Electrical and mechanical properties of carbon nanotubes

Transcription

1 Research Review Electrical and mechanical properties of carbon nanotubes Leonard Burtscher February 2005 Carbon nanotubes show a variety of fascinating properties interesting for both basic physics research and industrial applications. By changing the wrapping angle the band gap is varied from a few ev to 0 ev making it possible to produce both semiconducting and metallic nanotubes from the same material. Being a single molecule, nanotubes have displayed never before seen values of tensile strength up to 150 GPa which is about 30 times higher than the tensile strength of steel. The most common fabrication methods arc discharge, laser ablation and Chemical Vapour Deposition (CVD) are introduced and their advantages and disadvantages discussed. The carbon nanotube field effect transistor (TUBEFET) is presented as one of the most promising applications of nanotubes in the near future. After the discovery of the C 60 buckminsterfullerene by Curl, Kroto and Smalley in 1985 [35] a lot of research has been undertaken on carbon structures. But it was only in 1991 that Sumo Iijima identified carbon nanotubes using an electron microscope [21]. A wide field of applications opened up almost instantly, from having the perfect material for proving theories about one dimensional (1D) materials to new possibilities for electronic devices as silicon devices are believed to be near their physical limit with regard to miniaturisation. 1 From Graphite to Nanotubes Wrapping up a monolayer of planar graphite also called graphene in the carbon literature results in a tubular structure known as single-walled carbon nanotube (SWNT). Nesting multiple SWNTs results in a multi-walled nanotube (MWNT). For the understanding of nanotube physics it is easier to first consider SWNTs and then add more layers. For the geometry of SWNTs see figure 1. The graphene is rolled up in such a manner that the point indicated by (0, 0) coincides with the point indicated by (8, 4). The ends of a nanotube can be open or capped with half a fullerene molecule as shown schematically in figure 2. The nanotube s diameter and helicity are uniquely defined by the chiral vector C which connects two crystallographically equivalent points on the graphene sheet. C = na 1 + ma 2 (1) where the a i are the hexagonal lattice vectors. The chirality of the nanotube is thus given by (n, m). The tube axis is always perpendicular to C. The chirality is described by the chiral angle θ, the angle between the zigzag (or sawtooth) direction (n, 0) and C; the angle between the zig-zag and the armchair direction is 30. Because of the honeycomb structure there are six definable angles. Usually θ 30 or equivalently n 1 n 2 n 1 (n 1 > 0) is chosen [11]. (n, 0) nanotubes are called zig-zag nanotubes, (n, n) nanotubes where C halves every other hexagon are referred to as armchair tubes. All other tubes are called chiral or helical tubes. The smallest nanotube possible is the (5, 5) armchair nanotube with tube diameter d = 0.39 nm as its cap is the smallest possible fullerene molecule, C 60. This nanotube can therefore be described as C 60+10j where for each j one armchair row of 10 carbon atoms is added. School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK; k lhb2@hw.ac.uk

2 2 Electrical Properties tube axis (0,0) θ zig-zag (9,0) a 1 chiral 90 a 2 armchair (8,4) C (5,5) Figure 1: Geometry of a carbon nanotube. By wrapping up graphene in such a manner that the two points labelled (0, 0) and (8, 4) and connected by the chiral vector C = na 1 + ma 2 coincide a carbon nanotube with chiral angle θ is produced. The a i are the hexagonal lattice vectors. The tube axis is always perpendicular to C as shown for the chiral tube (8, 4). A nanotube is thus uniquely specified by (n, m). The smallest possible nanotube is the (5, 5) armchair type nanotube. The smallest zig-zag nanotube, indicated by (9, 0) is also shown. given by d = C π = n2 + m 2 + nm a (2) π where the length of the unit vector a = 3 a C C = nm = nm. ac C is the graphite carbon-carbon distance. More on nanotube geometry and symmetry can be found in [32, 33]. 2 Electrical Properties Figure 2: Fullerene-derived tubules : Models of nanotubes and their fullerene caps. Here all the chiral vectors C lie in the up-down direction. (a) (5, 5) armchair nanotube, the smallest possible nanotube, capped by the smallest stable fullerene, C 60. (b) The smallest possible zigzag nanotube, (9, 0). (c) Chiral (10, 5) nanotube [32]. Generally the diameter of an (n, m) nanotube is Electronic Structure One of the most fascinating aspects of SWNTs is that their electrical nature depends sensitively on the chiral vector C in that little variations in C alter their band structure dramatically. Only a short time after the discovery of nanotubes [21] theorists predicted this property [11] but it took six more years until this could be proven experimentally [7], [24]. This is also probably the most important property of nanotubes with regard to applications as it allows for diffusion-free metal-semiconductor junctions a few atoms wide using just one material, carbon, and other fascinating applications (see section 5). To understand this behaviour the best starting point is to look at the electronic structure of 2D graphite as shown in figure 3. 2

