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Introduction

Crossed nanotube Junctions M. S. Fuhrer, J. Nygård, L. Shih, M. Forero, Young-Gui Yoon, M. S. C. Mazzoni, Hyoung Joon Choi, Jisoon Ihm, Steven G. Louie, A. Zettl, Paul L. McEuen. Presentation by Alberto Caviglia & Enrico Costa for the course of Nanotecnologie 1 held by Prof. Ermanno Di Zitti.

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Introduction

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  1. Crossed nanotube JunctionsM. S. Fuhrer, J. Nygård, L. Shih, M. Forero, Young-Gui Yoon,M. S. C. Mazzoni, Hyoung Joon Choi, Jisoon Ihm,Steven G. Louie, A. Zettl, Paul L. McEuen Alberto Caviglia & Enrico Costa

  2. Presentation byAlberto Caviglia & Enrico Costafor the course ofNanotecnologie 1held by Prof. Ermanno Di Zitti Alberto Caviglia & Enrico Costa

  3. Introduction • SINGLE-WALLED carbon nanotubes (SWNTs) are nanometer-diameter cylinders consisting of a single graphene sheet wrapped up to form a tube. Since their discovery in the early 1990s, there has been intense activity exploring the electrical properties of these systems and their potential applications in electronics. Alberto Caviglia & Enrico Costa

  4. Growth of SWNT (1)(J. Phys. Chem. B, Vol. 103, No. 51,1999 pg 11246) • The principal methods for obtaining high-quality single-walled nanotube are arc discharge and laser vaporization. • Both methods involve evaporating carbon atoms from solid carbon sources at ≥3000 °C, which limits the scale-up of SWNTs. • Nanotubes synthesized by the evaporation methods are in tangled forms that are difficult to purify, manipulate, and assemble for building addressable nanotubes architectures. Alberto Caviglia & Enrico Costa

  5. Arc discharge(http://students.chem.tue.nl/ifp03/synthesis.html#_Toc33936434) • A direct current of 50 to 100 A driven by approximately 20 V DC creates a high temperature discharge between the two electrodes. • The discharge vaporises one of the carbon rods and forms a small rod shaped deposit on the other rod. Alberto Caviglia & Enrico Costa

  6. Laser vaporisation(http://students.chem.tue.nl/ifp03/synthesis.html#_Toc33936434) • The laser vaporisation apparatus used by Smalley's group is used to vaporise a graphite target in an oven at 1200 °C. Alberto Caviglia & Enrico Costa

  7. Growth of SWNT (2)(78 IEEE Transaction on nanotechnology, VOL. 1, N° 1, March 2002, pg.80) • (a) Schematic of a SWNT growing from a catalyst seed particle. • (b) Atomic force microscope images of a single nanotube device fabricated using electron beam lithography. Alberto Caviglia & Enrico Costa

  8. Chemical vapor deposition(J. Phys. Chem. B, Vol. 103, No. 51,1999,pg.11248) • Chemical vapor deposition methods have been very successful in synthesizing carbon fibers, filaments. • CVD synthesis of high-quality SWNTs is only recent by using methane as carbon feedstock and iron oxide nanoparticles supported on high surface area alumina as the catalyst. • It is found that methane is stable at the elevated growth temperatures without appreciable self-pyrolysis. Alberto Caviglia & Enrico Costa

  9. Methane importance(J. Phys. Chem. B, Vol. 103, No. 51,1999,pg.11248) • The methane stability prevents the formation of amorphous carbon that tends to cause catalyst poisoning and overcoating of the nanotubes. • The chemical and textural properties of the catalyst materials dictate the yield and quality of SWNTs. • The diameters of the SWNTs are dispersed in the range 0.7-5 nm with a peak at 1.7 nm. Alberto Caviglia & Enrico Costa

  10. SWNT image(J. Phys. Chem. B, Vol. 103, No. 51,1999, pg.11248) • On the left the TEM image of SWNTs synthesized in bulk. Alberto Caviglia & Enrico Costa

