A brief paper I wrote recently on the basics of carbon nanotubes; a fascinating idea to use them in electronics:

New discoveries are always exciting.  Since the discovery of carbon nanotubes (CNTs) nearly 20 years ago, we have learned a great deal about the characteristics and applications of them.  The precise history of CNT is a bit grey, but Sumio Iigima from Japan has been credited with discovering them in 1991 (‘History of…’).  However, some say that Morinoby Endo had prepared samples of carbon nanotubes for his PhD in the 1970′s in the United States (Davies, A.G., PPT).  At the time, Iigima and others knew very little about the implications of CNTs.  Regardless, the characteristics that they carry are very interesting and may eventually have a significant impact on the way we live our lives.

Carbon nanotubes are basically made of folded graphene (a single graphite layer) layers, which are sheets of carbon atoms arranged into a hexagonal lattice.  They are considered to be 1D conductors, which means the electrons passed through them only move in the direction of the tubes axis, and the momentum is quantized as they move around the tube.  Because of this, the electrons experience many quantum effects.  CNTs have periodic boundary conditions in the circumferential direction, meaning that the electron wave functions match up nicely as you go once around a tube.  Additionally, CNTs can be single-walled (SWNT) or multi-walled (MWNT).  As the names suggest, SWNT consist of one layer folded into a tube, while MWNT consist of multiple shells.  Depending on the way the layers are folded together, as well as the size (diameter) of the CNT, the electrical properties will vary significantly (see below).  The CNTs are capped with fullerene (made entirely of carbon) sphere-like structures.  These structures that cap the CNTs are known as ‘buckyballs’ (Harris, Carbon…).  Since the way CNTs are folded can be controlled, we have great control over the electrical properties that a specific CNT will have. This is what makes the CNT so interesting and powerful.  Additionally, the CNTs are quite strong, hard, and elastic.  Since CNTs are on a nanometer (1×10^-9) scale, it is hard for us to put their strength into perspective.  Assuming that a CNT was blown up to have a cross-sectional area of 1 square milimetetr, it would be able to withstand a tensile force of over 13,000lbs (MenFeng, Yu). The facinating part of this is that even though they have this strength, they can still be manipulated to their desired positions, which is incredibly powerful and intriguing to physics and electronic engineers around the world.

A key characteristic of CNTs is that they are made of only one kind of atom, carbon.  Additionally, they are made of only one kind of bond, sp², and CNTs have a simple periodic lattice (stacked hexagons) in which each atom is joined to three neighbours (graphite) (Harris, Carbon…).

One of the most powerful things about CNTs is that we can manually change the way the tube conducts, based off the way the CNT was created.  Conductivity depends on orientation of nanotube, the wrapping angle of the nanotube, and the size of the nanotube.  In order to describe the way this works, we must first introduce a notation which allows us to discuss the orientations of folded CNTs (the way the a CNT is wrapped).  By looking at one hexagonal graphene lattice, you can define 2 vectors which are equal in length, but point in different directions (see Figure 1 below).  These allow any lattice point to be referenced with respect to any other by a vector <A, B> (assume 2-dimensional).

Figure 1: Vectors A and B are used to denote the different types of CNTs that can be made, and allow for analysis of its electrical properties.
These vectors can then be used as a coordinate system to locate different locations on the nanotube.  When a sheet is wrapped into a tube, a point of contact between the 2 ends of the sheet is picked.  Now image unwrapping the tube into a sheet.  This notation basically references the point on a tube into 2 points on the sheet.  Using these 2 vectors, you can determine how the CNT was wrapped, and hence determine its electrical properites.  These are 3 types of vectors which are used to describe a CNT, and they each have different electrical properties (Saito, Dresselhaus, M. Dresselhaus, 39-41).