3 2 Electrical Properties Figure 3: Energy dispersion relations for 2D graphite. Insert: high symmetry directions ΓMK. Graphite is an isolator except for electrons with k vectors crossing the K points [10]. Graphite is a so-called zero band gap material or semi-metal as conductance is only possible in those directions where the π and π orbitals overlap which is the case at the high-symmetry K points. In all other directions graphite can be considered an isolator. When wrapping up a graphene sheet to an SWNT the electron s k vector gets quantized in the circumferential direction because of the periodic boundary conditions of the nanotube. where q is an integer. k C = 2πq (3) 2n + m = 3q (4) For integer values of q the tubes are metallic, otherwise they are semiconducting. Therefore all armchair (n, n) tubes are metallic, zig-zag (n, 0) tubes are only metallic if n is a multiple of 3. So, if no chiral angle is preferred during production there should be twice as many semiconducting as metallic nanotubes which indeed is what has been observed, see figure 4 and [7]. Figure 4: Atomically resolved STM image of an individual SWNT. Linking the electronic strucure of an SWNT to their geometry has first been reported by Wildöeer [7] and Odom [24] in Here T is the tube axis, φ = 30 θ where θ is the chiral angle as defined above and H is a vector perpendicular to the armchair direction [7]. So substituting the k vector of the K high symmetry point into equation (3) leads to a condition for metallic nanotubes [10]: Figure 5: Energy gap versus tube diameter d. Fit (straight line) E gap = 2γ 0a C C/d with γ 0 = 2.5 ev, the nearest neighbour overlap integral, a C C = nm, the carbon-carbon atom distance, d is the tube diameter [25]. 3

4 3 Mechanical Properties For the semiconducting tubes the bandgap is expected to fall linearly with diameter E g 1 d (5) For SWNTs the theoretical limit of conductance is G SW NT = 4e 2 /h where e = As is the electron fundamental charge and h = Nms, Planck s quantum [29]. It can be seen in figure 7 that this limit is almost reached at low temperatures indicating ballistic electron transport. where the tube diameter d is defined by equation (2) [7]. This has been experimentally verified, see figure 5 and [25] for a summary of several studies. This even holds in the limit case d which is planar graphite where E g 0 which is a correct description for the zero bandgap material as mentioned above. Electrical conductance Generally surface states degrade the conductance of bulk semiconductors [29]. Nanotubes do not show surface states as their raw material graphite is 2D to start with and does not have chemically reactive bonds. Then, to get rid of the edges, nanotubes use the topological trick [29] of wrapping themselves up to form a cylinder which does not have any edges. Additionally the conductance was expected to be very high because in 1D structures the only way phonons can scatter electrons is backwards. The energy needed for backscattering in SWNTs is 150 mev [29] so not much backscattering was expected to happen at room temperature where kt 25 mev. Electron transport in nanotubes therefore is described as ballistic, i.e. the resistance of the nanotube does not depend on its length as the mean free path λ m is longer than the nanotube itself. λ m = 30 µm has been found by Berger et al. [6] which was much longer than the nanotube used. Figure 7: Differential conductance di/dv of a metallic SWNT as a function of voltage V. At low V differential conductance is near the theoretical value of 4e 2 /h [29], [9]. The corresponding value for the saturation current is 25 µa or even more impressively the current density j = A/cm 2 for a 1 nm tube. Saturation occurs because electrons emit phonons at high voltages that lead to backscattering [9]. Typical tube mobilities for CVD-grown tubes (see section 4) can be as high as cm 2 /Vs which is significantly higher than the mobility of a standard semiconductor like Si which has a mobility of 1350 cm 2 /Vs [23]. After the discovery of high-t c superconductivity in electron doped C 60 where transition temperatures of 117 K have been reached [30] there has been some research interest in nanotubes as superconductors. Recent measurements of the magnetic properties of nanotubes indicate that SWNT might be the longsought material for room-temperature superconductors [28, 27]. 3 Mechanical Properties Figure 6: Measuring differential conductance of an individual MWNT. The MWNT is contacted by four Au fingers from above, separation between the contacts is 350 nm [13]. Not only do carbon nanotubes have impressive electrical properties as described above but maybe even more intriguing special mechanical properties. Being only few nanometres in diameter nanotubes have recently been produced to lengths up to 100 metres [18] which makes them the highest aspect ra- 4

