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Single-Walled Carbon Nanotube Electronics

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3Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138AbstractSingle-Walled Carbon Nanotube Electronics Paul L. McEuen1, Michael Fuhrer2, and Hongkun Park3 1Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853 2Department of Physics, University of Maryland, College Park, MD 20742 3Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138 AbstractSingle walled carbon nanotubes (SWNTs) have emerged as a very promising new classof electronic materials. The fabrication and electronic properties of devices based onindividual SWNTs are reviewed. Both metallic and semiconducting SWNTs are found topossess electrical characteristics that compare favorably to the best electronic materialsavailable. Manufacturability issues, however, remain a major challenge.To be published in the inaugural issue of the IEEE Transactions on Nanotechnolgy (2002)I. INTRODUCTIONSingle-walled carbon nanotubes (SWNTs) arenanometer-diameter cylinders consisting of a singlegraphene sheet wrapped up to form a tube. Since theirdiscovery in the early 1990s[1, 2], there has beenintense activity exploring the electrical properties ofthese systems and their potential applications inelectronics. Experiments and theory have shown thatthese tubes can be either metals or semiconductors, andtheir electrical properties can rival, or even exceed, thebest metals or semiconductors known. Particularlyilluminating have been electrical studies of individualnanotubes and nanotube ropes (small bundles ofindividual nantoubes). The first studies on metallictubes were done in 1997[3, 4] and the first onsemiconducting tubes in 1998[5]. In the interveningfive years, a large number of groups have constructedand measured nanotube devices, and most majoruniversities and industrial laboratories now have at leastone group studying their properties. These electricalproperties are the subject of this review. The datapresented here are taken entirely from work performedby the authors (in collaboration with other researchers),but they can be viewed as representative of the field.The remarkable electrical properties ofSWNTs stem from the unusual electronic structure ofthe two-dimensional material, graphene, from whichthey are constructed[6, 7]. Graphene - a single atomiclayer of graphite - consists of a 2D honeycombstructure of sp2 bonded carbon atoms, as seen in Figure1(a). Its band structure is quite unusual; it hasconducting states at Ef, but only at specific points alongcertain directions in momentum space at the corners ofthe first Brillouin zone, as is seen in Fig. 1(b). It iscalled a zero-bandgap semiconductor since it is metallicin some directions and semiconducting in the others. Ina SWNT, the momentum of the electrons movingaround the circumference of the tube is quantized,reducing the available states to slices through the 2Dband structure, is illustrated in the Fig. 1(b). Thisquantization results in tubes that are either one-dimensional metals or semiconductors, depending onhow the allowed momentum states compare to thexyaEkxkybmetallicsemiconductingEfEfEEkxBZ boundaryBZ boundarycdxyaxyaEkxkybEkxkybmetallicsemiconductingEfEfEEkxBZ boundaryBZ boundarycdmetallicsemiconductingEfEfEEkxBZ boundaryBZ boundarycdFigure 1. (a) The lattice structure of graphene, ahoneycomb lattice of carbon atoms. (b) The energy ofthe conducting states as a function of the electronwavevector k. There are no conducting states exceptalong special directions where cones of states exist.(c), (d) Graphene sheets rolled into tubes. Thisquantizes the allowed k’s around the circumferentialdirection, resulting in 1D slices through the 2D bandstructure in (b). Depending on the way the tube isrolled up, the result can be either a metal (c) or asemiconductor (d).preferred directions for conduction. Choosing the tubeaxis to point in one of the metallic directions results in atube whose dispersion is a slice through the center of acone (Figure 1(c)). The tube acts as a 1D metal with aFermi velocity vf = 8x105m/s comparable to typicalmetals. If the axis is chosen differently, the allowed k’stake a different conic section, such as the one shown inFig 1(d). The result is a 1D semiconducting bandstructure, with a gap between the filled hole states andthe empty electron states. The bandgap is predicted tobe Eg = 0.9 eV/d[nm], where d is the diameter of thetube. Nanotubes can therefore be either metals orsemiconductors, depending on how the tube is rolledup. This remarkable theoretical prediction has beenverified using a number of measurement techniques.Perhaps the most direct used scanning tunnelingmicroscopy to image the atomic structure of a tube andthen to probe its electronic structure[8, 9].To understand the conducting properties ofnanotubes, it is useful to employ the two-terminalLandauer-Buttiker Formula, which states that, for asystem with N 1D channels in parallel: G = (Ne2/h)T ,where T is the transmission coefficient for electronsthrough the sample (see for example ref. [10]). For aSWNT at low doping levels such that only onetransverse subband is occupied, N = 4. Each channel isfourfold degenerate, due to spin degeneracy and thesublattice degeneracy of electrons in graphene. Theconductance of a ballistic SWNT with perfect contacts(T = 1) is then 4e2/h = 155 µS, or about 6.5 kΩ. This isthe fundamental contact resistance associated with 1Dsystems that cannot be avoided. Imperfect contacts willgive rise to an additional contact resistance Rc. Finally,the presence of scatters that give a mean free path lcontribute an Drude-like resistance to the tube, Rt =(h/4e2)(l/L), where L is the tube length. The totalresistance is approximately the sum of these threecontributions, R = h/4e2 + Rc + Rt. In the sectionsbelow, we will analyze the conducting properties ofmetal and semiconducting nanotubes to infer thecontact resistances, mean free paths, conductivities, etc.We will concentrate almost exclusively on roomtemperature behavior. At low temeperatures, SWNTdevices exhibit a number of interesting quantumphenomena, including single-electron charging,quantum interference, Luttinger liquid behavior, and theKondo effect, but these are not of direct relevance tomost device applications. We therefore refer the readerto existing reviews for further discussion of thesetopics[11-13].The critical issues with


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