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2008-03-26 notes on graphene

Having an interest in alternate transistors and self-replication (closed-form directed cyclical Hamiltonian subgraphs), coming across the April 2008 SciAm article was a treat. So here are my notes on how you can make graphene and possibly how to make a transistor out of it, in particular the applications of atomic force microscopy / DIY STM machines to make it happen (see also [1]). It is interesting to note that if graphene can be formed into transistors and logic circuits that the mechanical printing press can be made to be somewhat self-replicating in the sense that not only the instructions to build the press can be printed, but also rudimentary logic circuits, almost completing the dependency loops. To what extent does graphene-transistors require quantum tunneling? Have any amateurs achieved quantum tunneling at home? Yes [2] @ 10 GHz photons from microwave, paraffin, big setup. See here for links on building, say, a plastic AFM on the cheap. Slashdot discussion and there was somebody who had this to say:

Bah, Physicists and their QM simulations! They got it all wrong again. It isn't the length of the graphene ribbon that affects its properties, but the shape of its edges. If you look at benzene ring's molecular orbitals, you'll see that there are two ways to pack them in a ribbon. If they all line up, with resonant transfer going along the ribbon in a straight line, then you have metallic conductivity, with the electron just gliding across all the orbitals without hitting any gaps. If the orbitals don't line up, you end up with little dead ends here and there, which cause "turbulence" and reduce conductivity. Now, the packing of the orbitals is determined by the edges because of their constraints on orbital orientation. In the middle of the ribbon, you have a pure hex grid, and the orbitals, which can be visualized as taking half of each hex and painting a large C on it (these are not the same as the three bonding pi orbitals). Try it yourself: draw a hex grid and try to pack Cs. To visualize resonance, push on one end of a C and see how to repack the resulting structure. In the middle, you have three orientations at every node, but at the edges you don't. The more edges you have, the more constraints there are on the packing, and the more likely it is that the oribitals in the middle won't be in resonance with each other in a given direction. When you push on a C in such a grid, it will push other Cs sideways instead of along the ribbon, causing "resistance". There are two types of edges, familiar to tile game developers as the vertical and horizontal orientation. In the horizontal packing, the flat side of each hex is bordering the edge, in the vertical the flat side is perpendicular to the edge. It turns out that if you have horizontal edges on your graphene ribbon, it is metallic; if you have vertical ones, it is semiconductive (which is another way of saying it has more resistance). If the edges are not quite straight, which will quite likely happen if you are making your ribbons via CVD or duct tape or something, you'll see a mix of both behaviors, resulting in a conductivity somewhere in between full-out and almost-nothing. This is the trouble with modern physics - they just don't care about reality any more. If they only drew a few pictures, like real chemists do, they'd have seen this very easily. Instead they waste their time on simulations that only give them numbers they don't know how to interpret. Sheesh.


JR Minkel / SciAm DIY graphene method

  1. Work in a clean environment; stray dirt or hair plays havoc with graphene samples.
  2. Prepare a wafer of odxidized silicon, which helps you see graphene layers under a microscope. To smooth out the surface to accept the graphene and to clean it thoroughly, apply a mix of hydrochloric acid and hydrogen peroxide.
  3. Attach a graphite flake to about six inches of plastic sticky tape with tweezers. Fold the tape at a 45-degree angle right next to the flake, so that you sandwhich it between the sticky sides. Press it down gingerly and peel the tape apart slowly enough so that you can watch the graphite cleaving smoothly in two.
  4. Repeat the third step about 10 times. This procedure gets harder to do the more folds you make.
  5. Carefully lay the cleaved graphite sample that remains stuck to the tape onto the silicon. Using plastic tongs, gently press out any air between the tape and sample. Pass the tongs lightly but firmly over the sample for 10 minutes. With the tongs, keep the wafer planted on the surface while slowly peeling off the tape. This step should take 30 to 60 seconds to minimize shredding of any graphene you have created.
  6. Place the wafer under a microscope fitted with a 50x or 100x objective lens. You should see plenty of graphite debris: large, shiny chunks of all kinds of shapes and colors and, if you're lucky, graphene: highly transparent, crystalline shapes having little color compared with the rest of the wafer.


