Energy dissipation in submicrometer thick single-crystal silicon cantilevers

TLDR

The study examines four primary energy loss mechanisms—thermoelastic, air damping, support, and surface loss—in ultrathin silicon cantilevers ranging from 60 nm to 500 nm thick. Thermoelastic loss is negligible in sub‑500‑nm thick cantilevers longer than 10 µm but becomes significant when the beam is thicker than 500 nm and shorter than 10 µm, while air damping dominates unless the device is operated below 10⁻³ mbar, in which case support and surface losses govern the quality factor, with support loss limiting Q for L/H < 100 and surface loss dominating for lengths over 30 µm.

Abstract

Discusses four kinds of mechanical energy losses in ultrathin micro-cantilevers of 60 nm, 170 nm, and 500 nm in thickness: thermoelastic loss, air damping, support loss, and surface loss. For the cantilevers with thickness H<500 nm and length L>10 /spl mu/m, thermoelastic loss is negligible. But it becomes significant when the beam thickness H>500 nm and the length L<10 /spl mu/m. The cantilevers are very liable to air damping, hardly operated at pressure higher than 10/sup -3/ mbar. In a high vacuum (<10/sup -3/ mbar), air damping is negligible, the support and surface loss play an important role. The shorter the cantilevers, the larger the support energy loss. For the cantilevers with L/H<100, the quality factors (Q factors) are limited by the support loss. When the length L>30 /spl mu/m, the Q factors of the cantilevers are proportional to their thickness, i.e., surface loss dominates the mechanical behavior. Annealing the cantilevers of 170 nm thickness at 1000/spl deg/C for 30 s under an ultrahigh vacuum (UHV) condition results in an over one order-of-magnitude increase of the Q factor, up to about 2.5/spl times/10/sup 5/ for cantilevers of 30-90 /spl mu/m in length.