5 4 Fabrication of Nanotubes tio material available and therefore ideal to study the behaviour of 1D systems [26]. To determine the mechanical properties, a rope of SWNTs has been mounted between the tip of an AFM and the location where the SWNTs were grown and tensile strength was probed by removing the AFM tip slowly from the surface (see figure 8) [31]. nanotubes which could make macroscopic nanotube material almost as strong as nanotubes themselves. Figure 9: Small cracks propagate fast in conventional material (left); cracks in a hypothetical material made of carbon nanotubes would remain isolated (right). The overall material strength of a macroscopic material made of carbon nanotubes is expected to be almost as high as that of individual nanotubes. [34]. 4 Fabrication of Nanotubes Figure 8: SEM images of the tensile loading experiment by Yu et al. (a) A tensile-loaded rope of SWNT consisting of several individual tubes mounted between the tip of an AFM (top) and the location where the SWNTs were grown (bottom); (b) The attachment of the nanotube to the AFM tip; (c) The same SWNT rope, now broken; (d) The attachment is still fixed to the AFM tip after the rope has been broken [31]. Both theoretical calculations [12] and experiments on SWNTs [37] and MWNTs [31] resulted in a Young s modulus Y = TPa with a mean value of Y 1 TPa with lower values for SWNTs than for MWNT. For comparison, steel only has a Young s modulus of 200 GPa but its density is three times as high [19]. Similiarly high values are given in [37, 31, 19] for the nanotube s tensile strength of σ = GPa which beats steel with σ 0.4 GPa by far. Usually a macroscopic material is not as strong as its components as small cracks become bigger soon and eventually the material is torn apart as shown on the left hand side of figure 9. If a material consisted of several carbon nanotubes those elementary cracks would be isolated and would not propagate into other Several ways of producing carbon nanotubes have been established since their discovery in Depending on the desired type and purity of nanotubes highly sophisticated processes which are almost always followed by just as complicated purification techniques are facilitated. Many theories for nanotube growth have been suggested but none has been widely accepted yet. Therefore much research includes optimisation of yield and purity by changing fabrication parameters such as temperature, presence of catalysts, time, geometry of the production environment, magnetical and electrical field. The three best established families of fabrication methods are arc discharge, laser ablation and Chemical Vapour Deposition (CVD). Arc discharge MWNTs were discovered by Iijima using the arc discharge method which had already been in use for mass production of C 60 [21]. So it is not unlikely that nanotubes have been produced earlier but just have not been discovered before Iiijima took a closer look at the soot generated on the negative end of the carbon electrode using an electron microscope. In the arc discharge process two graphite rods are used as electrodes in an evaporated gas chamber. The chamber is then filled with an inert gas and an electric current of around 100 A is maintained at typically 20 V. Nanotubes then can 5