Refs

  1. Electrons in atomically thin carbon sheets behave like massless particles. Mark Wilson in Physics Today, Vol. 59, pages 21-23; January 2006.
  2. Drawing conclusions from graphene. Antonio Castro Neto, Francisco Guinea and Nuno Miguel Peres in Physics World, Vol. 19, pages 33-37; November 2006.
  3. Graphene: exploring carbon flatland. A. K. Geim and A. H. MacDonald in Physics Today, Vol. 60, pages 35-41; August 2007.
  4. The Rise of Graphene. A. K. Geim and K. S. Novoselov in Nature Materials, Vol. 6, pages 183-191; 2007.
  5. Andre K. Geim's mesoscopic physics group
  6. Philip Kim's research group

Drawing conclusions from graphene

How's this for MacGyver physics: Geim's group used adhesive tape to make a breakthrough in fundamental physics in 2004. Pencil graphite is made up of simple layers of honeycombe-shaped graphene molecules. Geim and Philip Kim confirmed an alternative method of producing graphene molecules: gently push graphite crystals across a hard surface. Look up Walt de Heer and Claire Berger at Georgia Tech for their epitaxial growth process (for industrial mass-volume fabrication of graphene molecules).

From what I can tell, Philip Russell Wallace (1947) predicted the theoretical properties of graphene, nobody paid much attention at the time, during the 1960s the thermodynamic and transport properties of graphite were well studied, getting lots of data on heat capacity, a good example of progress in condensed matter physics. The trademark behaviour that distinguishes a graphene sheet from an ordinary metal, for example, is the unusual form of the Hall effect. In the original Hall effect, discovered in 1879, a current flowing along the surface of a metal in the presence of a transverse magnetic field causes a drop in potential at right angles to both the current and the magnetic field. As the ratio of the potential drop to the current flowing (called the Hall resistivity) is directly proportional to the applied magnetic field, the Hall effect is used to measure magnetic fields. A century later, Klaus von Klitzing discovered that in a 2D electron gas at a temperature close to absolute zero the Hall resistivity becomes quantized, taking only discrete values of h/ne2 (where h is Planck’s constant, n is a positive integer and e is the electric charge). The quantization is so precise that this “quantum Hall effect” (QHE) is used as the standard for the measurement of resistivity.

Berry's phase
anomalous integer QHE
cyclotron energy
Eduardo Fredkin - 1986 - prediction of the universal resistance of graphene
ballistic transistor
massless Dirac fermions in graphene
fine-structure constant in quantum electrodynamics
Bloch waves in crystals
qausiparticle
Fermi-Dirac velocity
zitterbewegung
Klein paradox
electron-beam lithography
carving an entire microprocessor out of a single sheet of graphene


C Berger et al. Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics J. Phys. Chem. 108 19912
V P Gusynin and S G Sharapov 2005 Unconventional integer quantum Hall effect in graphene Phys. Rev. Lett. 95 146801
K S Novoselov et al. 2004 Electric field effect in atomically thin carbon films Science 306 666–669
K S Novoselov et al. 2005 Two-dimensional gas of massless Dirac fermions in graphene Nature 438 197–200
K S Novoselov et al. 2006 Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene Nature Physics 2 177–180
N M R Peres et al. 2006 Electronic properties of disordered two-dimensional carbon Phys. Rev. B 73 125411
Y Zhang et al. 2005 Experimental observation of quantum Hall effect and Berry’s phase in graphene Nature 438 201–204



Electrons in atomically thin carbon sheets behave like massless particles

Relativistic Dirac equations also describe the motion of electrons through a unique two-dimensional condensed matter system, graphene. Rubbing graphite and graphene on SiO2 produces interference patterns that can be used to identify the graphene. These patterns of interference can be used as guides for where to navigate with atomic force microscopy. How do particles behave differently in a crystal lattice when those particles are massles, relativistic fermions?

epitaxy machines
quantum wells
dispersion relations
valence conduction bands (hurray)



Graphene: exploring carbon flatland

The serendipitous choice in the Manchester lab for finding graphene was to use not paper, or any other writing surface, but an oxidized Si wafer -- the same material widely used by the semiconductor industry. The oxide surface reflects a rainbow of colors, and the interference pattern produced by layers of graphene on the oxide provides a faint but visible contrast, much like the fringes in an oily puddle (see figure 1). Fortunately, the human eye and brain are a team powerful enough to distinguish even that weak contrast in rapid optical microscope inspections of graphite debris. With a little experience, finding those few graphene crystallites takes only a couple of hours.

http://grapheneindustries.com/ -- business that sells graphene molecules that have been produced by the "rub graphite across a Si wafer" method.

