Terahertz Current Oscillations in Single-Walled Zigzag Carbon Nanotubes Akin Akturk, * Neil Goldsman, and Gary Pennington Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742, USA Alma Wickenden Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20783, USA (Received 26 September 2006; published 19 April 2007) We report time-dependent terahertz current oscillations on an n 10 single-walled zigzag carbon nanotube (CNT) that is 100 nm long. To obtain transport characteristics in this CNT, we developed an ensemble Monte Carlo (MC) simulator, which self-consistently calculates the electron transport and elec- trical potential. The ensemble MC simulations indicate that, under certain dc bias and doping conditions, the average electron velocity and concentration oscillate. This leads to current oscillations in space and time, on the tube, and at the contacts. We attribute this to accumulation and depletion of the CNT electrons at different locations on the tube, giving rise to low and high density electron regions. These local dipoles are a result of intra- and intersubband scatterings and different subband dispersion relations. This in turn forms propagating dipoles and current oscillations. DOI: 10.1103/PhysRevLett.98.166803 PACS numbers: 73.63.Fg, 73.22.f, 78.67.Ch I. Introduction.—Carbon nanotube (CNT) electrical be- havior has been theoretically and experimentally investi- gated [1–13]. Research indicates high electron drift velocities and large electron mobilities as compared with silicon. In addition to high drift velocities, earlier steady- state Monte Carlo (MC) simulations predict spatially de- pendent velocity oscillations under the presence of uniform applied electric fields. The periods of these oscillations are calculated to be in the range of tens of nanometers in single-walled zigzag 100 nm semiconducting tubes [4]. The presence of these velocity oscillations may lead to THz oscillators that are important for application in future wireless communication electronics. However, it must first be determined if these spatial oscillations will translate into time-dependent current oscillations in CNTs that are under dc bias. To investigate whether these time-dependent cur- rent oscillations do indeed occur, we built upon previous work [1– 4] and developed an ensemble MC simulator for CNTs. The MC simulator solves the semiclassical trans- port equations and the Poisson equation self-consistently inside the CNT. The ensemble MC calculations provide the potential and electron current, velocity, and concentration profiles as functions of space and time on the tube for an applied dc bias. Our calculations show the existence of terahertz current oscillations on the tube under several bias and tube doping conditions. We attribute these time- and space-dependent oscillations to intra- and intersubband electron-phonon couplings, influences from subband dis- persion curves, and the spatial-temporal variation in the potential. II. CNT energy spectra.—To investigate self-sustained oscillations in CNTs, we developed an ensemble MC simulator and used it to examine a 100 nm long single- walled zigzag semiconducting carbon nanotube with fun- damental indices of n; m10; 0 and a diameter (d) of approximately 0.8 nm. To initialize the MC calculations, we input the CNT subbands structure. The CNT subbands are obtained by applying zone-folding methods to the graphene energy spectra, which was calculated using the tight-binding model [9]: Ek; 1 4 cos Tk 2 cos n 4cos 2 n s : (1) Here k, , and T are the wave vector along the tube’s axis, the wave vector index around the tube’s circumfer- ence, and the length of the zigzag tube’s translational vector (4.31 A ˚ ), respectively. We take the value of nearest-neighbor -hopping integral as 3 eV [1,2]. Additionally, we here account for the lowest three CNT subbands in two valleys [1,2]. We next incorporate the longitudinal acoustic and opti- cal phonon dispersion curves that are obtained using the fourth nearest-neighbor tight-binding model and zone- folding methods [2]: E p q; E p0 @v s jqj d : (2) Above q is the phonon wave vector, is the azimuthal quantum number [14], E p0 is the energy of phonon associated with at zero momentum, v s is the sound velocity in graphene, is a step function, and is zero for optical phonons and one for acoustic phonons. The radial breathing mode (RBM) [15,16] is also incor- porated into calculations. Continuum modeling is used to determine the energy spectrum and deformation potential of the RBM [17]. For an n; m10; 0 single-walled CNT, the RBM energy and deformation potential per length have been calculated to be 35 meV and 2:3 eV= A, respectively, which are in relatively close agreement with other calculated values [15]. Furthermore, we do not con- PRL 98, 166803 (2007) PHYSICAL REVIEW LETTERS week ending 20 APRIL 2007 0031-9007= 07=98(16)=166803(4) 166803-1 2007 The American Physical Society