  11. SWNT purification methods (1)(“Fullerene Pipes” R.E. Smalley et al. Science 280, 1998 pg.1253) • In a typical procedure, a raw sample of nanotubes (8.5 g) was first refluxed in 1.2 liters of 2.6 M nitric acid for 45 hours. • Upon cooling, the solution was transferred to polytetrafluoroethylene centrifuge tubes and spun at 2400g for 2 hours. • The supernatant acid was decanted off, replaced by deionized water, and vigorously shaken to resuspend the solids, followed by a second centrifuge-decant cycle. Alberto Caviglia & Enrico Costa

  12. SWNT purification methods (2)(“Fullerene Pipes” R.E. Smalley et al. Science 280, 1998 pg.1253) • The solids were resuspended in 1.8 liters of water with 20 ml of Triton X-100 surfactant (Aldrich) and adjusted to pH 10 with sodium hydroxide. • The suspension was then transferred to the reservoir of a tangential flow filtration system (MiniKros Lab System; Spectrum, Laguna Hills, CA). • The cartridge inlet pressure was maintained at 6 psi. A control valve was added to the exit so that the outflow rate was restricted to 70 ml min-1. Alberto Caviglia & Enrico Costa

  13. SWNTs usage • Experiments and theory have shown that these tubes can be either metals or semiconductors, depending on their chirality and their electrical properties can rival, or even exceed, the best metals or semiconductors known. • Individual SWNTs may act as device such as field-effect transistors , single-electron-tunneling transistors or rectifiers. Alberto Caviglia & Enrico Costa

  14. Problems to solve • How can individual SWNTs be joined together to form multimedial devices and, ultimately, complex circuits ? • How can, in particular, SWNT-SWNT junctions, formed by nanotubes that lie across one another on a substrate, be used to solve the previous question ? Alberto Caviglia & Enrico Costa

  15. SWNT SWNT junctions • Consist of two crossed individual SWNT’s or small bundles (diameter<3nm) of SWNTs with four electrical contacts, one on each end of each SWNT or bundle. • This type of junction is easily constructed and, with the development of techniques to place nanotubes with precision on substrates, could be mass produced. Alberto Caviglia & Enrico Costa

  16. Image of the device • On the left we can see the atomic force microscope (AFM) image of a completed crossed nanotube device. • Two crossed SWNTs (green) interconnect the Cr/Au contacts (yellow). Alberto Caviglia & Enrico Costa

  17. Gate voltage(J. Phys. Chem. B, Vol. 103, No. 51,1999,pg.11248) • A gate voltage Vg can be applied to the substrate to change the charge density per unit length. Alberto Caviglia & Enrico Costa

  18. Dependence by gate voltage • Metallic SWNTs have a finite conductance that is nearly independent of Vg. • Semiconducting SWNTs are found to be p-type: • Conducting for Vg<0 • Insulating for Vg>0 • At room temperature the two type of SWNTs have different behavior . Alberto Caviglia & Enrico Costa

  19. SWNT composition • Crossed SWNT can be composed of: • Two metallic SWNTs (MM) • One metallic and one semiconducting (MS) • Two semiconducting SWNTs (SS) Alberto Caviglia & Enrico Costa

  20. MM junctions • In a MM junctions result that, if G is the conductance: G junction ≈ G individual tube Alberto Caviglia & Enrico Costa

  21. Mesure of the conductances • In order to measure the four-terminal conductances and so accurately determinate the junction conductance, current is passed, for example, into the 1->3 circuit and the contact 2 & 4 act as probe. Alberto Caviglia & Enrico Costa

  22. Landauer-Buttiker Formula (1)(78 IEEE Transaction on nanotechnology, VOL. 1, N° 1, March 2002, pg.78) • The two terminal Landauer-Buttiker formula states that, for a system with N 1-D channels in parallel: G= (Ne2/h)T, where T is the transmission coefficient for electrons through the sample. • For a SWNT at low doping levels such that only one transverse sub-band is occupied, N=4. Each channel is fourfold degenerate, due to spin degeneracy and the sublattice degeneracy of electrons in graphene. Alberto Caviglia & Enrico Costa

