Nanotube Junctions Research Articles

Negative differential resistance in nanotube devices

Carbon nanotube junctions are predicted to exhibit negative differential resistance, with very high peak-to-valley current ratios even at room temperature. We treat both nanotube p-n junctions and undoped metal-nanotube-metal junctions, calculating quantum transport through the self-consistent potential within a tight-binding approximation. The undoped junctions in particular may be suitable for device integration.

Electrical transport through carbon nanotube junctions created by mechanical manipulation

Using an atomic force microscope we have created nanotube junctions such as buckles and crossings within individual single-wall metallic carbon nanotubes connected to metallic electrodes. The electronic transport properties of these manipulated structures show that they form electronic tunnel junctions. The conductance shows power-law behavior as a function of bias voltage and temperature, which can be well modeled by a Luttinger liquid model for tunneling between two nanotube segments separated by the manipulated junction.

Local analysis of the morphological properties of single-wall carbon nanotubes by Fresnel projection microscopy

Direct observations of free-standing single-wall carbon nanotubes (SWNTs), either as individual tubes or bundled in ropes, are performed using a Fresnel projection microscope (FPM). The analysis is done with the support of systematic numerical simulations of Fresnel diffraction images. The images of individual SWNTs are characterized by bright lines, while semitransparency wire fringe patterns are observed for thin ropes. Ropes with a higher number of individual tubes present the conventional Fresnel fringe patterns of an opaque wire. This differentiation in the FPM images between fringe patterns and bright line patterns allows for an easy detection of individual SWNTs. FPM also allows us to detect the presence of localized defects along SWNTs, and, in particular, the characterization of nanotube junctions. Although the exact structure of the junctions cannot be deduced presently from the images they, at least, indicate the presence of strong electric fields associated with the structural connections between the SWNTs.

Manipulation and Imaging of Individual Single-Walled Carbon Nanotubes with an Atomic Force Microscope

The tip of an atomic force microscope is used to create carbon nanotube junctions by changing the position and shape of individual single-walled carbon nanotubes on a SiO2 surface. With this manipulation technique, we are able to bend, buckle, cross (see Figure), and break nanotubes, and to unravel a nanotube “crop circle” into a single tube. Tapping-mode atomic force microscopy measurements of the height of a carbon nanotube on the surface always yield values smaller than the nanotube diameter. Variation of the scan parameters shows that this is due to a tapping deformation by the tip. The tapping deformation of manipulated nanotube crossings and buckles is discussed as well.

Crossed nanotube junctions

Junctions consisting of two crossed single-walled carbon nanotubes were fabricated with electrical contacts at each end of each nanotube. The individual nanotubes were identified as metallic (M) or semiconducting (S), based on their two-terminal conductances; MM, MS, and SS four-terminal devices were studied. The MM and SS junctions had high conductances, on the order of 0.1 e(2)/h (where e is the electron charge and h is Planck's constant). For an MS junction, the semiconducting nanotube was depleted at the junction by the metallic nanotube, forming a rectifying Schottky barrier. We used two- and three-terminal experiments to fully characterize this junction.

Carbon nanotube based magnetic tunnel junctions

Spin-coherent quantum transport in carbon nanotube magnetic tunnel junctions is investigated theoretically. A spin-valve effect is found for metallic, armchair tubes, with a magnetoconductance ratio ranging up to 20%. Because of the finite length of the nanotube junctions, transport is dominated by resonant transmission. The magnetic tunnel junctions are found to have distinctly different transport behavior depending on whether or not the length of the tubes is commensurate with a 3N+1 rule, with N the number of basic carbon repeat units along the nanotube length.

Relation between transmission rates and the wave functions in carbon nanotube junctions

Electron transmission and wave functions through junctions with a pair of a pentagonal defect and a heptagonal defect connecting two metallic carbon nanotubes are analyzed by the analytical calculation with the effective-mass equation. The energy region $|E|<{E}_{c}$ is considered where the channel number is kept to two. Close relation between the transmission rate and the wave function is found; the transmission rate is given by the inverse squared absolute value of the wave function. The dependence of the transmission rates on the energy and on the size of the junction is clearly explained by the nature of the wave function. Though the wave function and the transmission rate calculated by the tight-binding model agree well with the corresponding analytical results by the effective-mass approximation, the discrepancy becomes considerable when $|E|\ensuremath{\simeq}{E}_{c}.$ To study the origin of this discrepancy, an efficient numerical calculation method is developed with a generalized transfer matrix for the tight-binding model. Their numerical results are compared with the corresponding analytical ones and the results show that the origin of the discrepancy comes from the evanescent waves with the longest decay length in the tube parts.