ref #3

vapor deposition of hydrocarbons on catalytic metallic surfaces that could later be etched away to leave graphene on an insulating substrate. Graphene can also be obtained in powder form, by exfoliation of "graphene oxide" from graphite oxide followed by reduction to graphene (ref 5; also bulk powder production). And then there's epitaxial growth for batch graphene fabrication.

graphene nanoribbons -- ultranarrow strips of the material in which a semiconducting gap can be opened due to quantum confinement of electrons (ref 16)


But rather than using a set of nanotubes as ingredients for a circuit, engineers could carve the entire circuit out of graphene -- the bulk electrodes, quantum barriers, central molecular switches, and quantum dots. At the single-nanometer scale, a few benzene rings cut out of a graphene sheet can leave behind a macromolecule attached to graphene-based electrical contacts, as suggested in figure 4. The central graphene island in this example can be considered as a quantum dot, separated from macroscopic contacts by either resistive or tunneling barriers. Making graphene circuitry operational at room temperature on such quantum principles will require dimensions smaller than 10 nm. In theory, the samller the graphene elements, the better they should serve electronics applications.

Ref 3 - See A. K. Geim, K. S. Novoselov, Nat. Matter. 6, 183 (2007), and references therein.

Ref 5 - S. Stankovich et al., Nature 442, 282 (2006)

Ref 16 - K. Nakada et al, Physics Rev. B 54, 17954 (1996).



Making graphene visible

The rise of graphene

Landau and Peierls argued that strictly 2D crystals were thermodynamically unstable and could not exist (refs 11, 12).
other free-standing 2D atomic crystals discovered about the same time as graphene - single-layer boron nitride, half-layer BSCCO, refs 7-10, 13, 14 17-19,
The theoretical limit for the number of layers of graphene to make graphite is said to be 10 (ref 20).
bulk graphite fabrication in a "sludge graphene" of sorts - ref 23 - infeasible/yuck

On the other hand, single- and few-layer graphene have been grown epitaxially by chemical vapour deposition of hydrocarbons on metal substrates28,29 and by thermal decomposition of SiC (refs 30–34). Such films were studied by surface science techniques, and their quality and continuity remained unknown. Only lately, few-layer graphene obtained on SiC was characterized with respect to its electronic properties, revealing high-mobility charge carriers 32,33. Epitaxial growth of graphene offers probably the only viable route towards electronic applications and, with so much at stake, rapid progress in this direction is expected. The approach that seems promising but has not been attempted yet is the use of the previously demonstrated epitaxy on catalytic surfaces28,29 (such as Ni or Pt) followed by the deposition of an insulating support on top of graphene and chemical removal of the primary metallic substrate.

Need to come up with a way to make quality graphene wafers to draw on.
micromechanical bulk cleavage of graphite (sticky tape / adhesive tape method) (ref 7 and 8 for the technique)
graphene has a clear signature in Raman microscopy (ref 37, 38)
Brillouin zone
pseudospin
chirality
the mystery of a missing pie
minimum conductivity of graphene
marginal Fermi liquid (ref 44, 69)
inter-valley scattering rates
Dirac point
excitonic gaps
see refs 45, 73-80 for theoretical studies of graphene
Dirac trajectories
Schottky barrier
IBM and Intel fund graphene research

For mainstream logic applications, the fact that graphene remains metallic even at the neutrality point is a major problem. However, significant semiconductor gaps ΔE can still be engineered in graphene. As mentioned above, ΔE up to 0.3 eV can be induced in bilayer graphene but this is perhaps more interesting in terms of tuneable infrared lasers and detectors. For single-layer graphene, ΔE can be induced by spatial confinement or lateral-superlattice potential. The latter seems to be a relatively straightforward solution because sizeable gaps should naturally occur in graphene epitaxially grown on top of crystals with matching lattices such as boron nitride or the same SiC (refs 30–34), in which superlattice effects are undoubtedly expected.

Owing to graphene’s linear spectrum and large νF, the confinement gap is also rather large (refs 85–87) ΔE (eV) ≈ αħνF/d ≈ 1/d (nm), compared with other semiconductors, and it requires ribbons with width d of about 10 nm for room-temperature operation (coefficient α is ≈½ for Dirac fermions)87. With the Si-based technology rapidly advancing into this scale, the required size is no longer seen as a significant hurdle, and much research is expected along this direction. However, unless a technique for anisotropic etching of graphene is found to make devices with crystallographically defined faces (for example, zigzag or armchair), one has to deal with conductive channels having irregular edges. In short channels, electronic states associated with such edges can induce a significant sample-dependent conductance (refs 85–87). In long channels, random edges may lead to additional scattering, which can be detrimental for the speed and energy consumption of transistors, and in effect, cancel all the advantages offered by graphene’s ballistic transport. Fortunately, high-anisotropy dry etching is probably achievable in graphene, owing to quite different chemical reactivity of zigzag and armchair edges.