The first type of vector is called a zigzag.  Zigzag vectors take the form <A,0>, meaning there are ‘A’ carbon hexagons around the circumference of the tube, but no helicity.  In other words, since the B component of the vector is 0, the 2 points are perfectly horizontal to each other (see Zigzag in Figure 2 below).  For example, <11,0> represents the zigzag below: 

Figure 2 (above): Shows the different types of vectors used to reference 2 points on a “unrolled” nanotube. (image taken from {Davies, A.G., PPT})

Because of the way we defined our vectors A and B, the <A,B> profile carries a “zig zag” shape (as shown in Figure 2), hence why that <A,0> vector is called a zigzag.

Another type of vector used which analyzing CNTs is called an armchair.  An armchair vector takes the form <A,B>, where A=B.  As shown in Figure 2, an armchair vector also has no helicity, and is called an “armchair” because of the way the lattices appear when the vector takes the armchair form.  The angle between the zigzag and armchair vectors is 30 degrees, which is phi+theta in Figure 2.

The last type of vector is a vector that is neither a zigzag or armchair, and it is called a chiral vector.  It carries a form of simply <A,B>, where B does not equal 0 and A does not equal B.  Unlike the zigzag or armchair vectors, a tube that has a chiral vector profile is somewhat of a helix.

In order to determine whether a CNT is a metal or a semiconductor, we need to analyze the characteristics of the vectors that define them (armchair, zigzag, or chiral).  Armchair (A=B) CNTs have electron states at the Fermi Energy, and are therefore metallic (Davies, A.G., PPT).  Chiral and zigzag tubes will be metallic if A-B is a multiple of 3 (i.e. <9,6>, which represents a chiral vector).  Similarly, chiral and zigzag tubes are semiconducting if A-B is not a multiple of 3 (i.e. chiral vector <4,5>).

The energy gap (distance between top of valance band and bottom of conduction band) of CNTs is dependent only on the tube diameter, as shown in the equation below:
Energy Gap = (2*X*Y)/D , where X is a constant representing the carbon tight-binding overlap energy, Y is the distance to the nearest neighbour (roughly 1.42 angstroms), and D is the tube diameter (Davies, A.G., PPT).  For CNT semiconductors, there energy gaps are typically quite small (~0.5 eV).

To put these conductivity characteristics into perspective, armchair and other metallic CNTs can have a current density upwards of 4×10^9 amps per square centimeter.  Since one amp is roughly 6.24×10^18 electrons passing through a point in one second, this means that CNTs can pass nearly 2.5×10^28 electrons per second through them.  This is roughly 1,000 more than that of copper (Meo, S.B.).

Many studies have been done on the current and voltage characteristics of CNTs.  As shown in figure on the left, the current/voltage curves fit into 3 categories based off their current/voltage forms.  The plots labeled no. 1-4 show a small level-off at 0V, and range from 0.40-1.0 nanoAmps (nA – 10x-9 amps).  Plots 5, 6, and 7 show a more linear system near 0V, with 7 being the most linear of the 3.  Plot no. 8 shows a the most linear of them all.  As stated in the figure, plots 1-6 are chiral, 7 is zigzag, and 8 is classified as armchair (based on its vector representation).  The CNTs used in plots 1-4 are semiconductors, while plots 5-8 are metallic.  The more plateaued the plot is near 0V, the more ohmic the CNT is, and hence it is likely to be metallic.  Conversely, non-ohmic plots, such as 1-4 are likely to be semiconductors.

Contrary to what you may think, we cannot use V=IR to determine the resistance of these nanotubes.  Perfect metallic CNTs can experience ballistic conduction in which the electrons have no impedance (electrons don’t scatter along the tube) (Davies, A.G., PPT).  They are not quite superconductive however due to the Meissner Effect (no magnetic field in the superconductor) not occuring in the CNT material (Rohlf, Modern Physics).  The resistance is therefore determined by the contacts to the 1-dimensional system (Davies, A.G., PPT).