Topological Effects on Conductance of Nanotubes

Electronic states in junctions of nanotubes with different circumferences are studied in an effective-mass approximation. The junction is characterized by boundary conditions which mix wave functions associated with K and K′ points. At ε=0, they decay linearly with the distance from the thicker nanotube, showing that the conductance decays with the junction length in proportion to its third power.

Transport through crossed nanotubes

In order to study the electronic properties of single-walled carbon nanotube junctions we have fabricated several devices consisting of two crossed nanotubes with electrical leads attached to each end of each nanotube. We correlate the properties of the junctions with the properties of the individual nanotubes: metal–metal, metal–semiconductor, and semiconductor–semiconductor junctions are all formed. We find that metal–metal SWNT junctions exhibit surprisingly high conductances of 0.1– 0.2 e 2/h . Semiconductor–semiconductor junctions also show significant linear response conductance. Metal–semiconductor junctions behave as p-type Schottky diodes. All the junction types can reliably pass currents of hundreds of nanoamps.

Degeneracy and repulsion between bands of periodic carbon nanotube junctions

The band structures of the periodic nanotube junctions are investigated by the use of effective mass theory (k·p approximation) and the tight binding model. The periodic junctions are constructed by the periodic introduction of defect pairs, consisting of a pentagonal defect and a heptagonal defect, into the carbon nanotube. We treat the periodic junctions whose unit cell is composed by two kinds of metallic nanotubes. The discussed energy region is near the undoped Fermi level where the channel number is kept to 2, so there are two bands. The degeneracy and repulsion between the two bands are determined only from symmetries.

Carbon nanotube intramolecular junctions

The ultimate device miniaturization would be to use individual molecules as functional devices. Single-wall carbon nanotubes (SWNTs) are promising candidates for achieving this: depending on their diameter and chirality, they are either one-dimensional metals or semiconductors1,2. Single-electron transistors employing metallic nanotubes3,4 and field-effect transistors employing semiconducting nanotubes5 have been demonstrated. Intramolecular devices have also been proposed which should display a range of other device functions6,7,8,9,10,11. For example, by introducing a pentagon and a heptagon into the hexagonal carbon lattice, two tube segments with different atomic and electronic structures can be seamlessly fused together to create intramolecular metal–metal, metal–semiconductor, or semiconductor–semiconductor junctions. Here we report electrical transport measurements on SWNTs with intramolecular junctions. We find that a metal–semiconductor junction behaves like a rectifying diode with nonlinear transport characteristics that are strongly asymmetric with respect to bias polarity. In the case of a metal–metal junction, the conductance appears to be strongly suppressed and it displays a power-law dependence on temperatures and applied voltage, consistent with tunnelling between the ends of two Luttinger liquids. Our results emphasize the need to consider screening and electron interactions when designing and modelling molecular devices. Realization of carbon-based molecular electronics will require future efforts in the controlled production of these intramolecular nanotube junctions.

Symmetry Effects on the Conductance of Nanotube Junctions

The ballistic conductance of various two-terminal and three-terminal carbon nanotube systems is calculated within the Landauer formalism. Using only metallic nanotubes as terminals, it is shown that only a subset of juctions topologies preserve the metallic function. This behavior is rationalized both in the two-terminal and three-terminal systems through symmetry considerations.

Supercurrents through single-walled carbon nanotubes

Proximity-induced superconductivity in single-walled carbon nanotubes below 1 kelvin, both in a single tube 1 nanometer in diameter and in crystalline ropes containing about 100 nanotubes, was observed. The samples were suspended between two superconducting electrodes, permitting structural study in a transmission electron microscope. When the resistance of the nanotube junction is sufficiently low, it becomes superconducting and can carry high supercurrents. The temperature and magnetic field dependence of the critical current of such junctions exhibits unusual features related to their strong one-dimensional character.

