Analytical analysis of heat conduction in a suspended one-dimensional object

Abstract

An analytical solution is given for the self-heating conduction equation of a suspended one-dimensional (1D) object. The conductivity of the 1D object is given by combining Umklapp and second-order three-phonon processes. Using this analytical solution, several relations among some important parameters are discussed and are shown to be consistent with existing experimental results. A method to retrieve the coefficients for thermal conductivity is proposed for a general thermal conductor without knowing the detailed temperature profile along the 1D object.

Energy dissipation and transport in nanoscale devices

“…7c) is a simple inverted parabola expressed as [36]: where again -L/2 < x < L/2 and T 0 is the temperature of the contacts at the two ends, and the power dissipation is assumed uniform along the CNT length. Analytic expressions for this temperature profile can also be obtained for a few cases of temperature-dependent thermal conductivity k [127]. The Raman-thermometry technique has directly measured this steeply varying temperature profile in suspended CNTs [125], and has confirmed the phonon non-equilibrium between optical and acoustic modes previously suggested on the basis of electrical characteristics alone (Fig.…”

Nanotube fountain pen: Towards 3D manufacturing of metallic nanostructures

“…When the external bias reaches 2.0 V (0 s), the dark contrast and the boiling sign indicate the molten state of the copper wire. As the voltage is increased to 2.2 V (7 s), the mass in the center suddenly evaporates, clearly revealing the thermal effect [37]. Nevertheless, by further increasing the voltage in 0.1 V increments until the external bias reaches a higher value (2.5 V, 11 s), the mass begins to migrate from the upper part to the lower portion of the tube, following the direction of the electromigration force.…”

“…3a and b should consistently move from cathode to anode; however, the mass evaporating in the center does not move in one single direction. Because the center of the nanotube is always the hottest spot [26,37,38], part of the mass is evaporated and diverted from the center (the hotter part) to the periphery (colder part) by thermal gradient force. Therefore, the thermal gradient effect dominates the mass migration at the beginning of the NFP writing.…”

Nanorobotic mass transport

“…In contrary, the mass move from center towards the two ends. According to the center of the nanotube was presumed to be the high-resistance point or "hottest spot" [15][16][17], parts of the mass was evaporated and the thennal gradient in tum diverted from the center towards the cooler locales (the two ends of tube), which highly suggestive of a thennal gradient effect at the beginning to evaporate the mass and driven the flow. However, as the current is sharply increased, the electromigration force was reinforced and dominant the main role for the migration, which results the mass ultimately flows from cathode to anode consistently.…”