Damping mechanisms in high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math>micro and nanomechanical string resonators

TLDR

Micro‑ and nanostrings exhibit exceptionally high quality factors, largely due to the large energy stored in their tensile stress, a phenomenon first observed in silicon nitride resonators. The study systematically varies geometry and tensile stress of silicon nitride microstrings and compares measured quality factors to an analytical bending‑damping model. The results show that narrow 3‑μm strings are limited by internal material damping, while wider strings suffer clamping losses and substrate interference, yielding a maximum Q of 7 million at 176 kHz.

Abstract

Resonant micro and nanostrings were found to have extraordinarily high quality factors (Qs). Since the discovery of the high Qs of silicon nitride nanostrings, the understanding of the underlying mechanisms allowing such high quality factors has been a topic of several investigations. So far it has been concluded that Q is enhanced due to the high energy stored in the string tension. In this paper, damping mechanisms in string resonators are systematically investigated by varying the geometry and the tensile stress of silicon nitride microstrings. The measured quality factors are compared to an analytical model for Q based on bending-related damping mechanisms. It is shown that internal material damping is limiting the quality factor of narrow strings with a width of 3 μm. Q is strongly width dependent and clamping losses evidently seem to be the limiting damping mechanism for wider strings. It is further shown that Q is influenced by interference effects in the substrate and thus by the clamping of the macroscopic chip. A maximum quality factor of up to 7 million is presented for high-stress silicon nitride strings with a resonance frequency of 176 kHz.