Nonlinear Switching Dynamics in a Nanomechanical Resonator

The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability [1], discontinuous jumps [2, 3] and hysteresis [3]. These can be utilized in applications leading, e.g., to precise frequency measurement [4], mixing [5], memory elements [6, 7], reduced noise characteristics in an oscillator [8] or signal amplification [9, 10, 11, 12]. Approaching the quantum regime[13], concepts have been proposed that enable low backaction measurement techniques [11] or facilitate the visualisation of quantum mechanical effects [14]. Here we study the dynamic response of nanoelectromechanical resonators in the nonlinear regime aiming at a more detailed understanding and an exploitation for switching applications. Whereas most previous investigations concentrated on dynamic phenomena arising at the onset of bistability [1, 4, 9], we present experiments that yield insight into the non-adiabatic evolution of the system while subjected to strong driving pulses and the subsequent relaxation. Modeling the behaviour quantitatively with 1 a Duffing oscillator, we can control switching between its two stable states at high speeds, exceeding recently demonstrated results by 10 [6, 7]. Nano-Electro-Mechanical Systems (NEMS) have been established as excellent devices to explore nonlinear dynamical behaviour, as they exhibit high mechanical quality (Q) factors [15, 16], fast response times [17], fairly low drift [1] and can be easily excited into the nonlinear regime [1]. Yet most systematic studies of the dynamics of such systems concentrated on the regime near the onset of bistability [1, 4]. Complementary, we explore the response of a driven nonlinear nanomechanical resonator to excitation by intense and short radio frequency (RF) pulses that drive the resonator away from the stationary points. The observed response is found to be in excellent agreement with simulations based on a Duffing oscillator [18]. Therefore we can make use of pulsed excitations to controllably switch the resonator between the stable points on a time scale that is no longer limited by the relaxation time of the system [6, 7]. The resonator consists of a doubly-clamped silicon nitride string of dimensions 35μm · 250 nm · 100 nm (length, width, height, respectively) under high tensile stress, leading to high mechanical Qfactors [19]. In vacuum and at room temperature we electrically excite the resonator at RF frequencies employing dielectric gradient forces provided by suitably located and biased electrodes [19, 20]. Illuminating the resonator with a light emitting diode, we detect the resonant motion by a small on-chip Schottky diode fabricated close to the resonator and serving as a photodetector for the oscillating component of the optical near-field as will be discussed in detail elsewhere [21]. The nonlinear resonator is continuously actuated by the RF output of a network analyzer as depicted in Fig. 1a. Applying sufficiently strong excitation amplitudes, the mechanical response around resonance tends to bend towards higher frequencies as depicted in Fig. 1b, corresponding to string-hardening. This behaviour can be quantitatively modeled by solving the so-called Duffing equation [18], an extension