaligned with the effect that they do not stack as closely. Few - layered graphene flakes are frequently turbostratic when they are formed by folding or misaligned gro wth  . Bernal stacking is an alternating A - B stacking. Adjacent layers are ‘ ! - ! ’ stacked, as the !
electrons are th ose makin g contact. This stacking can be visualized as one layer being a copy of the next, rotated 180° around one of the atoms. Thus, half of the atoms are directly above atoms in the next plane; the other half are lined up with the centers of the hexagons of both neighboring sheets  . Th e Bernal stacking thus maximizes the difference between the two basis atoms by letting one be in contact on both sides while letting the other be free on both sides.
Figure 1: a top - down view of the bond network of a section of two layers of graphite. T he bonds in the A layer are in black , the others are in B layer . The atom in the center and the atoms on the center of each side are directly stacked; the atoms at the 3 - way intersections are not.
Buckminsterfullerenes (or more briefly, ‘buckyballs’ or ‘f ullerenes’) were discovered in 1985 by Harry Kroto and the Smalley group at Rice University  and are the least related to graphene of these three. They are carbon cages, closed by the inclusion of pentagons . The most stable fullerene, and the first noticed  , has a ‘socce r ball’ shape: C 60 . Other shapes are less prominent, but have been catalogued  . For example, one
form of C 80 has two pentagon - containing caps, and a roll of hexagons is laid between.
A particular class of fullerene takes this concept to extremes: carbon nanotubes. They were likely created for some time as a byproduct of carbon fiber production, then certainly created during fullerene production, and finally entered scientific awareness in 1991 with a paper by Ijima  . Within two years, reliable processes for production of single - walled tubes were available [9,40] , and shor tly thereafter could be grown in bulk  . Carbon nanotubes wer e found to have the highest tensile strength known [26,99] , to grant their electrical charge carriers extraordinarily high mobility [26,27,99] , to be sensitive to very small changes in their environment  , and be extraordinarily black when grown as a ‘forest’  . All but the last of these properties were later discovered to also apply t o graphene, which exceeded carbon nanotubes in the first two categories.
Carbon nanotubes can be described nearly completely by a ‘wrapping vector’, which can be most easily understood by modeling the tube as rolled - up graphene. The wrapping vector is the smallest vector connecting two points on the graphene plane that map onto the same point of the nanotube. In Figure 2, the wrapping vector extends along the short side of the cut - out rectangle.
Figure 2: a cartoon of a carbon nanotube rolled up out of gr aphene. Image courtesy of Bob Johnson.
Graphene itself had been observed in peculiar and difficult - to - reproduce circumstances (reviewed in The Rise of Graphene  ), but it was in 2004 that André Geim and Konstantin Novosëlov devised a method for isolating it and made a good start on e xperimentally determining its properties [71,72] . Known affectionately and derisively (often at the same time) as the ‘scotch tape method’, this easy technique quickly opened graphene itself up to investigation by a large number of groups.
Graphene was soon found to have many of the same exceptional properties as carbon nanotubes, with graphene slightly edging out ca rbon nanotubes in most respects such as tensile strength  and carrier mobility  , and making claim to entirely new extremes such as the maximum elastic strain in a crystal.
A recent effort has been to develop methods for growing graphene over large areas rather than exfoliating it into tiny fragments. The older met hod, still with an element of promise, is to evaporate silicon out of a silicon carbide surface, producing epitaxial graphene  . More recently, catalyzed chemical vapor deposition has emerged [4,49,56,62,83] . In this family of processes, carbon feedstock is flowed over a metal film at 1000 K and dissolves into the surface layers of the metal. As the film cools, carbon falls out of suspension and forms graphene. The metal ca n be dissolved away, and the graphene transferred to any desired substrate.
1.3 Electronic theory of g raphene
The bonds between the carbon atoms in graphene are hybridized as sp 2 , leaving the p z
orbital only weakly hybridized. This orbital protrudes out of the plane in both directions. The sp 2 hybridization forms " bonds, which are sufficiently strong that the participating electrons’ contributions to the electronic structure of graphene are buried deep in the valence bands. The remaining p electrons are substantially freer to move, so the p z
o rbitals combine into less local ! orbitals. As the unit cell of graphene contains two atoms, there are two ! electrons per cell.
