Unusual scaling observations in the quality factors of cantilevered carbon nanotube resonators

This work examines the quality factors (Q factors) of resonance associated with the axial and transverse vibrations of single-wall carbon nanotube (SWCNT) resonators through the use of molecular dynamics (MD) simulation. Specifically, the work investigates the effect of device length, diameter, and chirality, as well as temperature, on the resonant frequency and quality factor of these devices, and benchmarks the results of MD simulation against classical theories of energy dissipation. Of note are the facts that the quality factors associated with transverse vibration decrease with increasing device diameter and are largely insensitive to chirality. Additionally, quality factors increase with increasing device length for transverse vibrations, but remain almost constant for axial vibrations. The predicted size dependence of the quality factors associated with axial vibration agrees well with classical theory, if the nanoscale size effect of thermal conductivity is properly accounted for. However, the size dependence of the quality factors associated with transverse vibrations deviates significantly from classical theory. INTRODUCTION Since their discovery in 1991 [1], carbon nanotubes (CNTs) have become the cynosure of nanotechnology with considerable efforts being made to explore their thermal, mechanical, electrical, and optical properties. One emergent application of CNTs is in resonant nanoelectromechanical systems (NEMS) [2-4], where they can be used as enabling elements in sensors, oscillator circuits, and electromechanical signal processing systems [5-7]. The distinct utility of CNTs in these applications stems in large part from their high elastic modulus, low mass density, and high natural frequencies, which are typically in the GHz-THz range [8]. Generally speaking, the performance of a CNT resonator is constrained by the rate of energy dissipation associated with the device, which is commonly measured in terms of quality factor (Q). In most applications, a high Q is essential to optimizing performance metrics, such as device sensitivity or selectivity; and hence developing a complete understanding of dissipation in NEMS resonators is essential. In electromechanical resonators, energy dissipation can occur through a wide variety of mechanisms [9]. Amongst these mechanisms are intrinsic processes, such as thermoelastic dissipation (TED) [10], dissipation due to electron-phonon interactions, and dissipation due to phonon-phonon interactions [11]. These mechanisms are inherent in any material and thus are omnipresent in any functional device. In contrast, there are extrinsic processes that occur due to interactions with the device’s surrounding environment, such as fluidic damping and clamping losses [12]. These effects can be at least partially mitigated if proper care is taken in the course of device design and packaging. It is important to note that a small number of prior works have considered the sources and impact of various dissipation mechanisms in CNT resonator, using experimental, analytical and numerical approaches. For example, Huttel et al. experimentally investigated the Q factors of resonance associated with the transverse vibration of suspended CNTs at low temperatures [13]. Likewise, a series of works have considered the temperature dependence of quality factor using molecular dynamics (MD) simulation [14, 15]. For example, in [4], Jiang et al. calculated the quality factors associated with the flexural vibration of CNTs and observed a T dependence, which deviates from classical theory. They also estimated that energy losses would in fact increase with temperature for double-walled carbon nanotubes because of interlayer interactions [14]. Proceedings of the ASME 2010 International Mechanical Engineering Congress & Exposition IMECE2010 November 12-18, 2010, Vancouver, British Columbia, Canada