Luke Bouma



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BOUMA |


Name: Luke Bouma

Professor: Dr. Harlynn Ramsey



Bio: Born in Bethesda, MD and raised in Geneva, Switzerland, Luke Bouma studies physics, mathematics, and astronomy at the University of Southern California. He spent the summer of 2013 fabricating and electrically probing graphene field effect transistors in Mark Keller’s group at the National Institute of Standards and Technology (NIST) in Boulder, CO.

Keywords: graphene, carbon science, nanomaterials, nanotechnology, supercapacitor, flexible electronics, chemical vapor deposition, scotch tape, semiconductor physics, Manchester University, materials science

Suggested materials: Andre Geim’s 2010 Nobel lecture on the discovery and usefulness of graphene: http://www.nobelprize.org/mediaplayer/index.php?id=1418 (34 minute video). Colloquium on Graphene Physics and Devices http://nanohub.org/resources/7180 (free course, total lecture time ~6 hours). The Super Supercapacitor | Brian Golden Davis http://vimeo.com/51873011 (3 minute 27 second video).

Graphene: What It Is; What It Will and Won’t Do

Graphene is a thin layer of carbon; more precisely, it is an atomically thin sheet of carbon atoms packed in a honeycomb lattice. First isolated in 2004, graphene subsequently exhibited a dazzling display of physical and electrical phenomena, enticing scientists and the public alike. This atom-thick wonder-material is the strongest material ever measured, is incredibly flexible, and is also the best known conductor of heat. It conducts electricity better than any other material as well, with electron mobilities tens to hundreds of times higher than those of silicon. Given its relative novelty, the lasting influence of graphene on everyday living is still being determined. Challenges in the production of industrial-grade graphene sheets are being addressed, and it is unlikely to dethrone silicon in digital logic circuits any time soon. Yet, the overall outlook remains positive. Graphene’s applications elsewhere – in biological engineering, electronics, photonics, and other fields – are likely to benefit humanity over the coming decades.

The Story of Graphene

Graphene’s very existence took scientists by surprise. In the mid-1930s, Lev Landau and Rudolf Peierls argued that two-dimensional crystals, if ever isolated, would collapse due to thermal instability [1]. Experimental results throughout the 20th century supported this claim; scientists found that thinner films had lower boiling points, and thus were more “unstable”. In 2004, a surprising twist came from the laboratory of Manchester-based scientist Andre Geim that refuted this thinking. Geim’s group made a breakthrough: by repeatedly thinning out flakes of graphite using scotch tape, they proved that they could obtain monolayer flakes of carbon, flakes just 0.3 billionths of a meter thick. They made and characterized electrical devices from these flakes with promising results, and through their work, they won the 2010 Physics Nobel Prize [2, 3]. To reiterate for emphasis, an experiment conducting using scotch tape not only garnered the Nobel Prize but also was heralded as a landmark development in chemistry, physics, material science, and engineering. On a curious historic note, this discovery made Andre Geim the first scientist to win both the Nobel and the less-serious Ig Nobel prizes, the latter having been awarded to him in 2000 for work magnetically levitating frogs [4].

Following the Manchester group’s landmark papers, graphene research exploded. Further studies on graphene’s structure suggest that the strength and proximity of carbon-carbon bonds are responsible for preventing the thermal fluctuations Landau predicted in 1937. But graphene researchers explore more than just the reasoning behind how the material exists: multiple scientific papers developing graphene’s potential applications are published daily (see: graphenetimes.com). Trying to guess the relevance of all this research to future living is difficult. Niche commercial applications of graphene, notably in composite materials, are only just coming to market [5, 6]; the true relevance of graphene has yet to be realized. Even so, graphene’s incredible mechanical and electrical properties are likely to make it competitive for a smorgasbord of applications. In order to understand these potential uses for graphene, one must first understand what makes it unique.

What is Graphene, and What Makes it Special?

