Mittuniversitetet

The technological interest in a material depends very much on its electrical, magnetic, optical and/or mechanical properties. In carbon nanotubes the atoms form a cylindrical structure with a diameter of the order 1 nm, but the nanotubes can be up to several hundred micrometers in length. This makes carbon nanotubes a remarkable model for one-dimensional systems. A lot of efforts have been dedicated to manufacturing carbon nanotubes, which is expected to be the material for the next generation of devices. Despite all the attention that carbon nanotubes have received from the scientific community, only rather limited progress has been made in the theoretical understanding of their physical properties. In this work, we attempt to provide an understanding of the electron-phonon and electron-defect interactions in semiconducting zigzag carbon nanotubes using a tight-binding approach. The electronic energy dispersion relations are calculated by applying the zone-folding technique to the dispersion relations of graphene. A fourth-nearest-neighbour force constant model has been applied to study the vibrational modes in the carbon nanotubes. Both the electron-phonon interaction and the electron-defect interaction are formulated within the tight-binding approximation, and analyzed in terms of their quantum mechanical scattering rates. Apart from the scattering rates, their components in terms of phonon absorption, phonon emission, backscattering and forward scattering have been determined and analyzed. The scattering rates for (5,0), (7,0), (10,0), (13,0) and (25,0) carbon nanotubes at room temperature and at 10K are presented and discussed. The phonon scattering rate is dependent on the lattice temperature in the interval 0-0.17 eV. We find that backscattering and phonon emission are dominant over forward scattering and phonon absorption in most of the energy interval. However, forward scattering and phonon absorption can be comparable to backscattering and phonon emission in limited energy intervals. The phonon modes associated with each peak in the electron-phonon scattering rates have been identified, and the similarities in the phonon scattering rates between different nanotubes are discussed. The dependence of the defect scattering rate on the tube diameter is similar to that of the phonon scattering rate. Both the phonon and the defect scattering rates show strong dependence on the tube diameter (i.e., the scattering rate decreases as a function of the index of the nanotube). It is observed that the backscattering and forward scattering for electrons interacting with defects occur with same frequency at all energies, in sharp contrast to the situation for phonon scattering. It is demonstrated that the differences in the scattering rate between different tubes are mainly due to the differences in their band structures.

Since the advent of nanoscale material based electronic devices, there has been a considerable interest in exploring carbon nanotubes from fundamental science and technological perspectives. In carbon nanotubes, the atoms form a cylindrical structure with a diameter of the order 1nm. The length of the nanotubes can extend up to several hundred micrometers. Carbon nanotubes exhibit a variety of intriguing electronic properties such as semiconducting and metallic behaviour, due to the quantum confinement of the electrons in the circumferential direction. Much of the study dedicated to describe the behaviour of carbon nanotube-based devices assumes for simplicity the nanotube to be a ballistic material. However, in reality the phonon scattering mechanism exists also in nanotubes, of course, and can generally not be neglected, except in very short nanotubes. In this work, we focus attention on exploring the steady-state electron transport properties of semiconducting single-walled carbon nanotubes, including both phonon scattering and defect (vacancy) scattering, using the semi-classical bulk single electron Monte Carlo method.

The electron energy dispersion relations are obtained by applying the zone folding technique to the dispersion relations of graphene, which are calculated using the tight-binding description. The vibrational modes in the carbon nanotubes are studied using a fourth nearest-neighbour force constant model. Both the electron-phonon and the electron-defect interactions are formulated within the tight-binding framework, and their corresponding scattering rates are computed and analyzed. In particular, the dependence of the phonon scattering rate and the defect scattering rate on the diameter of the nanotube, on temperature and on electron energy is studied. It is shown that the differences observed in the scattering rate between different nanotubes mainly stem from the differences in their band structure.

A bulk single electron Monte Carlo simulator was developed to study the electron transport in semiconducting zigzag carbon nanotubes. As a first step, we included only electron-phonon scattering, neglecting all other possible scattering mechanisms. With this scattering mechanism, the steady-state drift velocity and the mobility for the nanotubes (8,0), (10,0), (11,0), (13,0) and (25,0) were calculated as functions of the electric-field strength and lattice temperature, and the results are presented and analysed here. The dependence of the mobility on the lattice temperature can be clearly seen at low electric-field strengths. At such electric-field strengths, the scattering is almost entirely due to acoustic phonons, whereas at high electric-field strengths optical phonon emission processes dominate. It is shown that the saturation of the steady-state drift velocity at high electric-field strengths is due to the emission of high-energy optical phonons. The results indicate the presence of Negative differential resistance for some of the nanotubes considered in this work. The discrepancy found in the literature concerning the physical reason for the appearance of negative differential resistance is clarified, and a new explanation is proposed. It is also observed that the backward scattering is dominant over the forward scattering at high electric-field strengths.

We then included also defect scattering, actually electron-vacancy scattering, for the nanotubes (10,0) and (13,0). The steady-state drift velocities for these nanotubes are calculated as functions of the density of vacancies, electric-field strength and the lattice temperature, using three different vacancy concentrations. The results indicate the presence of Negative differential resistance at very low concentration of defects, and how this feature may depend on the concentration of defects. The dependence of the steady-state drift velocity on the concentration of defect and the lattice temperature is discussed. The electron distribution functions for different temperatures and electric field strengths are also calculated and investigated for all the semiconducting nanotubes considered here. In particular, a steep barrier found in the electron distribution function is attributed to the emission of high energy optical phonons.