  23. Landauer-Buttiker Formula (2)(78 IEEE Transaction on nanotechnology, VOL. 1, N° 1, March 2002, pg.78) • The conductance of ballistic SWNT with perfect contacts (T=1) is then 4e2/h = 155 µS, or about 6.5 kΩ. • Two-terminal conductances of metallic SWNTs at room temperature can vary significantly, ranging from as small as ~ 6 kΩto many MΩ. • Most of this variation is due to variations in contact resistance between the electrodes and the tube. • The best contacts have been obtained by evaporating Au or Pt over the tube, often followed by a subsequent anneal. Alberto Caviglia & Enrico Costa

  24. Measured conductances • At 200K the slope of I-V shown in the figure corresponds to: G = 0.13 e2/h • Other MM junctions gave the following value : • G = 0,086 e2/h • G = 0,120 e2/h • G = 0,260 e2/h Alberto Caviglia & Enrico Costa

  25. Transmission probabability • The transmission probabilityfor the junction is: T = G/(4e2/h) • The previous values of G gave that: 0.02 <Tj < 0.06 • MM junctions make surprisingly good tunnel contacts, despite the extremely small junction area (on the order of 1 nm2). Alberto Caviglia & Enrico Costa

  26. Other configurations • For two SWMTs with wrapping indices (5,5) separated by the Van der Waals distance of 0,34 nm experiments gave: Tj ≈ 2 x 10-4 Alberto Caviglia & Enrico Costa

  27. Crossed junction composition (1) • If the nanotubes interact with the SiO substrate included, they deforms significantly at the junction. • In a following article (Structural Deformation and Intertube Conductance of Crossed Carbon Nanotube Junctions) is performed a study of the conductance as a function of the contact force. Alberto Caviglia & Enrico Costa

  28. Crossed junction composition (2) • In a crossed junction composed of SWNTs: • for a diameter of 1.4 nm, this contact force must be about 5 nN. • for a diameter of 5.5 nm, this contact force has been estimated to be about 15 nN • The junction geometry is determined by performing a constrained total energy minimization in a supercell, in which they fully relax the position of the atoms near the junction while fixing the center-to-center intertube distance at the boundaries to produce the desired contact force. Alberto Caviglia & Enrico Costa

  29. Crossed junction composition (3) • The structure needs to be accurate, since the interatomic in the experimental devices, they expect that the strong adhesion of the SWNTs to the SiO2 substrate generates a significant contact force between the two crossed SWNTs. • In this case: Tj≈ 0,04 Alberto Caviglia & Enrico Costa

  30. Charge density in MM SWNTs • The charge density in the contact region became sizeable as the nanotubes became closer and more deformed, resulting from a significant overlap of intertube wave function. Alberto Caviglia & Enrico Costa

  31. SS junctions (1) • The measurement of SS junctions are complicated by the often very resistive contacts to semiconducting SWNTs. • The SS junction, like MM junctions, make relatively good tunnel contacts. Alberto Caviglia & Enrico Costa

  32. SS junctions (2) • The two terminal conductances of SS junctions measure at 200 K give: • G = 0.011 e2/h • G = 0.06 e2/h • In the figure on the left is represented the higher measure with open circles. Alberto Caviglia & Enrico Costa

  33. MM & SS comparison • In the two figures are represented the expected band structures near the junctions of the MM & SS. • Both junctions are expected to have a finite density of states available for tunneling on either side of the junction. Alberto Caviglia & Enrico Costa

  34. MS junctions (1) • In this case charge transfer at the junction between a dropped semiconducting SWNT and a metallic SWNT is expected to form a Schottky barrier. • Semiconducting & metallic SWNTs both share the same graphene band structure. Alberto Caviglia & Enrico Costa

  35. MS junctions (2) • The Fermi level EF of the metallic SWNT should align within the band gap of the semiconducting SWNT at the junction, depleting the doping of the semiconducting SWNT at the junction. • EF far for the junction is in the valence band of the semiconducting SWNT. Alberto Caviglia & Enrico Costa

