Statics and dynamics of a nanowire in field emission

We simulate the nonlinear behaviour of a cantilevered nanowire in field emission to understand and exploit the self-oscillations experimentally observed in this nanoelectromechanical system. Statics and dynamics of this oscillator are predicted with a low-dimensional model consisting of a bi-articulated cantilevered beam flowing electrons and immersed in an electrostatic environment. We set up the qualitative nonlinear governing equations of the system and also highlight the original coupling between the electrostatic field, the nanowire motion and the electric field emission current. A linear stability analysis of the nonlinear static fixed points aims at determining the instability threshold as a function of the applied DC voltage. It is found that instability is mostly due to the competition between the field emission current dependence on the nanowire position and the voltage. As a consequence, the emergence of flutter requires specific external conditions such as an initial angular imperfection, a strong mechanical Q factor or a high electrical resistance. Finally, a direct integration of the nonlinear governing equations confirms the presence of high-frequency self-oscillations, i.e. the possibility of DC/AC conversion in this autonomous electromechanical device.