An alternative route to graphene-based electronics is to consider graphene not as a new channel material for field-effect transistors (FET) but as a conductive sheet, in which various nanometre-size structures can be carved to make a single-electron-transistor (SET) circuitry. The idea is to exploit the fact that, unlike other materials, graphene nanostructures are stable down to true nanometre sizes, and possibly even down to a single benzene ring. This allows the exploration of a region somewhere in between SET and molecular electronics (but by using the top-down approach). The advantage is that everything including conducting channels, quantum dots, barriers and interconnects can be cut out from a graphene sheet, whereas other material characteristics are much less important for the SET architecture (88,89) than for traditional FET circuits. This approach is illustrated in Fig. 6, which shows a SET made entirely from graphene by using electron-beam lithography and dry etching (Fig. 6b, inset). For a minimum feature size of ≈10 nm the combined Coulomb and confinement gap reaches >3kT, which should allow a SET-like circuitry operational at room temperature (Fig. 6b), whereas resistive (rather than traditional tunnel) barriers can be used to induce Coulomb blockade. The SET architecture is relatively well developed (88,89), and one of the main reasons it has failed to impress so far is difficulties with the extension of its operation to room temperature. The fundamental cause for the latter is a poor stability of materials for true-nanometre sizes, at which the Si-based technology is also likely to encounter fundamental limitations, according to the semiconductor industry roadmap. This is where graphene can come into play. It is most certain that we will see many efforts to develop various approaches to graphene electronics. Whichever approach prevails, there are two immediate challenges. First, despite the recent progress in epitaxial growth of graphene (33,34), high-quality wafers suitable for industrial applications still remain to be demonstrated. Second, individual features in graphene devices need to be controlled accurately enough to provide sufficient reproducibility in their properties. The latter is exactly the same challenge that the Si technology has been dealing with successfully. For the time being, to make proof-of-principle nanometre-size devices, one can use electrochemical etching of graphene by scanning-probe nanolithography (ref 90).