The potential of CNTs is endless.  In one experiment, a SWNT was used to create a transistor in which a single electron was used to create the digital swtich ((Postma, Teepen, Yao, Gifonia, and Dekker 76-79).  This was done at room temperature, which makes it application much more realistic.  Simply by attaching leads to CNTs which have specific properties (semiconducting/metallic), electronic devices can be created.  Metallic and semiconducting CNTs have been made into transistors (McEuen 15,17) (Martel, 2447-449).

In Trans et al., Nature 393 (Davies, A.G., PPT), researchers used a gate electrode to alter whether the CNT was metallic or semiconducting.  To create this, a semiconducting SWNT was placed on three Pt electrodes, and the the three electrodes were placed on a silicone dioxide substrate.  The silicone acted as a gate electrode which altered the electronic properties (current/voltage characteristics) between the tube and the contacts (Davies, A.G., PPT).

Additionally, CNTs have been used to create solar cells (New Jersey Institute of Technology).  The CNTs capped with buckyballs trapped electrons, and then sunlight was added to excite polymers around the CNT which made the electrons in the CNT flow (creating current).

Researchers at MIT used CNTs to create batteries, which could potentially power cars and other electronic devices (Trafton 1,5).  Utilizing these CNTs made the batteries more efficient (much lighter, and allowed energy to transfer faster).

There is no doubt that CNTs have a significant place in the electronic engineering industry.  The 21st century may very well be shaping up to be a carbon electronic based century as electronics begin to go quantum.

Works Cited:

Davies, A.G. , Molecular Electronics, ppt, Univeristy of Leeds, February, 2010.

Harris, Peter. “Carbon nanotube science and technology.” Carbon Nanotube Page. Centre for Advanced Microscopy, 01 Mar 2007. Web. 15 Mar 2010. <http://www.personal.rdg.ac.uk/~scsharip/tubes.htm>.

Martel, R., T. Schmidt, H.R. Shea, T. Hertel, and Ph. Avouris. “Single- and multi-wall carbon nanotube field-effect transistors.” Applied Physics Letters. 73.17 (1998): 2447-449. Print.

McEuen, Paul. “Carbon-based Electronics.” Nature 07 May 1998: 15,17. Print.

Meo, S.B.; Andrews, Rodney (2001). “Carbon Nanotubes: Synthesis, Properties, and Applications”. Crit. Rev. Solid State Mater. Sci. 26: 145. doi:10.1080/20014091104189.

New Jersey Institute of Technology. “New Flexible Plastic Solar Panels Are Inexpensive And Easy To Make.” ScienceDaily 19 July 2007. 21 March 2010 <http://www.sciencedaily.com­ /releases/2007/07/070719011151.htm>.

Postma, Henk, Tijs Teepen, Zhen Yao, Milena Gifonia, and Cees Dekker. “Carbon Nanotube Single-Electron Transistors at Room Temperature .” Science Magazine 293.5527 (2001): 76-79. Web. 21 Mar 2010. <http://www.sciencemag.org/cgi/content/full/293/5527/76>.

Rohlf, James William, Modern Physics from a to Z0, Wiley 1994

Saito, Riichiro, G. Dresselhaus, and M.S. Dresselhaus. Physical properties of carbon nanotubes. Illustrated, reprint. 1. London, UK: Imperial College Press, 1998. 39-41. Print.

“The History of Carbon Nanotubes.” Intro to Nanotechnology. DigitalNature, 17 Jun 2009. Web. 15 Mar 2010. <http://nanogloss.com/nanotubes/the-history-of-carbon-nanotubes-who-invented-the-nanotube/>.

Trafton, Anne. “New virus-built battery could power cars, electronic devices.” MIT Tech Talk 53.21 (2009): 1,5. Web. 15 Mar 2010. <http://web.mit.edu/newsoffice/2009/virus-battery-0402.html>.

Yu, Min-Feng; Lourie, O; Dyer, MJ; Moloni, K; Kelly, TF; Ruoff, RS (2000). “Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load”. Science 287 (5453): 637–640. doi:10.1126/science.287.5453.637. PMID 10649994

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