Mid Sweden University

The electron transport in semiconducting zigzag carbon nanotubes containing vacancies is studied using the Monte Carlo method. The electronic band structure is derived from that of graphene using the zone folding method, and the phonon spectrum is obtained using a fourth nearest-neighbour force constant model. The scattering rates describing the electron-phonon interaction and the electron-vacancy interaction are both derived within the tight-binding formalism, and are calculated using Fermi's Golden rule. The steady-state drift velocity and the mobility for (13,0) and (10,0) nanotubes are calculated as functions of the electric field strength, density of vacancies and lattice temperature. We find that, apart from an expected overall reduction of the drift velocity (mobility), the effects of the vacancies are-fold: (1) the degree of levelling-off of the drift velocity as a function of the electric field-strength can be altered substantially by a high concentration of vacancies, and (2) the negative differential resistance disappears if the vacancy concentration is sufficiently high.

Electron-phonon and electron-defect scattering rates have been calculated within a tight-binding approach for semiconducting zigzag carbon nanotubes. The scattering rates for (5,0), (7,0), (10,0), (13,0) and (25,0) nanotubes have been investigated. The electron-phonon scattering rate shows both diameter and temperature dependence, and the dependence of the electron-defect scattering rate on nanotube diameter is similar to that of the electron-phonon scattering rate. Backscattering and forward scattering for electrons interacting with defects occur with equal probability at all energies. The importance of electron-defect scattering relative to electron-phonon scattering depends very much on the energy of the electron.

Electron transport in semiconducting zigzag carbon nanotubes is studied by solving the Boltzmann transport equation using the single-particle Monte Carlo technique. The electronic band structure is based on a standard nearest-neighbour tight-binding parameterisation, and the phonon spectrum is calculated using a fourth nearest-neighbour force constant model. The electron-phonon scattering probabilities are calculated within a tight-binding formalism. The steady-state drift velocities for the semiconducting zigzag nanotubes (8,0), (10,0), (11,0), (13,0), and (25,0) are computed as functions of electric field strength and temperature, and the results are analysed here. The results show the presence of negative differential resistance at high electric fields for some of the nanotubes. The drift velocity and the low field mobility reach a maximum value of and, respectively, for a (25,0) nanotube.

The energy dependence of the scattering rate for electrons interacting with phonons in semiconducting zig-zag carbon nanotubes has been investigated using a tight-binding method. Apart from the scattering rates, their components in terms of phonon emission, phonon absorption, backscattering and forward scattering have been determined. Results for (7, 0), (10, 0), (13, 0) and (25, 0) nanotubes at both room temperature and at 10K are presented and discussed. It is demonstrated that backscattering of the electron generally is more likely than forward scattering, and that phonon absorption can be comparable to, or even more important than, phonon emission in limited energy intervals. Furthermore, the phonons responsible for the main features in the scattering rates have been identified, and the similarities in the scattering rates between different nanotubes are clarified.

The electron transport properties of single walled carbon nanotubes are of fundamental importance for the development of carbon based nanotechnology. Carbon nanotubes can display both chemical and structural defects, which affect electronic states near the Fermi level. This is further complicated by the fact that the concentration of defects depends upon the method of synthesis. In this work, we have investigated both electron-phonon and electron-defect scattering in semiconducting zigzag carbon nanotubes by calculating and analyzing the quantum-mechanical scattering rates for these processes. One objective of this work is to give a theoretical limit for the concentration of defects at which electron-defect scattering rates would be comparable to the electron-phonon scattering rates.

Using a one-dimensional jellium model and standard beam theory we calculate the spring constant of a vibrating nanowire cantilever. By using the asymptotic energy eigenvalues of the standing electron waves over the nanometer-sized cross-section area, the change in the grand canonical potential is calculated and hence the force and the spring constant. As the wire is bent more electron states fits in its cross section. This has an impact on the spring "constant" which oscillates slightly with the bending of the wire. In this way we obtain an amplitude-dependent resonans frequency that should be detectable.

Genom att använda en endimensionell fri elektronmodell där vi bortser från atomstrukturen i metallen (eng jellium model) och vanlig balkteori beräknar vi fjäderkonstanten hos en vibrerande nanotråd inspänd i ena änden. Vi använder de asymptotiska egenvärdena hos de stående elektronvågorna med vilkas hjälp vi beräknar den storkanoniska (dvs med variabelt elektronantal) potentialen hos elektrongasen. Från denna potential beräknar vi kraften vi måste använda för att böja tråden och därmed fjäderkonstanten. När nanotråden böjs ökar dess tvärsnittyta enligt den vanliga balkteorin och fler elektrontillstånd passar i ytan. Detta påverkar "fjäderkonstanten" vilken oscillerar något med hur mycket tråden är böjd. På detta sätt erhåller vi en amplitudberoende egensvängningsfrekvens hos tråden vilken borde vara mätbar.

We have studied the time evolution of an ensemble of holes in Wurtzite GaN under the effect of a high electric field. The density matrix equation used as a foundation in the study includes band-to-band tunneling, but disregards collisions. In the description of the ensemble dynamics the full band structure is used. The average energy and group velocity for the ensemble is calculated, as well as velocity components corresponding to the non-diagonal elements of the velocity operator (interference). The calculations have been carried out for the electric field strengths 0.4 and 4 MV/cm. A comparison is presented of the results with and without inclusion of band tunneling in the ensemble dynamics. There is also a comparison of the velocity with and without the non-diagonal elements of the velocity operator terms. A conclusion is that Monte Carlo simulations considering band tunneling, but not interference, can give accurate results.

The influence on the conductance of armchair carbon nanotubes due to the presence of extended vacancy pairs has been investigated using a conventional pi-electron tight-binding model. It is found that the conductance in the linear band region around the Fermi energy contains resonance peaks and dips, which can be understood as double-barrier scattering resonances and Fano antiresonances and whose number depends on the longitudinal intervacancy separation. Furthermore, for a given longitudinal intervacancy separation, only two distinctly different conductance spectra appear in this energy region as the second vacancy in the pair assumes all different lateral positions around the tube circumference. It is also found that the conductance can be very sensitive to minimal changes in the relative intervacancy positions.

A set of equations for calculating the probability for electric-field-induced interband transitions in periodic crystals (Krieger and Iafrate 1986 Phys. Rev. B 33 5494) can be used in combination with the full band Monte Carlo method to study high-field electronic transport properties in semiconductors. However, when the equations are applied to realistic cases in which the underlying band structure is obtained from numerical band structure programmes, the equations are not directly solvable because of the indeterminacy of the phases of the band structure Bloch wavefunctions. Here we discuss this problem and present a method for choosing the phases of the Bloch functions in such a way that the equations yield physically correct interband transition probabilities.