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Monte Carlo simulation of electron transport in semiconducting zigzag carbon nanotubes
Mid Sweden University, Faculty of Science, Technology and Media, Department of Electronics Design. (EKS)
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Sundsvall: Mid Sweden University , 2013. , 139 p.
Series
Mid Sweden University doctoral thesis, ISSN 1652-893X ; 132
Keyword [en]
Carbon nanotubes, Monte Carlo method, drift velocity, mobility, electron-phonon scattering, and electron-defect scattering.
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:miun:diva-18799Local ID: STCISBN: 978-91-87103-28-5 (print)OAI: oai:DiVA.org:miun-18799DiVA: diva2:617606
Public defence
2013-05-23, L111, Mid Sweden Univeristy, Sundsvall, 13:30 (English)
Opponent
Supervisors
Available from: 2013-04-29 Created: 2013-04-23 Last updated: 2016-10-20Bibliographically approved
List of papers
1. Electron-phonon scattering rates in semiconducting zigzag carbon nanotubes
Open this publication in new window or tab >>Electron-phonon scattering rates in semiconducting zigzag carbon nanotubes
2011 (English)In: Journal of Computational and Theoretical Nanoscience, ISSN 1546-1955, Vol. 8, no 9, 1694-1702 p.Article in journal (Refereed) Published
Abstract [en]

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.

Keyword
Carbon Nanotubes; Electron-Phonon Scattering; Scattering Rates; Backscattering
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:miun:diva-12152 (URN)10.1166/jctn.2011.1868 (DOI)000298514100009 ()2-s2.0-84856886654 (Scopus ID)STC (Local ID)STC (Archive number)STC (OAI)
Available from: 2010-10-22 Created: 2010-10-22 Last updated: 2016-10-14Bibliographically approved
2. Electron-Phonon and electron-defect Scattering Rates in Semiconducting Zig-Zag Carbon Nanotubes
Open this publication in new window or tab >>Electron-Phonon and electron-defect Scattering Rates in Semiconducting Zig-Zag Carbon Nanotubes
2012 (English)In: Physica Status Solidi. C, Current topics in solid state physics, ISSN 1610-1634, E-ISSN 1610-1642, Vol. 9, no 1, 22-25 p.Article in journal (Refereed) Published
Abstract [en]

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.

Keyword
carbon nanotubes; electron-phonon scattering; electron-defect scattering rate; tight-binding approximation
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:miun:diva-14995 (URN)10.1002/pssc.201084156 (DOI)000301545800004 ()2-s2.0-83755224763 (Scopus ID)STC (Local ID)STC (Archive number)STC (OAI)
Conference
8th International Vacuum Electron Sources Conference (IVESC)/NANOcarbon; OCT 14-16, 2010; Nanjing, PEOPLES R CHINA
Available from: 2011-11-30 Created: 2011-11-30 Last updated: 2017-12-08Bibliographically approved
3. High-field electron transport in semiconducting zigzag carbon nanotubes
Open this publication in new window or tab >>High-field electron transport in semiconducting zigzag carbon nanotubes
2012 (English)In: Nanotechnology, ISSN 0957-4484, E-ISSN 1361-6528, Vol. 23, no 26, 265703-265709 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Bristol, England: , 2012
Keyword
Carbon nanotubes, electron-phonon scattering, drift velocity, mobility, Monte Carlo simulation
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:miun:diva-16551 (URN)10.1088/0957-4484/23/26/265703 (DOI)000305411400015 ()2-s2.0-84862657954 (Scopus ID)STC (Local ID)STC (Archive number)STC (OAI)
Note

Correction: Source: NANOTECHNOLOGY  Volume: 24  Issue: 39  Article Number: 399502  DOI: 10.1088/0957-4484/24/39/399502  Published: OCT 4 2013

Available from: 2012-06-25 Created: 2012-06-25 Last updated: 2017-12-07Bibliographically approved
4. Effects of vacancies on the electron transport in semiconducting zigzag carbon nanotubes
Open this publication in new window or tab >>Effects of vacancies on the electron transport in semiconducting zigzag carbon nanotubes
2015 (English)In: JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE, ISSN 1546-1955, Vol. 12, no 3, 473-477 p.Article in journal (Refereed) Published
Abstract [en]

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.

Keyword
Carbon Nanotubes, Drift Velocity, Monte Carlo Simulation, Tight-Binding Approximation, Scattering Rates, Vacancies
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:miun:diva-18865 (URN)10.1166/jctn.2015.3755 (DOI)000352288500022 ()2-s2.0-84925272852 (Scopus ID)STC (Local ID)STC (Archive number)STC (OAI)
Available from: 2013-04-29 Created: 2013-04-29 Last updated: 2017-08-28Bibliographically approved

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