Frequency self-tuning of carbon nanotube resonator with application in mass sensors

This paper presents a new model for a doubly clamped carbon nanotube (CNT) resonator to investigate the tunability of its resonant frequency under joule heating with the application in adjusting the mass detection sensitivity while it is used as the mass sensor. Taking into account the temperature dependence of resistance, temperature distribution of the CNTs with various sizes under the joule heating has been analyzed using the thermal transfer theory. Temperature profiles and induced thermal stresses of both short and long CNTs have been obtained. The axial thermal stress is then treated as the loading factor in the mechanical Euler-beam equation to calculate the resonant frequency shift. The surface effect has been considered because of the nanoscale of the CNTs. Based on the law of energy conservation and the Euler-Lagrangian equations, the dynamic model of the CNT resonator has been built. Through a systematic multiphysical simulation approach, relations between the applied electrical current and the resonant frequency, the applied electrical current and the mass detection sensitivity of the CNT resonator have been obtained. It is found that the tuning ranges from 2.575 GHz to 7.241 GHz and from 2.759 THz to 3.544 THz for the fundamental resonant frequency of both a long (5.325 μm) and a short (5.67 nm) CNT resonators are obtained respectively. With respect to the mass detection sensitivity, it is found that the mass detection sensitivity of one particular CNT resonator can be improved from 1.783 MHz/zeptogram (zg) to 5.013 MHz/zg and from 1.795 GHz/yoctogram (yg) to 2.305 GHz/yg when varying the electrical current from 0.015 μA to 0.75 μA for the added 5 zg and 5 yg mass, respectively.