graphenium microprocessors in 20 years

References to get:
  1. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).
  2. Novoselov, K. S. et al. Two-dimensional atomic crystals. Proc. Natl Acad. Sci. USA 102, 10451–10453 (2005).
  3. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).
  4. Zhang, Y., Tan, J. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).
  5. Peierls, R. E. Quelques proprietes typiques des corpses solides. Ann. I. H. Poincare 5, 177–222 (1935).
  6. Landau, L. D. Zur Theorie der phasenumwandlungen II. Phys. Z. Sowjetunion 11, 26–35 (1937).
  7. Landau, L. D. & Lifshitz, E. M. Statistical Physics, Part I (Pergamon, Oxford, 1980).
  8. Mermin, N. D. Crystalline order in two dimensions. Phys. Rev. 176, 250–254 (1968).
  9. Stankovich, S. et al. Graphene-based composite materials. Nature 442, 282–286 (2006).
  10. Meyer, J. C. et al. The structure of suspended graphene sheets. Nature (in the press); doi:10.1038/nature05545.
  11. Nelson, D. R., Piran, T. & Weinberg, S. Statistical Mechanics of Membranes and Surfaces (World Scientific, Singapore, 2004).
  12. Partoens, B. & Peeters, F. M. From graphene to graphite: Electronic structure around the K point. Phys. Rev. B 74, 075404 (2006).
  13. Dresselhaus, M. S. & Dresselhaus, G. Intercalation compounds of graphite. Adv. Phys. 51, 1–186 (2002)
  14. Land, T. A., Michely, T., Behm, R. J., Hemminger, J. C. & Comsa, G. STM investigation of single layer graphite structures produced on Pt(111) by hydrocarbon decomposition. Surf. Sci 264, 261–270 (1992).
  15. Nagashima, A. et al. Electronic states of monolayer graphite formed on TiC(111) surface. Surf. Sci. 291, 93–98 (1993).
  16. van Bommel, A. J., Crombeen, J. E. & van Tooren, A. LEED and Auger electron observations of the SiC(0001) surface. Surf. Sci. 48, 463–472 (1975).
  17. Forbeaux, I., Themlin, J.-M. & Debever, J. M. Heteroepitaxial graphite on 6H-SiC(0001): Interface formation through conduction-band electronic structure. Phys. Rev. B 58, 16396–16406 (1998).
  18. Berger, C. et al. Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics. J. Phys. Chem. B 108, 19912–19916 (2004).
  19. Berger, C. et al. Electronic confinement and coherence in patterned epitaxial graphene. Science 312, 1191–1196 (2006).
  20. Ohta, T., Bostwick, A., Seyller, T., Horn, K. & Rotenberg, E. Controlling the electronic structure of bilayer graphene. Science 313, 951–954 (2006).
  21. Ferrari, A. C. et al. Raman spectrum of graphene and graphene layers. Phys. Rev. Lett. 97, 187401 (2006).
  22. Gupta, A., Chen, G., Joshi, P., Tadigadapa, S. & Eklund, P. C. Raman scattering from high-frequency phonons in supported n-graphene layer films. Nano Lett. 6, 2667–2673 (2006).
  23. González, J., Guinea, F. & Vozmediano, M. A. H. Unconventional quasiparticle lifetime in graphite Phys. Rev. Lett. 77, 3589–3592 (1996).
  24. Das Sarma, S., Hwang, E. H., Tse, W. K. Is graphene a Fermi liquid? Preprint at http://arxiv.org/abs/cond-mat/0610581 (2006).
  25. Nakada, K., Fujita, M., Dresselhaus, G. & Dresselhaus, M. S. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Phys. Rev. B 54, 17954–17961 (1996).
  26. Brey, L. & Fertig, H. A. Electronic states of graphene nanoribbons. Phys. Rev. B 73, 235411 (2006).
  27. Son, Y.W, Cohen, M. L. & Louie, S. G. Energy gaps in graphene nanoribbons Phys. Rev. Lett. 97, 216803 (2006).
  28. Tilke, A. T., Simmel, F. C., Blick, R.H, Lorenz, H. & Kotthaus, J. P. Coulomb blockade in silicon nanostructures. Prog. Quantum Electron. 25, 97–138 (2001).
  29. Takahashi, Y., Ono, Y., Fujiwara, A. & Inokawa, H. Silicon single-electron devices. J. Phys. Condens. Matter 14, R995–R1033 (2002).
  30. Tseng, A. A., Notargiacomo A. & Chen T. P. Nanofabrication by scanning probe microscope lithography: A review. J. Vac. Sci. Tech. B 23, 877–894 (2005).
Theoretical studies of graphene:
  1. Schakel, A. M. J. Relativistic quantum Hall effect. Phys. Rev. D 43, 1428–1431 (1991).
  2. Nomura, K. & MacDonald, A. H. Quantum Hall ferromagnetism in graphene. Phys. Rev. Lett. 96, 256602 (2006).
  3. Yang, K., Das Sarma, S. & MacDonald, A. H. Collective modes and skyrmion excitations in graphene SU(4) quantum Hall ferromagnets. Phys. Rev. B 74, 075423 (2006).
  4. Apalkov, V. M. & Chakraborty, T. The fractional quantum Hall states of Dirac electrons in graphene Phys. Rev. Lett. 97, 126801 (2006).
  5. Khveshchenko, D. V. Composite Dirac fermions in graphene. Preprint at http://arxiv.org/abs/cond-mat/0607174 (2006).
  6. Alicea, J. & Fisher, M. P. A. Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes, Phys. Rev. B 74, 075422 (2006).
  7. Khveshchenko, D. V. Ghost excitonic insulator transition in layered graphite. Phys. Rev. Let 87, 246802 (2001).
  8. Abanin, D. A., Lee, P. A. & Levitov, L. S. Spin-filtered edge states and quantum Hall effect in graphene. Phys. Rev. Lett. 96, 176803 (2006).
  9. Toke, C., Lammert, P. E., Crespi, V. H. & Jain, J. K. Fractional quantum Hall effect in graphene. Phys. Rev. B 74, 235417 (2006).

Graphene nanoribbon electronics

Method of production of single graphene layers - ref 3. Intense study, 4-7. ... Being, however, a zero-gap semiconductor, graphene cannot be used directly in applications such as field-effect transistors (FETs). However, in addition to the 2D confinement, the graphene electrons can be further confined by forming narrow ribbons, e.g quantizing ky. The width confinement is expected to result in a split of the original two-dimensional (2D) energy dispersion of graphene into a number of one-dimensional (1D) modes. Depending on the boundary conditions, some sets of these 1D modes do not pass through the intersection point of the conduction and valence band, and these quasi-1D graphene ribbons become semiconductors with a finite energy gap. The properties of GNRs would be quite different from those of graphene, for example the carrier mobility is expected to decrease as the gap increases [9].