The band structure of graphene is usually calculated with a simple tight binding model taking into account the crystal symmetri es and nearest neighbor interactions, but not wave function overlap  .
This approximation yields the relatively compact expression
Figure 3: Three views of the approximate band structure of graphene , not cutting off at the edge of the Brillouin zone . A (l eft ) : A top - down (or bottom - up) view; the Brillouin zone boundary stretches directly between the small dark dots (red online) , while the origin is on the central peak. B (c enter ) : A side view –
the dark dots in A are the sharp meeting points here . C (r ight ) : a close - up of one of the K - points.
This simple tight binding approximation is very good around the K - points, where the bands meet. Away from them, and in particular around the # (origin) and M (directly between two adjacent K - points) points, this approximation is not so good . A ccounting for the direct overlap between the p z states improves the approximation drastically for these ranges of momentum  .
Each carbon atom contributes one p z electron, and there are two atoms per unit cell. Two electrons per unit cell are enough to fill one band with spin up and spin down states. Thus, the valence and conduction bands mee t at the K - points. This is where the tight binding approximation is good, so the electronic structure as pertains to conduction is indeed well - described by this tight binding model. The most pertinent observation is that the band structure can be closely a pproximated as two double cones. This can be most clearly seen by shifting the Brillouin zo ne to be centered on an M - point.
Having a conical band structure has several consequences. First, all of the charge carriers, regardless of momentum, have the same s peed, around 0.3 % of c. This makes electron dynamics in graphene a highly unusual two - dimensional system of effectively massless charged fermions. Their behavior is best modeled using the Dirac equation. This in itself has many consequences, such as Klein tunnelling  .
The most pertinent of these effects is an unusual for m for electrical field screening. Because the energy of carriers varies linearly around the K - points, the density of states is only
This limits the charge concentration in a different way than in a massive carrier system, in which a large number of carr iers become available at modest energies in excess of a band minimum. Rather than decaying exponentially, a voltage applied at one surface decays as the inverse square of the number of layers [24,77,84] .
The Fermi velocity of the carriers is also important. Though this speed is not extraordinary for a metal, it is extraordinary for a semiconductor near charge neutrality. This contributes to one half of its most outstanding feature: its extremely large electron mobil ity.
D ( E ) = 2 E π ( V F ) 2
The other material factor in mobility is the scattering length, L. Graphene has an extremely long scattering length – in the best cases, the scattering length of 1.2 $ m arose solely from the edges of the graphene and the electrical contacts  . This long scattering length arises from graphene’s having little of two of the three principal sources of scattering: cry stal defects, phonons, and external scatterers.
First, graphene frequently occurs with high crystal perfection. This is due in part to the strong in - plane bonds but also to the material’s two - dimensional nature. Even holding the fraction of misplaced atoms constant, laying them out flat will give a larger distance between defects than arraying them in three dimensions.
Second, electron - phonon scattering is extremely weak. In contrast to 2 - dimensional electron gases, which also have very high mobility at low temperatures, the temperature dependence of graphene - phonon scattering is only linear  . At low temperatures, GaAs 2 dimensional electron gases have much larger electron mobility than in graphene, but the phonon scatterin g rises exponentially; with its linear dependence, graphene tolerates temperature much better . Above 200 K, substrate phonons become a significant contributor to the phonon scattering on Silicon Oxide substrates. 
The t hird form of scattering is from external defects. This consists of charges in the substrate (if there is a substrate), and debris under and on top of the graphene. For graphene this is usually the strongest form of scattering, especially under commonly enc ountered circumstances. That is, electronic circuits involving graphene are usually backed by silicon oxide, which has an abundance of charge traps acting as scattering sites. Scum from lithography, and even adsorbed water, will aggravate this unless it is
specially removed. 
