Nano-beam clamping revisited

Abstract

Within recent years, the field of nano-mechanics has diversified in a variety of applications, ranging from quantum information processing to biological molecules recognition. Among the diversity of devices produced these days, the simplest (but versatile) element remains the doubly clamped beam: it can store very large tensile stresses (producing high resonance frequencies [Formula: see text] and quality factors [Formula: see text]), is interfaceable with electric setups (by means of conductive layers), and can be produced easily in clean rooms (with scalable designs, including multiplexing). Besides, its mechanical properties are the simplest to describe. Resonance frequencies and [Formula: see text]s are being modeled, with as specific achievement the ultrahigh quality resonances based on “soft clamping” and “phonon shields.” Here, we demonstrate that the fabrication undercut of the clamping regions of basic nano-beams produces “natural soft clamping,” given for free. We present the analytic theory that enables to fit experimental data, which can be used for [Formula: see text] design: beyond finite element modeling validation, the presented expressions provide a profound understanding of the phenomenon, with both [Formula: see text] enhancement and a downward frequency shift.

On the link between mechanics and thermal properties: mechanothermics

“…The internal contribution is chosen to reproduce a conventional viscous damping; in mechanics terms, this is usually realized by introducing a complex Young's modulus with an imaginary part representing the damping coefficient [29]. This simply means that locally, friction is modeled by a stress field [χ ij ] proportional to the rate of change of the strain [30]:…”

“…Note that equation (75) contains all contributions that arise from the distortion, including the shear generated by the angle appearing between the anchoring point and the rod experiencing flexure [38,39]. Again, through a clever design distortions at the anchor can be minimized, which leads to a decrease in friction named 'soft clamping' [30,40].…”