Graphene is the thinnest possible sheet of the element carbon, arranged in a honeycomb lattice similar to that of beehives. It is a two-dimensional layer of graphite, the material commonly used in pencils for writing, and also abundant in nature. Real-world graphene is rarely perfectly uniform (see Fig. 1b below). Moreover, its electronic structure reacts quite different to the presence of different materials such as silicon or silicon dioxide, which are often used in





Figure 1. a) 15*15nm2 scanning tunneling microscopy image of graphene on Ir(111). The small dark spots, overlayed in white on the bottom left, are the centers of individual carbon rings, and the larger hexagonal pattern results from a superposition of graphene with the lattice underneath [7]. b) A grain boundary on graphene; this defect would decrease the sheet’s electrical quality [8]. c) Artist’s conception of graphene, with slight rippling [9].

conjunction with graphene to make electrical devices. For these devices, ranging from transistors to supercapacitors, graphene’s structural defects and its sensitivity to external influences can mean both challenge and opportunity. If the sensitivity can be taken advantage of, for example in photodetectors or photonic devices, research efforts can benefit [10, 11]. However, if defects impede device performance, as in transistors, desalination membranes, or transparent conducting electrodes, obtaining high-quality uniform graphene can be a challenge.

Graphene’s impressive mechanical and electrical characteristics can be understood at a simple level through considering how carbon atoms bond together. Elemental carbon has six electrons, of which two exist in a low-energy “core” state and four exist in a higher-energy “valence” state. In order for graphene to keep its honeycomb arrangement, the outer four “valence” electrons of each carbon atom in the crystal lattice mix their atomic orbitals to allow for a precise bonding arrangement. As shown in Fig. 2, for each carbon three electron-pairs are shared in plane (σ bonds), and single the remaining electron lives perpendicular to the plane (π bonds). The in-plane bonds are strong and account for graphene's robust mechanical properties, as well as its flexibility. Conversely, the π bonds perpendicular to the plane are less tightly bound, and they are



Figure 2. In-plane (bottom) and out-of-plane (top) bonding in graphene explains its basic mechanical and electrical properties. Adapted from [12].

responsible for graphene’s electrical properties. By way of analogy, the electrons in the π bonds act something like the unbound electrons in a highly conducting metal. Consequently, graphene is sometimes dubbed a semi-metal.

However, the true nature of graphene’s ‘energy band structure’ is more nuanced, as outlined in the supplement below. In short, graphene is a high quality conductor, but it has no “bandgap.” Bandgaps represent an energy barrier that must be overcome in order for a material to conduct electricity (a better explanation is in the supplement). Graphene’s lack of a bandgap means that while it is very good at conducting, it cannot easily be turned off in the way that semiconductors can be turned off in order for logic-gate transistors to function. Various strategies have been applied towards opening a bandgap in graphene to allow it to switch off, but none have succeeded to the required degree [6, 13, 14, 15]. Without major advances, graphene will not dethrone silicon as the lead material in digital logic circuits at any point soon.

Challenges in Graphene Research, and a Note on Popular Science Articles

Aside from the need to engineer a bandgap into graphene in order to make it viable for logic circuits, graphene faces other challenges on the road towards adoption, particularly in production. The previously described scotch tape method, also called “mechanical exfoliation,” is not scalable; exfoliation is great for research, but it is not viable for industrial applications. Chemical vapor deposition (CVD) is currently the best prospect for making scalable, high-quality graphene sheets, but it requires graphene growth on specific metal substrates like copper or aluminum. To make devices, this graphene must then be transferred off the metal, but there are no methods that maintain graphene quality while making the transfer. An alternative to growing CVD graphene is synthesizing graphene on silicon carbide, but this raises cost and processing issues. For ubiquitous commercial use of graphene, growth must be controlled such that impurity levels and crystallographic uniformity can be specified to a high level of precision in a cost-effective manner. Numerous groups are working to address these challenges.