In this report we describe the field switching and transport at different temperatures in narrow GNRs produced by electron beam lithography and etching techniques. Ribbons as narrow as 20 nm have been measured. Like CNTs, GNRs have defects that can scatter the carriers. These defects can be structural, chemical, or charged substrate sites. Furthermore, unlike CNTs, where periodic boundary conditions are present, GNRs have edges with localized states [10] that can also affect transport. As very narrow GNRs are needed to achieve the gap of even large diameter CNTs, the effect of the edges can be critical. Another question that is connected to scattering is the issue of electrical noise. Noise is known to increase with decreasing size, as described by Hooge’s rule [11]. In the case of CNTs it was found that the dominant form of noise is 1/f noise and its origin was ascribed to charge fluctuations involving substrate traps [12]. It is therefore, important to find if the same holds true for GNRs.

Graphene sheets were extracted by micromechanical cleavage [3] from three-dimensional highly ordered pyrolytic graphite (HOPG) (IIRC, the same stuff used in DIY STM mounts) and deposited onto heavily p-doped Si substrates covered with a 200 nm SiO2 layer. Atomic force microscopy (AFM) was used to measure the thickness of the sheet to identify whether it is a single or few layer graphene. The graphene was patterned with e-beam lithography (see 1, Wp, convert electron microscope -> electron beam lithography system see C. R. K. Marrian et al. (1992). "unknown title". J. Vac. Sci. Tech. 10 (B): 2877-2881. for using an STM as an electron beam source, also try TEM), followed by an oxygen plasma etching process in which the e-beam resist, HSQ, was used as the etching mask, forming GNRs with various widths. As shown in the SEM image in Fig. 1, palladium (Pd) source drain contacts were deposited on top of the GNR, forming a three terminal field-effect transistor (FET) device with the Si substrate used as the back gate. All devices fabricated have a channel length of 1µm, and the width of the GNR studied ranges from 20 nm to 500 nm.

These methods are relatively simple in comparison to semiconductor manufacturing techniques -- in particular, an amateur in his home can experiment with revolutionary graphene transistor technology with a few STMs, AFMs, electron beam machines, and so on. The transistor research that still needs to be done includes characterizing graphene transistors and making accurate measurements about voltage, resistivity, and making sure we can link up transistor theory with the theoretical physics of graphene as studied over the past 60 years.

Arrhenius plot
semiconductor channel
universal conductance fluctuation
potassium doping process (ref 21) --> the potassium (relying on charge transfer) acts as an electron donor and shifts the Fermi level of the GNR into the conduction band.


... with the A ~ 1/N behavior. Therefore, while the GNR devices exhibit a width-dependent resistivity due to contributions from edge states (see Fig. 2), the fact that the noise amplitude A follows the 1/N relation suggests that the 1/f noise is not significantly affected by the presence of the edge states ...

In conclusion, we have shown that GNRs as narrow as 20 nm can be fabricated by e-beam lithography and etching techniques and be incorporated as channels of field effect transistors. We have found that both boundary scattering and trapped charges in the substrate strongly affect the transport properties and minimum conductivity of the GNRs. A confinement-induced gap of the order of 30 meV was inferred in the narrowest 20 nm ribbon. The dominant electrical noise at low frequencies was found to be 1/f noise arising from fluctuations in the occupancy of charged traps in the substrate.

Chemically derived, ultrasmooth graphene nanoribbon semiconductors

-- Solution-phase derived; stably suspended in solvents with nonconvalent polymer functionalization

lattice-defined graphene junctions for GNRs
on-off ratios
carrier mobility
quantum confinement
single-walled carbon nanotubes (SWTs)

Lithographic patterning of graphene sheets has fabricated GNRs down to widths of ~20 nm thus far (12, 13), but there are difficulties in obtaining smooth edges (for example, with roughness < ~5 nm) and reaching true nanometer-scale ribbon width. Chemical approaches (14–17) and self-assembly processes may produce graphene structures with desired shape and dimensions for fundamental and practical applications.

