Zoran P. Popović, et al., Transport in helically coiled carbon nanotubes: semiclassical approach Contemporary Materials, VI−1 (2015) Page 15 of 19 Original scientific papers UDK 66.017/.018:548.7 doi: 10.7251COMEN1501015P TRANSPORT IN HELICALLY COILED CARBON NANOTUBES: SEMICLASSICAL APPROACH Zoran P. Popović * , Tatjana Vuković, Božidar Nikolić, Milan Damnjanović, Ivanka Milošević NanoLab, Center for Quantum Theoretical Physics, Faculty of Physics, University of Belgrade, Studentski trg 12, 11158 Belgrade, Serbia Abstract: Semiconducting single wall carbon nanotubes (SWCNTs) exhibit high electron mobility in low electric field. Tube diameter and temperature have been found to strongly affect transport properties of SWCNTs. We have investigated electron mobility of helically coiled carbon nanotubes (HCCNTs). Electron and phonon band structures of HCCNTs are used in calculation of electron-phonon matrix elements. Scattering rates are calculated using the first order perturbation theory while taking care of energy and momen- tum conservation law. In order to obtain electron drift velocities, steady state simulation of charge transport is performed using Monte Carlo method. Keywords: carbon nanotubes, electron-phonon scattering, drift velocity, electron mobility, charge transport. 1. INTRODUCTION In semiconducting single-wall carbon nano- tubes (SWCNTs), low intensity of electron scatter- ing on acoustic phonons causes their high electron mobility. The theoretically predicted charge mobility in semi-conducting zig-zag carbon nanotubes (CNTs) is in the range 10 3 − 10 5 cm 2 /Vs [1]. Elec- trons accelerated by high bias voltage are scattered by optical phonons, mostly through the interband relaxation processes, while when moving in a low electric field, they emit or absorb acoustic phonons. The most demanding task in the charge carrier mobility calculations is to obtain the scattering rate of an electron in a specified state. The electron scat- tering rate increases with the concentration of impur- ities or defects in a crystal lattice. Besides, electron- electron interaction impacts the electron relaxation time, as well. However, electron-phonon (el-ph) in- teraction gives the largest contribution to the elec- tron scattering rate and plays an important role in processes like charge transport, Raman scattering and also in fast optical spectroscopy [2]. Here, we calculate the scattering rates of con- duction band electrons in semiconducting infinitely long single-walled HCCNTs without impurities, caused only by electron-phonon interaction, neglect- ing all other contributions. Given are also the results obtained from the single-particle Monte Carlo simu- lations of electron free flight interrupted by a sto- chastic scattering event. Drift velocity is obtained as a time averaged velocity of free flight in the k-space during the total simulation time [3,4]. All the calcu- lations are simultaneously derived for semiconduct- ing straight single-wall carbon nanotubes, in order to make a comparison based on the results obtained by the same method of calculation. 2. MODEL Models of helically coiled carbon nanotubes (HCCNTs) are generated from symcell atoms apply- ing line group symmetry from the fifth family. Heli- cally coiled nanotubes are multiple orbit systems, the symcell of which is a half of the monomer. Ge- nerators of the symmetry group of HCCNTs are screw axis, rotation followed by a fractional transla- tion, U axis (rotation around X axis for π) [5,6]. Generally, HCCNTs are not translationaly periodic and do not have pure rotational symmetry. Group parameters are simple functions of geometrical parameters: monomer length (a) (distance between two successive knees along the helix), helical radius (R) and inclination angle χ (Figure 1). Except hexagons, carbon network of HCCNTs contains also pentagons and heptagons. Every monomer has pairs of heptagons at negative and pentagons placed at positive * Corresponding author: zokapop@yahoo.com brought to you by CORE View metadata, citation and similar papers at core.ac.uk