While these challenges are real, they are rarely mentioned in popular science articles. Similarly, the superlatives that describe graphene – “strongest material” and “best conductor of electricity” – only technically apply under a stringent set of qualifying criteria that are often overlooked in popular science reports. For example, graphene’s record-breaking electric mobility is measured in suspended exfoliated graphene in high vacuum at ultra-low temperatures. These conditions are impractical for real-world applications, as a typical device will have graphene in contact with something, will be exposed to air, and will operate near room temperatures. The best demonstrated CVD-graphene has electrical mobilities less than ten times that of silicon because of real-world effects. In short, the miracle material is far from perfect.

What leads to oversimplifications in popular science? On one hand, researchers may overstate the importance of their results for career advancement. Similarly, reporters may amplify their claims to maximize readership. Given the quantity of readily-accessible information, the onus of untangling popular science news and the scientific literature it conveys ultimately rests on the inquisitive reader. Since the advent of graphene-based materials has yet to result in market-ready products, claims about graphene’s imminent importance should be taken with a healthy dose of salt. On that note, here are some areas in which graphene might make an impact.



Graphene’s Potential Applications and Future Outlook

Graphene supercapacitors are one technology that might revolutionize both energy storage and electrical engineering [16, 17]. Compared with batteries, ordinary capacitors are capable of releasing energy very quickly, but they can store far less. Supercapacitors fix the storage problem of ordinary capacitors; they can store far more charge than capacitors, while still releasing it 100-1000 times faster than batteries. They are fabricated by taking two conductive plates in a cell, coating them with porous activated carbon, and then immersing the cell in electrolyte solution [18]. The high surface area of the porous carbon gives the supercapacitor a high capacitance, which allows it to store large amounts of charge. However, the high costs of this fabrication method prohibit commercialization. This is where graphene comes in. Recent research at UCLA has shown that it is possible to reduce costs by substituting the porous carbon in a supercapacitor with cheaply-produced graphene, using just a computer’s DVD burner and standard materials [19]. If this technology reaches commercial viability, it would mean charging your cell phone, laptop, or other portable device in mere seconds. The benefits extend outward from there. It would be possible to charge electric vehicles in minutes, and backup generators for home and business use would provide great utility for disaster survival.

Flexible electronics, such as LCD touch screens, rollable electronic paper (e-paper), and foldable organic LEDs (OLEDs) use transparent conductive coatings that have low resistance and high light transmittance [6]. In the case of e-paper and OLEDs, the coatings also need to be flexible. Graphene fits the requirements for these applications, and can be produced for lower cost and at higher quality than the current industry-standard, indium tin oxide. Producing low resistance graphene is easy compared to more demanding electrical specifications, since one can introduce dopants into graphene in order to lower its resistance. Given the relatively minimal material requirements for graphene in these applications, flexible electronics are one of the most immediate areas in which graphene technology is predicted to emerge in the coming decade [6].

Other applications are varied and constantly evolving – those explained above are only a few promising near-term prospects. As with any new material, there will be spinoffs. For example, the Zettl group at Berkeley recently made a graphene earphone (see Fig. 3a) with an audio response comparable or above high-end commercial earphones [20]. In biological engineering, graphene’s electrical sensitivity could improve DNA sequencing (Fig 3b); promising steps have been taken towards graphene nanopore-based single molecule detectors [21]. Graphene’s impermeability makes it a candidate material for nanoporous membranes that filter water. Its ability to hold a magnetic spin for a relatively long period of time makes it viable for an emerging technology dubbed “spintronics” in which polarized magnetic spin currents carry information, replacing standard electron currents in electronics.



Figure 3. a) images of the Zettl group’s graphene earbud, and b) concept art of leading DNA through a nanopore in graphene in order to electrically ‘read’ the DNA strand and sequence its base pairing. Adapted from [20] and [22] respectively.

Conclusion

With the abundance of potential uses for graphene, one is reminded of Maslow’s observation that given a hammer, everything looks like a nail. Graphene research is still in its infancy, and the full effects of its development have yet to be seen. In the near-term, it is reasonable to expect developments in flexible electronics, high frequency (not logic) transistors, and possibly even supercapacitors. In the longer term, logic and thin-film transistors may be decades away in even research, let alone commercial, contexts. Yet, while it may be too early to compare graphene’s pending influence to that of stone, bronze, iron, or silicon, “graphene age” does have a ring to it (in more ways than one).