We report that, by using a widely available and abundant graphite material, we can develop simple chemical methods to produce GNRs. We exfoliated commercial expandable graphite (Grafguard 160-50N, Graftech Incorporated, Cleveland, OH) by brief (60 s) heating to 1000°C in forming gas (3% hydrogen in argon). The resulting exfoliated graphite was dispersed in a 1,2-dichloroethane (DCE) ([buy]) solution of poly(m-phenylenevinylene-co-2,5-dioctoxy-p-phenylenevinylene) (PmPV) ([buy]) by sonication for 30 min to form a homogeneous suspension. Centrifugation ([DIY centrifuge]) then removed large pieces of materials from the supernatant (Fig. 1A and fig. S1) (18).

Accurate measurements of GNR width were difficult because of the finite AFM tip radius (~10 to 20 nm), especially for ultranarrow ribbons. To circumvent the problem, we used the same tips to measure the apparent widths of Hipco (Carbon Nanotechnologies Incorporated, Houston, TX) SWNTs in a diameter-separated sample and deduced tip size (18). All GNR widths reported in this work have their basis in AFM measurements after correcting for the tip-size effect.

Transmission electron microscopy (TEM, fig. S5) (18), electron diffraction (fig. S5) (18), and Raman spectroscopy (fig. S6) (18) (graphene G-band) were used to characterize the GNRs. Because of their topographical resemblance to SWNTs, we carried out extensive control experiments to ensure that the sub-10-nm GNRs in our samples were not SWNTs present from contamination or other causes. For example, we performed surface-enhanced Raman measurements on many GNR samples deposited on Au substrates and never observed any radial breathing modes intrinsic to SWNTs (fig. S6) (18). Further, all of our w < 10 nm GNRs were semiconductors (see below), unlike SWNTs, which form as mixtures in which one-third of nanotubes are metallic.

The formation of our GNRs constitutes several key steps. First, ~350-mm-scale graphite flakes were made into expandable graphite by chemical intercalation of oxidizing sulfuric acid and nitric acid, with oxidation of carbon atoms likely occurring at the edge, step, and defect sites of graphite (19, 20). Second, rapid heating of the expandable graphite to 1000°C caused violent formation of volatile gaseous species from the intercalant and exfoliates graphite into a loose stack of few-layered graphene sheets. This thermal exfoliation step is critical and responsible for the formation of one- to few-layer graphene and was evidenced by a visible, dramatic volume expansion of graphite by ~100 to 200 times after exfoliation (fig. S1) (18). The 1000°C treatment can also reverse oxidation and functionalization of graphite by thermally desorbing covalently attached species and repair defects (21).

Solution-phase sonication and functionalization by PmPV of few-layered graphene sheets formed by 1000°C exfoliation led to stably suspending graphene in DCE. The PmPV conjugated polymers (Fig. 1A), known to adsorb onto SWNT sidewalls via p stacking, noncovalently functionalized the exfoliated graphene to afford a homogeneous black suspension during sonication (fig. S1) (18, 22, 23). We were not able to form homogeneous suspension by the same process without using PmPV. We suggest that sonication is responsible for chemomechanical breaking of the stably suspended graphene sheets into smaller pieces, including nanoribbons. Sonochemistry and ultrahot gas bubbles involved in sonication cause graphene to break into various structures, with an appreciable yield of GNRs. The supernatant after centrifugation contains micrometer-sized graphene sheets and GNRs (albeit at lower yield than sheets) in various sizes, shapes, and morphologies. What does the chemical reaction look like here?

Besides regularly shaped ribbons, we observed graphene structures that were shaped irregularly, such as wedges (Fig. 2), GNRs with bends and kinks (Fig. 2, A, B, and E), and ribbons coming off larger pieces of graphene with varying widths along the ribbon length [Fig. 1E, middle image, and fig. S5, TEM data (18)]. These results suggest that GNRs could be formed by breaking off narrow pieces of graphene from larger sheets during sonication. However, we found that continuous sonication does not lead to higher yield of GNRs and that the degree of sonication needs to be controlled for optimal yield of GNRs. Imaging with AFM indicated that almost no sub-10-nm ribbons were obtained if sonication were excessive (for hours) because of continued cutting and breaking of ribbons into small particle-like structures.

The observed graphene nanoribbons narrowing down to diminishing width and to a point (Fig. 2, C and D) indicate that GNRs reaching true nanometer dimensions with potentially atomic-scale smoothness can form. GNRs comprised of segments of varying widths (Fig. 1E, middle image, and 2B) could be used for graphene molecular electronics with varying band gaps along the ribbon. Interestingly, GNR junctions with sharp kinks at 120° angle were observed (Fig. 2B), apparently through the joining of two GNRs with edges along well-defined atomic lattice of graphene (such as zigzag edges). Single-layered GNRs displayed remarkably mechanical flexibility and resilience, with mechanical bending and folding without obvious breakage (Fig. 2E).