6 4 Fabrication of Nanotubes be found in the deposit formed on the cathode rod. Using pure graphite electrodes MWNTs are grown, using metal catalysts as anode dopants favours the growth of SWNTs, see figure 10. Advantages of the arc discharge process are the high quality of the nanotubes and the relatively simple set-up. More on nanotube growth in the arc discharge can be found in [15, 38]. The most important disadvantage is that nanotubes grown in the arc discharge have random sizes and therefore often need intense purification which in turn degrades the quality of the tubes [5, 14]. Figure 10: The arc discharge process. Doping the anode with metal catalysts leads to SWNT growth, using pure graphite electrodes produces MWNTs [5]. Laser ablation A very similar process to the arc discharge method is the laser ablation or vaporization process where a laser vaporises a block of graphite which condenses as nanotubes along the tip of a cooled collector, see figure 11. This process has been invented by R. Smalley s group in 1995 and improved the yield 1 from 15% to 50% [36]. In 2003 yields of about 70 % could be achieved [5]. Again, depending on dopants, either SWNTs or MWNTs are grown. This method is mainly used for producing high-quality SWNTs though because the required high-power laser is quite expensive [5] and cheaper methods to produce MWNTs (e.g. the arc discharge describe above) are available. Chemical Vapour Deposition (CVD) A different method of nanotube production is used in CVD. In this process a gas containing carbon, e.g. acetylene, HC CH, is heated up to several hundred degrees Celsius until it disintegrates and single reactive carbon atoms are generated. A substrate containing metallic catalytic atoms is used where the carbon atoms first build graphene sheets that wrap around the catalytic atoms to form carbon nanotubes. Patterns made of catalysts can be printed on the surface favouring growth of nanotubes in these regions so that nanobrushes, vertically standing nanotubes can be built, see figure 13 and [22]. Figure 11: Laser ablation is another method of producing carbon nanotubes. Here an Nd:YAG laser is used to vaporise graphite at 1200 C. Nanotubes form on the cooled catalytically doped collector [34]. Figure 12: Alcohol catalytic CVD (ACCVD) is one of the many different kinds of CVD techniques used to grow carbon nanotubes. ACCVD is of big interest to the industry as it allows for production of high quality nanotubes at low cost and can be scaled up easily. At operating temperatures < 600 C it is also compatible to established semiconductor techniques [5]. With yields up to 100 % and the good control of nanotube growth as well as the possibility for scaling it up for industrial production CVD is the most promising fabrication method although the quality of the nanotubes is often poor and selective growth of either SWNTs or MWNTs is not easy to guarantee. 1 i.e. the mass of carbon having formed nanotubes compared with the original mass of the carbon rod 6

7 5 Applications Figure 13: Nanobrushes, vertically standing rows of nanotubes, can be built by selectively printing catalysts and then growing nanotubes using CVD [22]. Fabrication issues seem to be the only reason why nanotubes are not already widely used for industrial applications and are still an important topic for nanotube research. 5 Applications Suggested applications for nanotubes include nanoelectronic devices such as heterojunctions [4] and transistors [8], sensors for mechanical stress [2], nano-electro mechanical machines [20] and energy storage [5] to name only a few of them. Even sciencefiction-like applications as a space-elevator [3] would theoretically be possible due to the enormous tensile strength of the nanotubes. A rope needed to build such an elevator would need to reach geosynchroneus orbit (ca. 36,000 km from the earth s surface) for the cable to stay in place. The only material known so far which could hold its own weight for such a length is carbon nanotubes. However, this will not happen anytime soon and much more literally down to earth applications could go to mass production soon once fabrication problems will be solved. One of these is the TUBEFET the carbon nanotube field emission transistor, first built by Tans et al. in 1998 [8]. Infineon technology demonstrated last year that they can build the world s smallest transistor with a diameter of just about 1 nm and a channel-length of only 10 nm: a TUBEFET [16]. In today s state-of-the-art semiconductor technology the typical gate length is 90 nm [17]. The smaller the device, the smaller the conductance and therefore higher clock rates can be achieved. Nanotube operation at 2.6 GHz was reported in 2004 by Li et al. [1] with potential scalability up to THz [8]. Figure 14: Two probe I V bias curves by Tans et al. Inset: Conduction at V bias = 0 as a function of V gate. The conductance through this single molecular transistor could be varied over at least six orders of magnitude [8]. 6 Conclusion Much has been achieved in both theoretical and experimental understanding of carbon nanotubes since their discovery in Electrical properties have been linked to the atomic structure and the predicted sensitive dependency on the chiral vector C could be proven experimentally. Very high values of tensile strength and Young s modulus have been found that have never been seen before. So carbon nanotubes are promising candidates for large-scale industrial applications. But fabrication issues remain critical for the future use of nanotubes. A process which is both cheap and guarantees selectivity (length, diameter, chirality) is still to be found. Also nanotubes are potentially harmful for humans (cf. the similar dimensions of asbestos) and more research needs to be done on this before using nanotubes in every-day devices. Considering the large number of research groups working on these problems worldwide combined with the potentially large industrial impact the chances for overcoming these problems are not bad and carbon could indeed become tomorrow s silicon. 7

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