Supplement: On Bandgaps and Rudimentary Semiconductor Physics

In the body of this article, I argue that graphene is unlikely to replace silicon in digital logic circuits because it has no bandgap. To grasp where the idea of a bandgap originates, we first consider a deceptively simple question: why do materials conduct electricity differently? Band theory, a branch of physics, argues that electric current can only flow when a material’s electrons can be easily excited to higher energy states. The energy barrier electrons need to overcome in order to conduct is called a bandgap. Commercially-used metals such as copper or aluminum conduct electricity very well and have small or nonexistent bandgaps (see Fig. 4). Looking at the copper wires that power our homes, electrons move freely because they can be easily excited to higher energy states and then move about inside the wire. Insulators, on the other hand, do not conduct electricity very well and have large bandgaps; electrons struggle to move about inside them because a large amount of energy is required for electrons to reach their higher energy states. Semiconductors, the class of material responsible for personal computers, cell phones, solar cells, and other technologies, conduct somewhere in between the high-conductivity of metals and the low-conductivity of insulators. Thus the bandgap of a semiconductor like silicon is smaller than the bandgap of something like wood, but larger than that of most metals.





Figure 4. The size of a material’s bandgap determines how well it can conduct electricity; small-bandgap metals are good conductors, and the opposite applies to insulators1. Adapted from [S1].

In this bandgap spectrum of conductors and insulators, graphene exists at an awkward place. Modeling the previously discussed π orbitals shows us that graphene is a “zero-bandgap semiconductor.” At special points, the gap between the conducting and not conducting energy states goes to zero like in a metal, shown in Fig. 5. This lack of a bandgap (at these special points) is what makes graphene a semi-metal, or a zero-bandgap semiconductor. This means that graphene will usually conduct, making its use in logic-gate transistors (and other devices that require switching) difficult.





Figure 5. Graphene’s conducting and not conducting energy states touch at Dirac points, making it a good conductor of electricity. Ek on the box is the energy of electrons in graphene, while kx and ky components can be ignored, save for the inquisitive reader who is directed towards [S2]. Adapted from [S3].

As an aside for those interested in physics research, the truly interesting part about electrons’ behavior at the charge neutrality points of graphene is that they behave like quasi-relativistic particles called Dirac fermions while at room temperature. This enables the use of graphene as a room-temperature experimental laboratory to test theories in quantum electrodynamics (see [S4]), something never before thought feasible.



Bibliography

[1] A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nature Materials, vol. 6, no. 3, pp. 183–191, Mar. 2007.

[2] K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proceedings of the National Academy of Sciences, vol. 102, no. 30, pp. 10451–10453, Jul. 2005.

[3] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science, vol. 306, no. 5696, pp. 666–669, Oct. 2004.

[4] M. Abrahams, “Geim becomes first Nobel & Ig Nobel winner.” (2010, Oct. 5) Improbable Research. Available: improbable.com

[5] K. S. Novoselov, V. I. Fal′ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature, vol. 490, no. 7419, pp. 192–200, Oct. 2012.

[6] M. v. Meer, “Investing in Graphene: the Good, the Bad and the Ugly,” (2013, Aug. 29), SeekingAlpha Opinion. Available: seekingalpha.com (registration required)

[7] C. Busse et. al, “Strong inside, weak outside: Graphene on Ir(111),” (2011, Oct. 28), ESRF. Available: http://www.esrf.eu/news/spotlight/spotlight144/index_html

[8] B. Dumé, “Defective graphene is still cool,” (2012, Feb. 7), nanotechweb.org, Available: http://nanotechweb.org/cws/article/tech/52307

[9] J. Hedberg, “Free Science Images,” (2013), James Hedberg Creative Commons, Available: http://www.jameshedberg.com/img/samples/graphene-sheet-wavey.jpg

[10] F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nature Photonics, vol. 4, no. 9, pp. 611–622, Aug. 2010.

