An Introduction to Carbon NanotubesJohn [email protected] of TennesseeSolid State IIDr. DagottoSpring2009March 24, 2009AbstractThis paper will introduce many of the interesting aspects of car-bon nanotubes. It will give an overview of the geometry, metallicity,physical properties, transport and applications of carbon nanotubes.1 IntroductionNanomaterials are a fairly new and fascinating subject in physics. The proto-typical subjects to study are the carbon based materials. Carbon nanotubesare the high aspect ratio carbon based nanomaterial. Carbon nanotubes canbe classified into two major groups. Single-wall carbon nanotubes (SWCNT)can be thought of as a single sheet of graphite, also known as graphene, rolledup into a cylinder. Multi-walled carbon nanotubes (MWCNT), on the otherhand, can be thought of as several sheets of carbon stacked on each otherthat roll up together into a cylinder.2 HistoryThe discovery of Carbon nanotubes is somewhat contriversial. The discoveryof SWCNT is pretty clear. There were two papers submitted to Nature1Figure 1: A roll up vector is defined by (n,m). It defines the type of Carbonnanotube and tell us something about its metallicity and chirality. Picturedis an armchair, zigzzag and chiral nanotube.independently in 1993 by Iijima and Ichihashi and Bethune et al. fromIBM. The controversy begins when considering MWCNTs. In 1991 Iijimabrought MWCNTs to the attention of the scientific community at large, butin 1952 in the Jurnal of Physics and Chemistry of Russia, Radushkevich andLukyanovich reported TEM images of hallow nanodiameter carbon fibers.The problem was that during the Cold War Western scientists would nothave had this report and it was only published in Russian. It is somewhatunclear who should get the credit for discovering CNTS[1].3 GeometryIt is important to be able to discuss the different ways carbon nanotubescan be rolled up. As one can see in see in Figure 3 you can define the waythe tube rolls up by two integers (n,m) that define a chiral vector Chthathave units√3aC−C, aC−Cbeing the carbon bond length 2.46˚A, and a chiralangle θ which can be defined as sin(θ) =√3m2√n2+m2+nm[2]. θ is confined to be0 ≤ θ ≤ 30◦.A zigzag carbon nanotube is one that is of the form (n,0) and a armchairnanotube is one of the from (n,n). All other carbon nanotubes are called2Figure 2: Carbon nanotubes of different chiral angles shown in profile. Pic-tured is an armchair, zigzag and chiral nanotube. Notice that the carbonsites line up differently.[3].chiral nanotubes. You can see in Figure 3 the way in which the carbonatoms line up in profile is different depending on the chiral angle. Anotherimportant feature the chiral vector reviles is the metallicity. If n-m is divisibleby 3 then the carbon nanotube is a metal otherwise it is a semiconductor[2].4 Physical PropertiesCarbon nanotubes have some amazing physical properties. These SWCNTcan be spun together to create ropes. The elastic and shear modulus of thesematerials have been studied and the reports are noteworthy. The reducedelastic modulus, Er, and shear modulus, G, where measured as a functionof radius of different SWCNT ropes. The ropes were cast over a porousmembrane. An AFM is then used to apply a force to the rope over one ofthe pores. This force and the amount the rope is displaced is measured.A simple model would treat the ropes as noninteracting tubes but thiswas found to be incorrect. This assumption led to unrealistically large elasticmoduli. This insinuates that there is significant shear even when bending.The carbon nanotube ropes seemed to have large Er≈ 1T P a but a much3Figure 3: SWCNT rope is cast over a porous membrane and probed withAFM tip. Used to determine physical properties of CNT rope[4].smaller than expected G ≈ 1GP a. The elastic modulus is much larger thanmost conventional materials but the shear modulus is not very good[4].5 TransportThe electrical transport properties of carbon nanotubes are also very inter-esting. First one could consider the metallic tubes. It has been reportedthat a large number of sturcturally similar armchair carbon nanotubes, allof which much be metallic because n − m = 0, could be produced. Theindividual SWCNTs then had their transport properties measrued using afour point probe. It was interesting to note that the conductance seemedto have a strong peak that decreased with temperature. This is a strangebehavior that implies that the conduction took place in a single molecularorbital. This molecular orbital would then have to stratch the length of therope, 140nm, and shows that the electrons are not stronly localized eventhough the SWCNTs are strongly one dimensional.Another interesting application for carbon nanotubes is in the produc-tion of molecular field-effect transistors. As one can see from figure citegatethe MWNT or SWNT is laid across the usual transistor substrate. Withthe SWCNT transistors the source-drain current drastically decreases with4Figure 4: Reduced elastic modulus and shear modulus as a function of roperadius[4].Figure 5: Strongly temperature dependent conductance peak consistant withsingle molecular orbital transport. Shows that the CNT does not have con-tineous density of states and therefore conduction is done by nonlocalizedelectrons in single molecular orbital[5].5Figure 6: Make up of molecular transistor using CNT to transport current[6].increasing gate-voltage showing that the device works as a field-effect tran-sistor and that the carriers are holes.Also as you can see from Figure [?] the conductance of the transistorchanges about 5 orders of magnitued over the measured gate voltages.Next MWNT devices were measured. This was less successful but it didshow some promise when the MWCNT collapesed as can be seen in Figure[?]. Clearly nanotubes can be used to make field effect transistors[?].6 seperationOne challenge to using carbon nanotubes in industrial applications is theproduction of a single species of nanotubes. An interesting way to do this isto use the difference in density between the species to seperate them. Usingultracentrifugation Arnold et.al were able to seperate SWCNTs such thatmore than 97% of the SWCNTs are within 0.02nm of each other in diameter.Diameter correlates to chiral angle so this technique should allow one toisolate a specific species of SWCNTs[7].6Figure 7: This figure shows the increase in current with gate voltage andthe drastic change in conductance