The best effo rts to maximize graphene’s mobility required etching away the substrate, leaving graphene suspended, and baking it clean; this resulted in a mobility of 2 • 10 5
cm 2 /Vs, which is the highest recorded room - temperature electron mobility in any material  . Even removing only the lithographic scum results in a substantial improvement in room temperature mobility, rising for instance from 1600 to 5500 cm 2 /Vs  . This mobility is already well in excess of the mobility of Silicon, around 750 cm 2 /Vs. Short of removing the substrate altogether, the scattering from charge traps and substrate phonons can be red uced by selection of a new substrate; this is an ongoing search [25,38] .
Intriguingly, if graphene is layered turbostratically, it typically displays electronic behavior most similar to a single layer, with its mass less behavior intact though modified. This can be understood through perturbation theory – the two sets of single - sheet K - points are misaligned, and so the mixing of their states with the states from the other sheet will face a large energy difference , inh ibiting hybridization
[59,65] . This is in contrast to A - B graphite, in which dispersion is quadratic, yielding an effective mass for low energies  . For moderate energies, even A - B - stacked few layer graphene has effectively massless carriers .
1.4 Graphene t ransistors
We have compared graphene to silicon above because it has the potential to be an excellent switchin g material for electronics. Its large mobility makes it a good material µ = ( q e n ρ ) − 1 = V F L q e E F
for analog amplifiers; however, for digital electronics, the ability to turn off nearly completely is vital. Bulk graphene is semimetallic lacking a gap. The reduction in the density o f states around the k - point has produced an on - off ratio as high as 30, though this is exceptional  .
However, higher on - off ratios are possible in graphitic structures: long before this was an issue for graphene itself, carbon nanotubes had already achieved on - off ratios of 10 5 , with 1000 being common. Modeling a carbon nanotube with graphene this requires imposing a periodic boundary condition for separations equal to the wrapping vector; thus restricting the possible states. 1/3 of the wrapping vectors are lined up so as to include the K points as valid wavevectors. The other 2/3 of wrapping vectors exclude the K points; such tubes thus have a gap, and are semiconducting.
Figure 4: the correspondence between a real - space lattice (lef t) and a K - space Brillouin zone. This (7,0) zigzag tube is semiconducting because the valid k - states (dotted lines) do not intersect the K - points.
Carbon nanotubes with on/off ratios in excess of 10 5 have been found  . A similar effect can be produced in flat graphene through a boundary effect. By constricting the lateral extent of the graphene, the l ateral momentum is similarly quantized, permitting the development of FET with high on/off ratio [5,41,55,61] . A difficulty arises from the extreme narrowness of the constriction required to make a transistor that c an turn off strongly: 10 nm is a rough maximum on this width. Standard lithographic techniques cannot produce such dimensions. The papers referenced earlier each used a different method for achieving such narrow strips; each method has distinct strengths a nd weaknesses.
For electronics applications, graphene is far more promising than carbon nanotubes, for several reasons. Principally, it is difficult to scale up production of carbon nanotube devices. 1/3 of carbon nanotubes are metallic, and separation tec hniques rely on solvation. This dirties the tubes, requiring further processing to re - clean them. An additional difficulty arises as the tubes must be deposited on the surface in precisely selected locations. In contrast, graphene can in principle be laid down as a single continuous layer, then the undesired parts etched away. Secondly, bulk graphene can be used for interconnects that seamlessly become the transistor material, minimizing carrier scattering.
1.5 DNA - decorated graphitic surfaces and gas sensi ng
Semiconducting carbon nanotubes make an excellent material for chemical sensing with optical or electrical readout. This is due to the confluence of several factors. First, these tubes have a high electron mobility. The sensitivity of the conductivity t o changes in carrier density are given by
so a carbon nanotube’s high mobility will let it produce a large change in current for a small change in carrier density. This directly amplifies the effect of charge injection mechanisms, which will be one of th e principal sensing mechanisms. It also helps indirectly, as this high mobility is in large part due to low scattering. If the presence of an analyte causes additional scattering, it will be a comparatively large addition to the scattering of the tube.