[11] T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nature Photonics, vol. 4, no. 5, pp. 297–301, Mar. 2010.

[12] K. Richter, courtesy of Ed McCann, “Transport in Graphene,” University of Regensburg. Available: esc.u-strasbg.fr/docs/2012/lectures/Richter_K.pdf

[13] J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, M. Muoth, A. P. Seitsonen, M. Saleh, X. Feng, K. Müllen, and R. Fasel, “Atomically precise bottom-up fabrication of graphene nanoribbons,” Nature, vol. 466, no. 7305, pp. 470–473, Jul. 2010.

[14] T. Ohta, “Controlling the Electronic Structure of Bilayer Graphene,” Science, vol. 313, no. 5789, pp. 951–954, Aug. 2006.

[15] R. R. Nair, W. Ren, R. Jalil, I. Riaz, V. G. Kravets, L. Britnell, P. Blake, F. Schedin, A. S. Mayorov, S. Yuan, M. I. Katsnelson, H.-M. Cheng, W. Strupinski, L. G. Bulusheva, A. V. Okotrub, I. V. Grigorieva, A. N. Grigorenko, K. S. Novoselov, and A. K. Geim, “Fluorographene: A Two-Dimensional Counterpart of Teflon,” Small, vol. 6, no. 24, pp. 2877–2884, Dec. 2010.

[16] C. Liu, Z. Yu, D. Neff, A. Zhamu, and B. Z. Jang, “Graphene-Based Supercapacitor with an Ultrahigh Energy Density,” Nano Letters, vol. 10, no. 12, pp. 4863–4868, Dec. 2010.

[17] Y. Wang, Z. Shi, Y. Huang, Y. Ma, C. Wang, M. Chen, and Y. Chen, “Supercapacitor Devices Based on Graphene Materials,” The Journal of Physical Chemistry C, vol. 113, no. 30, pp. 13103–13107, Jul. 2009.

[18] J. de la Fuente, “Graphene Supercapacitors – What Are They?” Graphenea, Available: http://www.graphenea.com/pages/graphene-supercapacitors#.UoSDFhqkr68

[19] M. F. El-Kady, V. Strong, S. Dubin, and R. B. Kaner, “Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors,” Science, vol. 335, no. 6074, pp. 1326–1330, Mar. 2012.

[20] Q. Zhou and A. Zettl, “Electrostatic graphene loudspeaker,” Applied Physics Letters, vol. 102, no. 22, p. 223109, 2013.

[21] S. Garaj, W. Hubbard, A. Reina, J. Kong, D. Branton, and J. A. Golovchenko, “Graphene as a subnanometre trans-electrode membrane,” Nature, vol. 467, no. 7312, pp. 190–193, Aug. 2010.

[22] B. Coxworth, “Graphene could speed up DNA sequencing,” (2010, Sep. 13), Available: http://www.gizmag.com/graphene-rapid-dna-sequencing/16360/

Supplement

[S1] C. Hepburn, “Britney Spears’ Guide to Semiconductor Physics: The Basics of Semiconductors,” self-published, available: britneyspears.ac/physics/lasers.htm

[S2] Schroder, Dieter KSemiconductor Material and Device Characterization. New York: Wiley, 1990. Print.

[S3] A. H. Castro Neto, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Reviews of Modern Physics, vol. 81, no. 1, pp. 109–162, Jan. 2009.



[S4] M. I. Katsnelson, and K. S. Novoselov, "Graphene: New bridge between condensed matter physics and quantum electrodynamic," Solid State Communications vol.143, no. 1, pp. 3-13, Jul. 2007

1 This picture oversimplifies what is really happening. The ‘conducting’ band is close enough to the truth – electrons, once properly excited, move about in what physicists call the conduction band and chemists call the lowest unoccupied molecular orbital. The ‘not conducting,’ or valence band, oversimplifies things in that what the valence band conducts is an imaginary particle, called a “hole,” which is essentially the lack of an electron at the position where an excited electron would jump to the conduction band. The inquisitive reader is directed to [S1] and [S2].




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