Capacitive spring softening in single-walled carbon nanotube nanoelectromechanical resonators

We report the capacitive spring softening effect observed in single-walled carbon nanotube (SWNT) nanoelectromechanical (NEM) resonators. The nanotube resonators adopt a dual-gate configuration with both bottom-gate and end-gate capable of tuning the resonance frequency through capacitive coupling. Interestingly, downward resonance frequency shifting is observed with increasing end-gate voltage, which can be attributed to the capacitive softening of the spring constant. Furthermore, in-plane vibrational modes exhibit a much stronger spring softening effect than out-of-plan modes. Our dual-gate design should enable the differentiation between these two types of vibrational modes and open up the new possibility for nonlinear operation of nanotube resonators.