Role of fluctuations and nonlinearities on field emission nanomechanical self-oscillators

Abstract

A theoretical and experimental description of the threshold, amplitude and stability of a selfoscillating nanowire in a field emission configuration is presented. Two thresholds for the onset of self-oscillation are identified, one induced by fluctuations of the electromagnetic environment and a second revealed by these fluctuations by measuring the probability density function of the current.The AC and DC components of the current and the phase stability are quantified. An AC to DC ratio above 100% and an Allan deviation of 1.3·10 −5 at room temperature can be attained. Finally it is shown that a simple non-linear model cannot describe the equilibrium effective potential in the self-oscillating regime due to the high amplitude of oscillations.

Sensing and cooling of a nanomechanical resonator with an electron beam stimulated internal feedback and a capacitive force

“…This value is an order of magnitude higher than the spatial derivative of the field emission current in ref. 29 for the same DC current.…”

“…The acceleration voltage was typically in the tens of kV and the beam current was about 100 pA The voltage is obtained indirectly by estimating the nanowire resistance by the method detailed in ref. 8,29 . The typical resistance is about 1 GΩ and in some exceptional cases it can reach up to 1 TΩ but we never performed extensive experiments on such highly resistive samples.…”

“…The method to estimate C and C' has been explained elsewhere 29 . The capacitance is usually around 1 fF which gives an electrical frequency cut-off between 1 kHz and 1 MHz.…”

Frequency modulated self-oscillation and phase inertia in a synchronized nanowire mechanical resonator

“…The voltage changes modify the transparency of the barrier and the electrostatic force on the NW and thus, induce a counterreaction on the NW position. This generates self-oscillation at a frequency close to the original resonant frequency of the mechanical resonator [24].…”

“…Out of the synchronized region, both frequencies coexist and the system is said to be quasiperiodic [27,28]. The dynamics of the phase and amplitude of an individual SO in the simplest case are governed by a first-order time derivative and thus, by nature are overdamped [24]. For an abrupt change of the generator phase, the phase of the SO should relax exponentially to a new phase value that maches the generator phase, similar to an overdamped particle (OP) relaxing to a potential minimum.…”