Next, we fabricated field-effect transistor (FET)–like devices with our GNRs (w ~ sub- 10 nm to ~55 nm). The devices had palladium (Pd) as source/drain (S/D) metal contacts (chan- nel length L ~ 200 nm), a p++-Si backgate, and 300-nm SiO2 as gate dielectrics (18). We ob- served that the room-temperature on-off current switching (Ion/Ioff) induced by the gate voltage increased exponentially as the GNR width de- creased, with Ion/Ioff ~1, ~5, ~100, and >105 for w ~ 50 nm [fig. S7 (18)], w ~ 20 nm [fig. S7 (18)], w ~ 10 nm (Fig. 3A), and w ~ sub-10-nm (Fig. 3C) GNRs, respectively. This trend was consistent with lithographically fabricated GNRs with w > 20 nm (12). Importantly, all of the w = sub-10-nm GNRs characterized in our experi- ments (more than 30, with no exceptions) exhib- ited Ion/Ioff > 105 (Fig. 4A) even under a S/D bias Vds up to ~1 V. This suggests that the GNRs are semiconducting and have substantial band gaps. This result is in stark contrast to SWNTs (with circumference ~ sub-10 nm, or diameter < ~3 nm) that contain 1/3 metallic species. Thus, our chem- ically derived GNRs afford graphene transistors with orders of magnitude on/off switching at room temperature.


2008-03-27

Scanning tunneling lithography ([1] inc. AFM-only method (tungsten tip); [2]). STL tends to do 25 nm technology, with good results at 100 nm. Knowing that graphene transistors exhibit quantum tunneling more near 10 nm of separation, how much would double the distance matter in terms of quantum tunneling?

What about the nm-precise piezo actuators? Back in February 08 I looked up some companies and asked around for prices on nanometer and subnanometer precision, and the pricing information I got back commonly went well over $1k USD.

JohnFlux from ##physics on irc.freenode.net suggests using a poor man's piezo: a resistor hooked up to the metal. But then I have to wonder what it actually requires in the first place. Somehow I came up with the idea of just directly writing in graphene, with a very sharp pencil tip. Then, use mechanical force to move the pencil around on the sheet of paper (as well as up and down).
2008-03-29

I'd like to find a workable PDF copy of Electronic Structure and Stability of Semiconducting Graphene Nanoribbons. So, through my research on molecular dynamics and ab initio computational materials simulations (DFT, etc.) (for skdb), I came across the Scuseria research group over at Rice, opened up a few links from their pages, and found that on their research/publications page they mention graphene nanoribbons (particularly, "Electronic structure and stability of semiconducting graphene nanoribbons, V. Barone, O. Hod, and G. E. Scuseria, Nano Lett. 6, 2748 (2006).") -- a recent topic of interest. Here's the abstract:
We present a systematic density functional theory study of the electronic properties, optical spectra, and relative thermodynamic stability of semiconducting graphene nanoribbons. We consider ribbons with different edge nature including bare and hydrogen-terminated ribbons, several crystallographic orientations, and widths up to 3 nm. Our results can be extrapolated to wider ribbons providing a qualitative way of determining the electronic properties of ribbons with widths of practical significance. We predict that in order to produce materials with band gaps similar to Ge or InN, the width of the ribbons must be between 2 and 3 nm. If larger bang gap ribbons are needed (like Si, InP, or GaAs), their width must be reduced to 1-2 nm. According to the extrapolated inverse power law obtained in this work, armchair carbon nanoribbons of widths larger than 8 nm will present a maximum band gap of 0.3 eV, while for ribbons with a width of 80 nm the maximum possible band gap is 0.05 eV. For chiral nanoribbons the band gap oscillations rapidly vanish as a function of the chiral angle indicating that a careful design of their crystallographic nature is an essential ingredient for controlling their electronic properties. Optical excitations show important differences between ribbons with and without hydrogen termination and are found to be sensitive to the carbon nanoribbon width. This should provide a practical way of revealing information on their size and the nature of their edges.
Oddly enough, the ACS website has always disliked me, particularly their PDFs never register as real PDFs to me. Why is this? On an unrelated note, I dumped some notes on AFM nanolithography over at the local wiki (there's also now an extension to grab the XML to the entire database, have fun).




2008-04-28 - there are some good discussions re: the history of graphene at Wp, and see also graphene.org.