  36. Total barrier transmission probability • The depletion region in the semiconducting SWNT associated with the Schottky barrier represent an additional tunneling barrier. • The total barrier transmission probability is given by: TMS = Tj Td where: • Td is the transmission probability for tunneling through the depletion region to the location of the metal SWNT • Tj is the probability of tunneling between the SWNTs Alberto Caviglia & Enrico Costa

  37. MS conductance (1) • The I-V curves for two MS junctions, measured at a temperature of 50 K and Vg = -25 V is shown in the figure. • The low-bias conductances are for both devices: TMS ≈ 2 x 10-4 Alberto Caviglia & Enrico Costa

  38. MS conductance (2) • So if Tj = 0.04 (as the MS case) then must be: Td = 5 x 10-3 • This is in agreement with a recent calculation by Odintsov and a corresponding depletion width of 7 nm, for a similar doping level. Alberto Caviglia & Enrico Costa

  39. MS I-V characteristics • The I-V characteristics of the two MS devices are here shown over an expanded bias range. • The dotted lines are linear fits to the forward bias data (bias applied to the semiconducting SWNT). Alberto Caviglia & Enrico Costa

  40. Forward bias comportament (1) • The conductance grows with increasing bias and is greater for positive biases applied to the semiconducting SWNT than for negative biases. • The forward bias I-V curve saturates to a linear behavior. Alberto Caviglia & Enrico Costa

  41. Forward bias comportament (2) • The V intercept of the linear region gives a measure of the barrier height for the two devices: Ebarrier1 = 190 meV Ebarrier2 = 290 meV • This value agrees with the expected value for 1 to 1.5 nm semiconducting SWNTs : Ebarrier = Eg/2 500 meV<Eg<700 meV So: 250meV<Ebarrier<350 meV Alberto Caviglia & Enrico Costa

  42. Reverse bias comportament • Reverse biases increase the Schottky barrier, but because the depletion region is small, tunneling still occurs through the barrier and leads to a measurable current flow that increase with increasing reverse bias. Alberto Caviglia & Enrico Costa

  43. G through a semiconducting SWNT (1) • As shown in the figure (bias = 0), carriers charge in the depletion region in the semiconducting SWNT must pass a barrier twice as wide as in tunneling to the metallic SWNT. Alberto Caviglia & Enrico Costa

  44. G through a semiconducting SWNT (2) • The semiconducting SWNT contains two barriers, each with transmission probability Td, corresponding to the depletion regions in the semiconducting SWNT on either side of the metallic SWNT. • The total direct transmission through the semiconducting SWNT is then: Ts ≈ T2d Alberto Caviglia & Enrico Costa

  45. Measure of Ts (1) • To determinate Ts, excluding the process that involve the metal, it used the device geometry shown in the figure. • A voltage V was applied to one end of the semiconducting SWNT in a MS device. Alberto Caviglia & Enrico Costa

  46. Measure of Ts (2) • The other end was grounded through a current-measuring amplifier. • The metallic SWNT was grounded through a second amplifier to measure IM Alberto Caviglia & Enrico Costa

  47. Determination of Td value • The linear response conductance across the semiconducting SWNT is 4.3 nS, corresponding to a transmission probability Ts = 2.8 x 10-5. • This indicates that: Td≈ (Ts)1/2≈ 5.3 x 10-3 in excellent agreement with the two-terminal result obtained earlier: Td = 5.3 x 10-3 Alberto Caviglia & Enrico Costa

  48. Three-terminal behavior (1) • The test circuit is the same of the determination of Ts. • Two cases are possible: • Vbias <0 : the barrier to holes will remain intact, because the metallic SWNT remains at roughly the same potential as the grounded end of the semiconducting SWNT. Alberto Caviglia & Enrico Costa

  49. Three-terminal behavior (2) • Vbias >0 : the potential difference between the metallic and semiconducting SWNT is greater than the barrier height, holes may pass the barrier and current will flow through the semiconducting SWNT Alberto Caviglia & Enrico Costa

  50. Relation between Is and Vbias • For -700mV <Vbias< 700mV the current from the semiconducting SWNT is approximately 100 times greater. • The direction of the rectification is determined by the contact of the semiconducting SWNT to which the metal SWNT is connected. Alberto Caviglia & Enrico Costa

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