Controlled growth and electrical properties of heterojunctions of carbon nanotubes and silicon nanowires

Nanometre-scale electronic structures are of both fundamental and technological interest: they provide a link between molecular and solid state physics, and have the potential to reach far higher device densities than is possible with conventional semiconductor technology1,2. Examples of such structures include quantum dots,which can function as single-electron transistors3,4 (although theirsensitivity to individual stray charges might make them unsuitable for large-scale devices) and semiconducting carbon nanotubes several hundred nanometres in length, which have been used to create a field-effect transistor5. Much smaller devices could be made by joining two nanotubes or nanowires to create, for example, metal–semiconductor junctions, in which the junction area would be about 1 nm2 for single-walled carbon nanotubes. Electrical measurements of nanotube ‘mats’ have shown the behaviour expected for a metal–semiconductor junction6. However, proposed nanotube junction structures7 have not been explicitly observed, nor have methods been developed to prepare them. Here we report controlled, catalytic growth of metal–semiconductor junctions between carbon nanotubes and silicon nanowires, and show that these junctions exhibit reproducible rectifying behaviour.

Band Structures of Periodic Carbon Nanotube Junctions and Their Symmetries Analyzed by the Effective Mass Approximation

The band structures of the periodic nanotube junctions are investigated by the effective mass theory and the tight binding model. The periodic junctions are constructed by introducing pairs of a pentagonal defect and a heptagonal defect periodically in the carbon nanotube. We treat the periodic junctions whose unit cell is composed by two kinds of metallic nanotubes with almost same radii, the ratio of which is between 0.7 and 1 . The discussed energy region is near the undoped Fermi level where the channel number is kept to two, so there are two bands. The energy bands are expressed with closed analytical forms by the effective mass theory with some assumptions, and they coincide well with the numerical results by the tight binding model. Differences between the two methods are also discussed. Origin of correspondence between the band structures and the phason pattern discussed in Phys. Rev. B {\bf 53}, 2114, is clarified. The width of the gap and the band are in inverse proportion to the length of the unit cell, which is the sum of the lengths measured along the tube axis in each tube part and along 'radial' direction in the junction part. The degeneracy and repulsion between the two bands are determined only from symmetries.

Geometry of Multi-Tube Carbon Clusters and Electronic Transmission in Nanotube Contacts

The geometry of general structures based on carbon multi-tube contacts is discussed and some characteristics of the electronic transport in a metal-semiconductor (6,0)–(5,1) nanotube junction are presented. A theoretic method allowing us to construct the structure of a multi-tube carbon cluster composed of two or more tubes of different characteristics is developed by introducing heptagonal and pentagonal defects in the hexagonal graphitic net. By defining the ‘strip’ concept, we propose a general classification and notation of these structures and develop a method to determine the indices of the outgoing tubes from the multi-tube structure. We also demonstrate that is always possible to connect two tubes of arbitrary indices with only one heptagon-pentagon pair, and the method to obtain the specific geometry of the two-tube union is presented. Electron packet movement in a (6,0)–(5,1) nanotube junction is analysed by numerical integration of the nonstationary Schrodinger equation in the π -electron tight-binding approximation, using the norm-conserving numeric scheme based on a Pade approach of the evolution operator. The method developed can be applied to a general contact of two arbitrary nanotubes.

Relations between global and local topology in multiple nanotube junctions

General topological rules determine the carbon ring structures in arbitrary ${\mathrm{sp}}^{2}$-bonded structures, particularly nanotube junctions.

Effective-Mass Theory of Carbon Nanotube Junctions

Electronic states in junctions of nanotubes with different circumferences are studied in an effective-mass approximation. The junction is characterized by boundary conditions which mix wave functions associated with K and K' points. The wave functions obtained analytically at e = 0 decay linearly with the distance from the thicker nanotube, showing that the conductance decays with the junction length in proportion to its third power.

Analysis of quantum conductance of carbon nanotube junctions by the effective-mass approximation

The electron transport through the nanotube junctions which connect the different metallic nanotubes by a pair of a pentagonal defect and a heptagonal defect is investigated by Landauer's formula and the effective mass approximation. From our previous calculations based on the tight binding model, it has been known that the conductance is determined almost only by two parameters,i.e., the energy in the unit of the onset energy of more than two channels and the ratio of the radii of the two nanotubes. The conductance is calculated again by the effective mass theory in this paper and a simple analytical form of the conductance is obtained considering a special boundary conditions of the envelop wavefunctions. The two scaling parameters appear naturally in this treatment. The results by this formula coincide fairly well with those of the tight binding model. The physical origin of the scaling law is clarified by this approach.

Carbon Nanotube Based Molecular Electronic Devices

Complex three-point junctions of single-walled carbon nanotubes are proposed as building blocks of nanoscale electronic devices. Both T- and Y-junctions, made up of tubes with differing diameters and chiralities, are studied as prototypes. All the proposed complex junctions have been found to be local minima of the total energy on relaxation with a generalized tight-binding molecular dynamics scheme.